ECE Fall 05. Undergraduate Research: Digital Signal Processing & Quantization Effects

Transcription

1 ECE Fall 05 Undergraduate Research: Digital Signal Processing & Quantization Effects Done By: Tanim Taher SID# Date: December 19, 2005 DSP & Quantization 1 Tanim Taher

2 ACKNOWLEDGEMENTS I would like to express my gratitude towards Dr. Erdal Oruklu and Dr. Jafar Saniiee for their strong support in making this project successful and a good learning experience for me. A special thanks to Dr. Saniiee for realizing my potential and suggesting that I should take up this research course. Thank you professors so much! Tanim Taher DSP & Quantization 2 Tanim Taher

3 Table Of Contents 1 Abstract.4 2 Introduction Types of Processing DSP Processor Complexity Factors Processor Architecture Quantization Issues Signal Flow Graphs Direct Form Transpose Filters 13 9 Lattice Filters Results: a. Simulation Program Overview.17 b. Software Performance..19 c. Software s Algorithm Description 25 d. Software Applicability..27 e. Simulations Interpretation Conclusion & Future Work Appix Program Listings.34 DSP & Quantization 3 Tanim Taher

4 1. ABSTRACT Digital Signal Processing (DSP) is one of the most powerful areas in the electrical engineering field, that lies at the root of the most exciting technologies today communications (wireless and all other kinds), image recognition and processing, and many others. DSP is so exciting because due to its digital nature, it allows the integration of computer technology with fields of science and engineering. Many DSP applications use their own specialized techniques and algorithms, but some basic methods are common to all and lie really at the core of the subject. Digital signal processing involves using digital signal processors, which can be programmed to act as filters to the digitized signals. Quantization is the process of representing numbers in a digital binary format. The objective of this research project was to learn how digital quantization parameters affect the performance of different kinds of digital filters. DSP & Quantization 4 Tanim Taher

5 2. INTRODUCTION Digital Signal Processing is distinguished from the rest of the digital computer field by the unique type of data it uses: signals. In most cases, these signals originate as sensory data from the real world, for example, sound signals being picked up by a microphone. Digital filters are a very important part of DSP. In fact, their extraordinary performance is one of the key reasons that DSP has become so popular. Filters have two uses: signal separation and signal restoration: 1) Signal Separation is the separation of signals that have been combined. Signal separation is needed when a signal has been contaminated with interference, noise, or other signals undesired. For example, when talking in a telephone s speakerphone, in addition to the person s voice at this of the line, the microphone picks up the sound being produced by the loudspeaker. This would normally cause the person at the other of the line to hear echoes of his or her own voice. Thus a filter is used that separates the sounds and eliminates the echo. 2) Signal restoration is used when a signal has been distorted in some way. For example, an audio recording made with poor equipment may be filtered to better represent the sound as it actually occurred. Filtering can be done with analog filters, but digital filters achieve much better results. This is because fine tuning analog filters can be difficult, as the analog components have tolerance issues with their stated property values and the actual ones. On the other hand, digital filters can be designed with precise characteristics. However, digital filters have their own limitations. The major limit is due to a finite word length. This limits the degree of precision with which the signal can be represented. Digital filtering is carried out by arithmetic operations (processing) that involve filter DSP & Quantization 5 Tanim Taher

6 coefficients. The finite word length also means that the results of the processing are not 100% accurate, but only an approximation deping on the word length and representation format. There are two main kinds of digital filters infinite impulse response (IIR) filters, and finite impulse response (FIR) filters. IIR filters have feedback, while FIR filters do not. Any digital filter can be represented as a polynomial transfer function. The coefficients of the polynomial represent the digital filter s coefficients mentioned before. The transfer function is usually represented as follows: H(z) = (b 0 + b 1 z -1 + b 2 z -2 + b M z -M ) / (1 + a 1 z -1 + a 2 z -2 + a N z -N ) Here z -1 is called a unit delay operator. It represents a digital component whouse output value is the same as the input value of the previous bus cycle. An FIR filter has the denominator (a) coefficients as all zero, while IIR filters have at least one non-zero a coefficients. The values of the a and b coefficients are determined based on the filtering characteristics that are required. Now these coefficients must also be represented in the computer in a digital format with finite precision, and hence the response of the filter can vary deping on how precisely these numbers are represented in the digital signal processor. In summary, quantization of the signal data, the coefficients and the finite precision possible in arithmetic processing affect the performance of digital filters. The purpose of my research was to look at the quantization effects more closely. An important objective of my work was also to learn more about the field of digital signal processing and digital signal processors. Hence a large portion of this report has been dedicated to summarizing what I have learnt. DSP & Quantization 6 Tanim Taher

7 3. TYPES OF PROCESSING There are two main types of processing in computer science real-time processing and off-line processing. Off-line processing is where data has been obtained before, but the processing is done later. Real-time processing is where the data is processed immediately after input. Off-line processing is used in situations where the results of the operations on the data collected are not immediately required. However, in real-time processing, the results need to be obtained immediately. For example, in speech to text computer systems, the spoken voice (input signal) must be processed in real-time to generate the text (result) when preparing a document in a word processing software. Time is a very crucial factor in real-time systems. Since the results are required immediately, digital filters in real-time applications need to be very fast. Hence, sometimes shortcuts may need to be made during processing, in order to produce results faster. If a computer system is being used in an application as a real time digital filter, this may mean that single precision word format is used instead of double precision, as single precision processing is faster. On the other-hand, time is not so crucial a factor in off-line processing. Hence, if we use the same computer in an off-line application that needs to use a digital filter, we can now use double precision arithmetic. Thus we can use higher precision in the digital filter which makes quantization effects minimal. Thus deping on the type of processing required real-time or off-line, the quantization effects on digital filters can vary. Off course we can use the same amount of higher precision in real-time digital filters, but this may make the design of the digital processor more complex, and hence more expensive. DSP & Quantization 7 Tanim Taher

8 4. DSP PROCESSOR COMPLEXITY FACTORS There are several factors which determine the design complexity and hence the cost of digital signal processors. Ideally, we want maximum performance at lowest cost. Since this is not always possible, we can hope to achieve optimum performance that meets the application requirements, at a reasonably low cost. The following are the main factors involved in determining this complexity: Processing Frequency Precision The type of filter used The number of coefficients in the filter 1) Obtaining higher processing frequency affects the processor complexity as follows. Processor uses more power Complex algorithms may need to be used to make the processing faster and more efficient. The algorithm complexity and the processor complexity are correlated. Processor may require more memory. Processor may need more adders, multipliers, etc to increase the amount of calculations possible per bus cycle. Hence more cost and more complexity. 2) Higher precision in a digital filter involves using longer word lengths. For high precision work, we would prefer a 32-bit processor over a 16-bit. Hence, the cost and complexity of the processor is more. 3) Type of filter Used: IIR filters usually have far fewer coefficients than FIR. Hence they are faster in processing, or require fewer arithmetic components in the processor. Lattice filters require a lot of multiplication and addition stages, and this means added processor complexity. DSP & Quantization 8 Tanim Taher

9 4) More the number of coefficients in a digital filter, the more calculations that need to be performed. Hence complexity and cost increases as does the number of coefficients. If we are to use the same processor for two filters one with more coefficients than another one, the former would require more processing time and hence will be slower. 5. PROCESSOR ARCHITECTURE DSP processors in the market commonly use the Super Harvard Architecture. This architecture lets the processor achieve more per bus cycle. The key features of this type of architecture are support for separate data and program buses, instruction cache and support for indepent data management in memory. The following figure shows this architecture: As can be seen the processor (CPU) uses separate buses for instructions and data. Also there is an instruction cache that stores the common instruction sequences required for signal processing. And finally, we can see data in the memory being written or read by an I/O controller indepent of the processor. This architecture, as is obvious, allows for faster processing. Reference: The Scientist and Engineer's Guide to Digital Signal Processing (2nd Edition) DSP & Quantization 9 Tanim Taher

10 6. QUANTIZATION ISSUES No digital system in the world can give us infinite precision while representing all numbers. There is always a size limit for a digital word. Rounding is the term used to describe the process of approximating a number in the digital domain. This is done by rounding the least significant bit such that the value of the digital number is closest to the actual value of the number. We are loosing some degree of precision by this approximation, and generating what is called a roundoff error. On average, this error amount is equal to a quarter of the least significant bit value. During analog to digital sampling, the roundoff error can be quite significant if the amount of noise inherent in the original signal is close to the average error amount. Another type of error is truncation error which occurs when the results of arithmetic operations like division are truncated after the word length has been reached. In recursive filtering operations, the quantization errors simply keep adding up each time with the digitally filtered data. Furthermore, roundoff error can cause stability issues when it comes to IIR filters. Rounding, as it causes loss in precision, changes the filter coefficients such that they no longer are the ideal values. If the pole (denominator in the transfer function) coefficients are close to 1, and rounding produces a coefficient equal to 1 or more, then the digital filter is unstable. There are three binary number formats that are in common use. The type of format used changes the impact of quantization effects in digital filters. The following are the formats: 1) Single Precision floating point this uses a 32 bit word. The format for storing the number is standard number format (e.g X 10 3 is a standard format number). 2) Double Precision floating point 64 bit, standard number format. 3) Fixed Point varying word lengths are in use (common 16, 32, 64 bits), where the decimal point is fixed and does not vary. DSP & Quantization 10 Tanim Taher

11 7. SIGNAL FLOW GRAPHS Previously, the transfer function for any digital filer was shown. The transfer function can be used to draw the direct form system diagrams. The system diagram simply represents the flow of data within a digital filter, and shows the operations carried out at each stage, like multiplication by the coefficients, and summation of the results. The direct form diagrams are very common, and I was introduced to them while taking the course, Digital Signal Processing (ECE 437). Since my focus in this report is on material that I learnt afterwards, we will not get into the details of the direct form diagrams. However, we shall look into signal flow graphs, which are another way of representing the digital filter pictorially. Signal flow graphs use nodes to represent the adders and as signal sources. If an arrow is pointing towards a node, it means that that node is adding that signal, or performing a process on the signal (like multiplication). If the signal arrow is pointing away, then it simply means that the result of the node s operation is taken out in that data path. Multiplication coefficients are represented simply as numbers on the data flow lines, and the unit delay as z -1 on the line. The following diagram makes this clear: DSP & Quantization 11 Tanim Taher

12 Based on this principle, an N order FIR filter would look like the following if shown in the form of a signal flow graph: Reference: DSP & Quantization 12 Tanim Taher

13 8. DIRECT FORM TRANSPOSE FILTERS Direct form filters are filters that realize the filter structure by using the same coefficients directly from the transfer function into the filter. I learned about direct form 1 and direct form 2 filters from ECE 437. However, during the course of my research, I came across Direct Form Transpose filter structures. These structures are generated from the signal flow graphs of their direct form counterparts. The procedure for converting from direct form to direct form transpose is as follows: 1) Draw the signal flow graph for the original direct form structure. 2) Redraw the signal flow graph, but reverse the arrow directions of the data flow paths. Physically this amounts to changing the nodes into adders and the adders into nodes. 3) Now interchange the input and the output. Thus the new signal flow graph represents the direct form transpose structure. The next two system diagrams shows the difference between direct form II and direct form II transpose filters. The small triangles are the coefficient multipliers. Source: Direct Form II Direct Form II Transposed DSP & Quantization 13 Tanim Taher

14 9. LATTICE FILTERS Lattice filters are very different from the direct form structures. They use entirely new coefficients called K coefficients. The following diagram shows how a lattice IIR filter would look like. Source: The K and V coefficients are a new set of coefficients that are generated from the IIR transfer function. The K coefficients are generated from the denominator (pole) coefficients, and they form the lattice structure. The V coefficients are generated from the numerator (zero) coefficients and form part of the ladder structure. The following example shows how to determine the K and V coefficients and also shows the equations employed. In order to find the coefficients, an FIR filter A(z) is first created by simply copying the denominator coefficients of the IIR filter. In the following notations, sub-script m denotes the order of the filter: α m (n) is the impulse response an m order FIR filter at time nt. i.e. h m (n)=α m (n) β m (n) = α m (m - n) DSP & Quantization 14 Tanim Taher

15 Example: if A 2 (z) = z z -2 then B 2 (z) = z z -2 so α 2 (2) = β 2 (0) = 0.3 And α 2 (1) = β 2 (1) = 0.2 And α 2 (0) = β 2 (2) = 1 First Step: K m = α m (m) Since A 2 (z) = z z-2 K m = K 2 = α m (m) = α 2 (2) = 0.3 Second: α m-1 (n) = [α m (n) - K m β m (n)] / (1 K 2 m) α 1 (0) = α 2 (0) K 2 β 2 (0)] / (1 K 2 2) = [1 (.3 X.3)] / [ ] = 1 α 1 (1) = α 2 (1) K 2 β 2 (1)] / (1 K 2 2) = [.2 (.3 X.2)] / [ ] =.1538 So K 1 = α 1 (1) = All the A m (n), for n = 0 to m, need to be determined so that the B m (n) can be found for all required filter orders. B m (z) is also required later on to find the V coefficients. Now that B m (z) is known for all m orders, we can find the V coefficients. To do this, we first create an FIR filter by copying the numerator of the transfer function of the original IIR. Let us call this filter C m (z). Then: Let c m (n) be the numerator coefficients. It is the response of an m order FIR filter at time nt. i.e. h m (n)=c m (n) First Step: v m = c m (m) Second: C m-1 (n) = C m (n) - v m β m (n) Thus both the V and K coefficients can be found in this way. DSP & Quantization 15 Tanim Taher

16 Now the question is why use lattice filters. It is indeed quite a lot of work to determine the K and V coefficients initially. However, during processing, a bigger problem occurs as is evident from the system diagram shown earlier. The problem is that a large number of extra multiplication and summation operations need to be carried out in lattice filters in comparison to their direct form counterparts. So there needs to be a good reason for choosing lattice filters. The answer is that the output of a lattice filter is less sensitive to the parameterization of the filter coefficients. This is specially relevant to stability, as otherwise slight changes in the coefficients during parameterization can make the entire filter system unstable. The following two diagrams explain this concept. Source of diagrams: homes.esat.kuleuven.ac.be/~moonen/ This figure shows all the possible pole locations for any IIR filter where the coefficient numbers are represented in 5 bits. Note due to areas of concentration, generally, slight changes in coefficients equal a significant change in the filter s characteristics This figure shows all the possible pole locations for any IIR lattice filter where the K coefficient numbers are represented in 5 bits. Note due to uniform concentration, slight changes in coefficients here do not affect much the filter s characteristics. DSP & Quantization 16 Tanim Taher

17 10a. RESULTS: Simulation Program Overview In an effort to explore the quantization effects in digital filters and to obtain a first-hand experience in programming digital filters in a computer, I developed a Digital Filter Simulator and Analysis Tool. I used Matlab to develop the software, and used Matlab s Graphics User Interface Design Environment (GUIDE) to make the user interface. Most of my research time was spent on this software development, and in my opinion the investment was worthwhile. The software lets the user easily change the quantization parameters, and at the click of a button change the structure of a digital filter. The output graphs are very useful in analyzing the performance of the filters in response to quantization parameter changes. The software has to GUIDE forms/menus. The first form is called the Waveform Generator and it is used to generate sample data to be fed into the digital filter. The advantage of this form is that virtually any periodic waveform can be used as input provided the fourier series coefficients are known. This is also very helpful to the electrical engineering student for two reasons: a) He/she can observe firsthand how the fourier series can be used to generate any waveform of choice, and hence understand the power of Fourier series. b) He/she can also observe the effect of aliasing which occurs significantly if the sampling rate is below the Nyquist frequency. The other form is the Digital Filter form. The user inputs the coefficients of a digital filter (FIR or IIR) from the transfer function coefficients. The user also chooses the filter structure to be used. The quantization parameters like word length, fixed-point/floating point can be changed at will. Then at the click of a button, the software simulates the digital filter. There are two outputs that can be produced by the program: a) Data output: Using the data-set of the waveform generated by the Waveform Generator, an output data-set is created and displayed by digitally filtering the DSP & Quantization 17 Tanim Taher

18 data input. Thus this represents the output of the digital filter. This means that the user can know how the output from the filter would be distorted or changed as the word length or other quantization parameters are changed. This is sometimes more useful than the frequency response, as it shows how easily the output can saturate even though the system may be stable. b) Frequency Response: The user can see the magnitude and phase responses of the digital filter. DSP & Quantization 18 Tanim Taher

19 10b. RESULTS: Software Performance In the following, all the waveforms were compared to their Matlab DSP tool counterparts. The results in each case match with each other. As per the discussion in the previous section, the following screenshot shows the Waveform Generator. The entry fields on the left let the user input the fourier series fundamental frequency (1 st harmonic frequency) and the coefficients (amplitudes) for various harmonics. The sampling frequency is important as it determines the aliasing effects. To demonstrate the aliasing effect, the sampling frequency was lowered. The resulted distorted input waveform is shown in the next screenshot. DSP & Quantization 19 Tanim Taher

20 The entry fields on the right side let the user determine the length of the data-set by specifying the start and stop times for the input waveform. The Total Window Points field is used to zoom in or zoom out, and it refers to the number of data points to be plotted on screen. This screenshot is that of the Digital Filter form. DSP & Quantization 20 Tanim Taher

21 The quantization options lets the user to select the word type (fixed point, single or double floating points), and the word length for the fixed point type. The output shown is that produced by the digital filter with input being the waveform shown in the Waveform Generator shown before. The digital filter is specified by the a and b coefficients that the user can input. The filter structure is chosen by selecting any bullet from the Implementation Type box area. The most important thing to note is that as the quantization options are changed, the actual filter coefficients used by the digital filter changes, and these are displayed in the two list boxes at the bottom of the form (A Coefficients, B coefficients). The following screenshot shows the magnitude phase response which is the other output. DSP & Quantization 21 Tanim Taher

22 Note, the aliasing effect can be observed here also, by lowering the Fs(Hz) entry-field value. This is shown in the next screenshot: The third output waveform is for the phase response: DSP & Quantization 22 Tanim Taher

23 Also the lattice coefficients generated by the software are displayed if the implementation type is Lattice. Finally, the poles of any filter system can be plotted by clicking Plot system poles button. For a filter, the poles are shown in the next figure. Red color indicates instability. DSP & Quantization 23 Tanim Taher

24 So we see that the user is given many options to play around with the digital filter and the input waveform. The results are good at experimentally demonstrating many principles of digital signal processing and quantization effects to the user. DSP & Quantization 24 Tanim Taher

25 10c. RESULTS: Software Algorithm Description 1) The Waveform Generator uses the following algorithm to generate the input waveform: Time Period, T = 1 / Sampling Frequency a. For sample n, input x(n) = 0 b. T0 = Start time c. Start with harmonic number h = 1 d. For harmonic number h, x(n) = [h th fourier Coeff] * Sin (h * fundamental frequency * n * T + T0) + x(n) e. Increment h by 1 f. If h <= highest harmonic number, repeat steps c to f. g. Increment n h. If n not last sample, then repeat steps c to h. The last sample count is determined from the start and stop times, and the time period T. 2) Once the quantization options are chosen, the program creates a fixed point data object type is created. Then the program uses this object type for all arithmetic, if the word type is fixed point. Otherwise, it uses single or double floating point objects (as specified by the user) for all calculations. Hence during filtering, the simulated digital filter is fully exposed to quantization effects. 3) Direct Form 1 Filter Implementation: The software uses two separate loops to perform the two separate summation operations of the IIR direct form 1 implementation equation shown below: DSP & Quantization 25 Tanim Taher

26 4) Direct Form 2 Filter Implementation: The software uses two separate loops to perform this filter function. Each of the loops perform one of the summation functions as specified by the IIR direct form 2 implementation equations shown below: 5) Generating Lattice Filter Coefficients: The software uses several loops to generate the lattice coefficients recursively using the equations given before in the Lattice Filters sections. While I was able to successfully generate the lattice coefficients, I faced constant difficulty recreating the filter model for the lattice structure, and never was able to successfully implement it. Hence, I used the lattice coefficient vectors generated by my algorithm, with Matlab s built in lattice filter function (keyword latcfilt()) for the filtering. 6) In order to generate the magnitude response, the software uses complex arithmetic. This algorithm uses the quantized coefficients, and replaces z within the filter s transfer function (given before) by z = e -jwt where, w is the sweep frequency being used. Then the value of H(z), i.e. H(e -jwt ) is calculated. This complex value s magnitude represents the magnitude response, and its phase represents the phase response. DSP & Quantization 26 Tanim Taher

27 10d. RESULTS: Software Applicability This was briefly mentioned before. Basically, the software is a powerful learning tool. I certainly learned a lot as the programmer. By simulating a lot of filters using the software, I was also able to learn and see the quantization effects, and to classify how different filter structures hold up to quantization effects. For an electrical engineering student, the software can help for the following: Learning tools for digital signal processing aliasing, fourier series, filter structures, stability, magnitude and phase response, etc. Students can use and modify this code to learn about: MATLAB Simulation Filter structure Students can test Quantization effects First Hand. By examining code, then can appreciate how Quantization errors build up. I would like to allow the source to be used as freeware, that can be modified by students and users. The condition is that the comments with my ID information are not modified. DSP & Quantization 27 Tanim Taher

28 10e. RESULTS: Simulation Results From my software, I was able to see how drastic changes occur when the word length is increased by even a few bits. The effects of moving from small word fixed point to single floating point, and then to double floating point were visible. From the simulations, it seems clear that as long as the word length is adequate to hold the maximum and minimum input and output values, word format did not matter. By playing around with the program, I was able to learn more about the general quantization effects. Anyways, I also carried out several simulations in MATLAB s DSP tools. Some output waveforms are shown as follows. LP is low pass, HP is high pass. The conditions and constraints used are mentioned too: 10kHz Lowpass, Order 25 FIR, Double, Floating Point 8 Bit, Fixed Point DSP & Quantization 28 Tanim Taher

29 10kHz Lowpass, Order 10 FIR, Double, Floating Point 8 Bit, Fixed Point DSP & Quantization 29 Tanim Taher

30 10kHz LP, Order 4 Chebyshev IIR, Double, Floating Point, Direct Form1 8 Bit, Fixed Point, DF1 DSP & Quantization 30 Tanim Taher

31 10kHz HP,Order 13 Chebyshev IIR, 6 Bit, Fixed Point, Lattice 8 Bit, Fixed Point, Lattice DSP & Quantization 31 Tanim Taher

32 11. INTERPRETATION: A lot was learned about quantization effects from the simulations. Listed below are the interpretation of the simulation results: Lattice Structure is most stable. Direct Form 1 and Direct Form 2 can give issue with stability. Direct Form 1 and Direct Form2 sensitive to slight parameterization changes. Cascade and Parallel structures (done in MATLAB) more stable than Direct Form 1 and Direct Form 2. This is due to the fact that the lower order structural units used in the cascade and parallel forms have lesser feedback continuation (only one level of feedback for second order units). The total number of coefficients in the IIR and FIR filter is the main factor that determines the filter performance. That is the order is a very important factor affecting filter performance. As long as the word length is adequate to hold the maximum and minimum input and output values, word format has little effect on performance. However, for input and output values with large ranges, the floating point data formats were decidedly better than the fixed point ones. The fixed point outputs often saturated. Even though lattice structure is more stable, the extra processing required (more multiplication and addition) cannot be really justified. This is because today, having large word lengths an inexpensive feat, and with large words, the direct form filters give performance close to that of lattice filters when parameterization effects are considered. DSP & Quantization 32 Tanim Taher

33 12. COCNCLUSION AND FUTURE WORK I must repeat again how valuable a learning experience this project was to me. On the one hand, I learnt how to use MATLAB, GUIDE, improved my simulation program development skills skills which will come in handy even in fields outside DSP. In the other, I learned a lot more about digital signal processing and processors. I feel confident now of my knowledge in this field, and many of the concepts that were not very clear to me before are now at the back of my head! I also gained experience in indepent study. As a person, I feel much more confident something which came due to the multiple presentations that I had to give during the course. For all this, I would again like to give special thanks to Dr. Oruklu and Dr. Saniiee. However much I learned and worked, there is always a lot of learning that can always be done. Directly related to this project, I believe that this project has the following future scope: Further development of Software Cascade Realization Parallel Realization Lattice Filter implementation Transpose direct forms: although it was my goal to add this functionality, I did not get any time to work on this. Generating the coefficients automatically using Chebyshev s/butterworth analog filter coefficients, followed by Bilinear transformation. Examine quantization effects on Multi-rate and adaptive filters. DSP & Quantization 33 Tanim Taher

34 GENERAL REFERENCES: The Scientist and Engineer's Guide to Digital Signal Processing (2nd Edition) DSP (Proakis, Manolakis) (Excellent Resources here) Other interesting finds: DSP Lab manual detailing chip programming and algorithms: Rutgers University, ADSP-2181 Experiments, Sophocles J. Orfanidis DSP & Quantization 34 Tanim Taher

35 13. APPENDIX: Program Listing The following is the listing for the Waveform Generator form. %Programmer Name: Tanim Taher % %Done as coursework for ECE 491, undergraduate research work %Fall 2005 function varargout = wavegen(varargin) % WAVEGEN M-file for wavegen.fig % WAVEGEN, by itself, creates a new WAVEGEN or raises the existing % singleton*. % % H = WAVEGEN returns the handle to a new WAVEGEN or the handle to % the existing singleton*. % % WAVEGEN('CALLBACK',hObject,eventData,handles,...) calls the local % function named CALLBACK in WAVEGEN.M with the given input arguments. % % WAVEGEN('Property','Value',...) creates a new WAVEGEN or raises the % existing singleton*. Starting from the left, property value pairs are % applied to the GUI before wavegen_openingfunction gets called. An % unrecognized property name or invalid value makes property application % stop. All inputs are passed to wavegen_openingfcn via varargin. % % *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one % instance to run (singleton)". % % See also: GUIDE, GUIDATA, GUIHANDLES % Copyright The MathWorks, Inc. % Edit the above text to modify the response to help wavegen % Last Modified by GUIDE v Dec :00:42 % Begin initialization code - DO NOT EDIT gui_singleton = 1; gui_state = struct('gui_name', mfilename,... 'gui_singleton', gui_singleton,... 'gui_layoutfcn', [],... 'gui_callback', []); if nargin && ischar(varargin{1}) DSP & Quantization 35 Tanim Taher

36 gui_state.gui_callback = str2func(varargin{1}); if nargout [varargout{1:nargout}] = gui_mainfcn(gui_state, varargin{:}); else gui_mainfcn(gui_state, varargin{:}); % End initialization code - DO NOT EDIT % --- Executes just before wavegen is made visible. function wavegen_openingfcn(hobject, eventdata, handles, varargin) global h_max ampl h_no Amp %intialize harmonic values h_max = 1; ampl = 1; Amp(1) = 1 h_no = 1; % Choose default command line output for wavegen handles.output = hobject; % Update handles structure guidata(hobject, handles); % UIWAIT makes wavegen wait for user response (see UIRESUME) % uiwait(handles.figure1); % --- Outputs from this function are returned to the command line. function varargout = wavegen_outputfcn(hobject, eventdata, handles) % Get default command line output from handles structure varargout{1} = handles.output; function edit4_callback(hobject, eventdata, handles) % --- Executes during object creation, after setting all properties. function edit4_createfcn(hobject, eventdata, handles) % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hobject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hobject,'backgroundcolor','white'); function edit5_callback(hobject, eventdata, handles) global h_max ampl h_no Amp h_no = str2double(get(handles.edit5,'string')); % Get entered harmonic no value DSP & Quantization 36 Tanim Taher

37 if h_no <= h_max set(handles.edit6,'string',amp(h_no)); else set(handles.edit6,'string',0); % --- Executes during object creation, after setting all properties. function edit5_createfcn(hobject, eventdata, handles) % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hobject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hobject,'backgroundcolor','white'); function edit6_callback(hobject, eventdata, handles) global h_max ampl h_no Amp %redundant % --- Executes during object creation, after setting all properties. function edit6_createfcn(hobject, eventdata, handles) % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hobject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hobject,'backgroundcolor','white'); % --- Executes on button press in pushbutton3. function pushbutton3_callback(hobject, eventdata, handles) global h_max ampl h_no Amp ampl = str2double(get(handles.edit6,'string')); % Get entered amplitude value h_no = str2double(get(handles.edit5,'string')); % Get entered harmonic no value Amp(h_no)=ampl; set(handles.edit5,'string',h_no+1); set(handles.edit6,'string',0); if h_no > h_max h_max = h_no set(handles.maxh,'string',h_max) ; %Find Nyquist frequency and set it as default value min_samp = (2 * h_max * str2double(get(handles.edit4,'string'))) / (2 * pi); w = str2double(get(handles.edit7,'string')); if w < min_samp set(handles.edit7,'string',min_samp); DSP & Quantization 37 Tanim Taher

38 % --- Executes on button press in pushbutton4. function pushbutton4_callback(hobject, eventdata, handles) global h_max ampl h_no Amp %Global makes these variables accessible throughout the MATLAB workspace clear dpts xs global st_time _time pts tot_pts xs dpts T% for slider T = 1 / str2double(get(handles.edit7,'string')); %Calculate the period w = str2double(get(handles.edit4,'string')); %fundamental frequency st_time = str2double(get(handles.edit9,'string')); %Get start and stop times _time = str2double(get(handles.edit10,'string')); tot_pts = ((_time - st_time) / (T * 1000)) %Calculate total number of points for m = 0:tot_pts n = int16(m+1); dpts(n)=0; xs(n) = m * T + (st_time / 1000); %nt sample for i = 1:h_max dpts(n) = dpts(n) + Amp(i)*sin(w*i*xs(n)); %Generate the waveform ; ; pts = str2num(get(handles.edit8,'string')); % Adjust Slider so that the plot is displayed properly if (tot_pts > pts) frac = pts / (tot_pts - pts) else frac = 500 Min = st_time; Max = st_time + T * 1000 * (tot_pts-pts); pcnt = (pts/tot_pts) *.05; set(handles.slider1,'min',min); %Set values and limits for the axes set(handles.slider1,'max',max); set(handles.slider1,'value',st_time); set(handles.slider1,'sliderstep',[pcnt frac]); xst = (get(handles.slider1,'value')) / 1000; x = xst + pts * T %determine density of pts in plot plot(xs(1:tot_pts),dpts(1:tot_pts),'--.b') axis ([xst x 0 10]) axis 'auto_y' function edit7_callback(hobject, eventdata, handles) % --- Executes during object creation, after setting all properties. function edit7_createfcn(hobject, eventdata, handles) % Hint: edit controls usually have a white background on Windows. DSP & Quantization 38 Tanim Taher

39 % See ISPC and COMPUTER. if ispc && isequal(get(hobject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hobject,'backgroundcolor','white'); % --- Executes on slider movement. function slider1_callback(hobject, eventdata, handles) global st_time _time pts tot_pts xstp dpts T xst = (get(handles.slider1,'value')) / 1000; x = xst + T * pts %determine density of pts in plot axis ([xst x 0 10]) %Redraw waveform as specified by slider position axis 'auto_y' % --- Executes during object creation, after setting all properties. function slider1_createfcn(hobject, eventdata, handles) % Hint: slider controls usually have a light gray background. if isequal(get(hobject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hobject,'backgroundcolor',[.9.9.9]); function edit8_callback(hobject, eventdata, handles) % --- Executes during object creation, after setting all properties. function edit8_createfcn(hobject, eventdata, handles) % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hobject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hobject,'backgroundcolor','white'); function edit9_callback(hobject, eventdata, handles) % --- Executes during object creation, after setting all properties. function edit9_createfcn(hobject, eventdata, handles) if ispc && isequal(get(hobject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hobject,'backgroundcolor','white'); function edit10_callback(hobject, eventdata, handles) % --- Executes during object creation, after setting all properties. function edit10_createfcn(hobject, eventdata, handles) % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. DSP & Quantization 39 Tanim Taher

40 if ispc && isequal(get(hobject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hobject,'backgroundcolor','white'); % --- Executes on button press in clearh. function clearh_callback(hobject, eventdata, handles) global h_max ampl h_no Amp global st_time _time pts tot_pts xs dpts T% for slider pts = 0; %Make all the fourier coefficients = 0, clear the plot tot_pts = 0; clear dpts; clear xs; h_max = 1; clear Amp; h_no = 1; set(handles.edit5,'string',1); set(handles.edit6,'string',1); set(handles.maxh,'string',1); Amp(1) = 1; plot(0,0); THE FOLLOWING IS THE CODE FOR THE DIGITAL FILTER SIMULATOR %Programmer Name: Tanim Taher % tanim_02@yahoo.com %Done as coursework for ECE 491, undergraduate research work %Fall 2005 function varargout = Filter_Coefficients_Parameterization(varargin) % FILTER_COEFFICIENTS_PARAMETERIZATION M-file for Filter_Coefficients_Parameterization.fig % FILTER_COEFFICIENTS_PARAMETERIZATION, by itself, creates a new FILTER_COEFFICIENTS_PARAMETERIZATION or raises the existing % singleton*. % % H = FILTER_COEFFICIENTS_PARAMETERIZATION returns the handle to a new FILTER_COEFFICIENTS_PARAMETERIZATION or the handle to % the existing singleton*. % % FILTER_COEFFICIENTS_PARAMETERIZATION('CALLBACK',hObject,eventData,handl es,...) calls the local % function named CALLBACK in FILTER_COEFFICIENTS_PARAMETERIZATION.M with the given input arguments. % % FILTER_COEFFICIENTS_PARAMETERIZATION('Property','Value',...) creates a new FILTER_COEFFICIENTS_PARAMETERIZATION or raises the % existing singleton*. Starting from the left, property value pairs are % applied to the GUI before Filter_Coefficients_Parameterization_OpeningFunction gets called. An % unrecognized property name or invalid value makes property application DSP & Quantization 40 Tanim Taher

41 % stop. All inputs are passed to Filter_Coefficients_Parameterization_OpeningFcn via varargin. % % *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one % instance to run (singleton)". % % See also: GUIDE, GUIDATA, GUIHANDLES % Copyright The MathWorks, Inc. % Edit the above text to modify the response to help Filter_Coefficients_Parameterization % Last Modified by GUIDE v Dec :24:45 % Begin initialization code - DO NOT EDIT gui_singleton = 1; gui_state = struct('gui_name', mfilename,... 'gui_singleton', gui_singleton,... 'gui_layoutfcn', [],... 'gui_callback', []); if nargin && ischar(varargin{1}) gui_state.gui_callback = str2func(varargin{1}); if nargout [varargout{1:nargout}] = gui_mainfcn(gui_state, varargin{:}); else gui_mainfcn(gui_state, varargin{:}); % End initialization code - DO NOT EDIT % --- Executes just before Filter_Coefficients_Parameterization is made visible. function update_listbox(handles) %This functions displays the A and B coefficients global a_no a_max b_no b_max c_a c_b a_string b_string oca ocb ock ocv clear a_string b_string a2_string b2_string k_string v_string b2_string(1)={' '}; a2_string(1) = {'A0 = 1'}; for n=1:a_max %Show the a coeff tmp = {strcat('a',num2str(n),' = ',num2str(c_a(n)))}; a_string(n) = tmp; for n=1:b_max %Show the b coeffs tmp = {strcat('b',num2str(n-1),' = ',num2str(c_b(n)))}; b_string(n) = tmp; DSP & Quantization 41 Tanim Taher

42 if get(handles.latt, 'Value') == 0 set(handles.paramak, 'Title','A Coefficients'); set(handles.parambv, 'Title','B Coefficients'); for n=1:numel(oca) tmp = {strcat('a',num2str(n),' = ',num2str(oca(n)))}; a2_string(n+1) = tmp; for n=1:numel(ocb) tmp = {strcat('b',num2str(n-1),' = ',num2str(ocb(n)))}; b2_string(n) = tmp; set(handles.listak,'string',a2_string); set(handles.listbv,'string',b2_string); else %Show the K and V coeffs if filter type is lattice set(handles.paramak, 'Title','K Coefficients'); set(handles.parambv, 'Title','V Coefficients'); for n=1:numel(ock) tmp = {strcat('k',num2str(n),' = ',num2str(ock(n)))}; k_string(n) = tmp; for n=1:numel(ocv) tmp = {strcat('v',num2str(n-1),' = ',num2str(ocv(n)))}; v_string(n) = tmp; set(handles.listak,'string',k_string); set(handles.listbv,'string',v_string); set(handles.a_list,'string',a_string); set(handles.b_list,'string',b_string); function Filter_Coefficients_Parameterization_OpeningFcn(hObject, eventdata, handles, varargin) % This function has no output args, see OutputFcn. % hobject handle to figure % varargin command line arguments to Filter_Coefficients_Parameterization (see VARARGIN) global a_no a_max b_no b_max c_a c_b PT WL FL oca ocb %Initialize oca=[]; ocb=[]; PT = 1; b_no = 1; b_max = 2; a_no = 1; a_max = 2; WL = 8; FL = 4; %c_b = [ ] % c_a = [ ] c_b = [ ] %Initialize the A and B coefficients to any desired value c_a = [ ] pushbutton4_callback(0, 0, handles) DSP & Quantization 42 Tanim Taher

43 % Choose default command line output for Filter_Coefficients_Parameterization handles.output = hobject; % Update handles structure guidata(hobject, handles); axes(handles.axes3); % UIWAIT makes Filter_Coefficients_Parameterization wait for user response (see UIRESUME) % uiwait(handles.figure1); % --- Outputs from this function are returned to the command line. function varargout = Filter_Coefficients_Parameterization_OutputFcn(hObject, eventdata, handles) % varargout cell array for returning output args (see VARARGOUT); % hobject handle to figure % Get default command line output from handles structure varargout{1} = handles.output; % function FileMenu_Callback(hObject, eventdata, handles) % hobject handle to FileMenu (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % function OpenMenuItem_Callback(hObject, eventdata, handles) % hobject handle to OpenMenuItem (see GCBO) file = uigetfile('*.fig'); if ~isequal(file, 0) open(file); % function PrintMenuItem_Callback(hObject, eventdata, handles) % hobject handle to PrintMenuItem (see GCBO) printdlg(handles.figure1) % function CloseMenuItem_Callback(hObject, eventdata, handles) % hobject handle to CloseMenuItem (see GCBO) selection = questdlg(['close ' get(handles.figure1,'name') '?'],... ['Close ' get(handles.figure1,'name') '...'],... 'Yes','No','Yes'); if strcmp(selection,'no') DSP & Quantization 43 Tanim Taher

44 return; delete(handles.figure1) % --- Executes on selection change in popupmenu1. function popupmenu1_callback(hobject, eventdata, handles) % hobject handle to popupmenu1 (see GCBO) % Hints: contents = get(hobject,'string') returns popupmenu1 contents as cell array % contents{get(hobject,'value')} returns selected item from popupmenu1 % --- Executes during object creation, after setting all properties. function popupmenu1_createfcn(hobject, eventdata, handles) % hobject handle to popupmenu1 (see GCBO) % Hint: popupmenu controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc set(hobject,'backgroundcolor','white'); else set(hobject,'backgroundcolor',get(0,'defaultuicontrolbackgroundcolor')) ; set(hobject, 'String', {'plot(rand(5))', 'plot(sin(1:0.01:25))', 'bar(1:.5:10)', 'plot(membrane)', 'surf(peaks)'}); % --- Executes during object creation, after setting all properties. function edit1_createfcn(hobject, eventdata, handles) % hobject handle to edit1 (see GCBO) if ispc && isequal(get(hobject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hobject,'backgroundcolor','white'); % --- Executes during object creation, after setting all properties. function edit2_createfcn(hobject, eventdata, handles) % hobject handle to edit2 (see GCBO) if ispc && isequal(get(hobject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hobject,'backgroundcolor','white'); % --- Executes during object creation, after setting all properties. function listbox1_createfcn(hobject, eventdata, handles) DSP & Quantization 44 Tanim Taher

45 % hobject handle to listbox1 (see GCBO) if ispc && isequal(get(hobject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hobject,'backgroundcolor','white'); % --- Executes during object creation, after setting all properties. function edit3_createfcn(hobject, eventdata, handles) % hobject handle to edit3 (see GCBO) if ispc && isequal(get(hobject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hobject,'backgroundcolor','white'); % --- Executes during object creation, after setting all properties. function edit4_createfcn(hobject, eventdata, handles) % hobject handle to edit4 (see GCBO) if ispc && isequal(get(hobject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hobject,'backgroundcolor','white'); % --- Executes during object creation, after setting all properties. function listbox2_createfcn(hobject, eventdata, handles) % hobject handle to listbox2 (see GCBO) if ispc && isequal(get(hobject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hobject,'backgroundcolor','white'); function wordlength_callback(hobject, eventdata, handles) % hobject handle to wordlength (see GCBO) global WL FL WL = str2num(get(hobject,'string')) FL = str2num(get(handles.frac,'string')) if WL <= FL WL = FL + 2; set(hobject,'string',wl) % --- Executes during object creation, after setting all properties. function wordlength_createfcn(hobject, eventdata, handles) % hobject handle to wordlength (see GCBO) if ispc && isequal(get(hobject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hobject,'backgroundcolor','white'); DSP & Quantization 45 Tanim Taher