GUI Signal Analysis and Filtering Design

Transcription

1 i GUI Signal Analysis and Filtering Design Axel Daniela Campero Vega, Electrical Engineering Project Advisor: Dr. Dick Blandford April 26, 2018 Evansville, Indiana

2 ii Acknowledgements I want to thank Dr. Blandford for his guidance, advice, collaboration and patience that have allowed me to successfully completed this project. I also want to thank Dr. Howe for her support and guidance in the preparation of this document.

3 iii Table of Contents I. Introduction II. Problem Definition Finite Impulse Response Filter (FIR) Minimum requirements III. Solution (Design) 3.1 FIR FILTERS GUI DESIGN Functions a) Reset function b) Preset function c) Parameter setting function d) Memory function e) Test with an audio signal Program Description a) Filter analysis program: b) Program of change of parameters c) Memory and loading program 3.2 IIR FILTERS GUI DESIGN Functions a) Preset function b) Setting function c) Visualizing Poles and zeros function d) Execute or leave function e) Modify Pole and zeros function f) Insert Poles or Zeros Function g) Reset Function Program Description a) Filter analysis program:

4 iv Safety Designing Filters IV. Costs V. Conclusions Appix A: Code for FIR Filters Analysis References List of figures Fig. 1 Specification of the filter Fig. 2: Design techniques Fig. 3 Design Fig. 4 GUI Screen for FIR Filters Fig. 5 Functional Block Diagram of the project Fig. 6 Results from Reset function Fig. 7 Results from Preset function Fig. 8 Parameter setting function Fig. 9 Memory and recall functions Fig 10 Test with an audio signal Fig. 11 Software Block Diagram Fig. 12 Flux Diagram of the Project Fig. 13 GUI Screen example of results for FIR Filters Fig. 14 GUI Screen for IIR Filters Fig. 15 IIR functions Fig. 16 Preset function for IIR Filters Fig. 17 Software Block Diagram for IIR Filters Fig. 18 GUI Screen example of results for IIR Filters Table 1. Cost of the project List of tables

5 1 I. Introduction A digital filter operates by applying mathematics to an input signal and modifies it to produce an output that we desire. Traditionally, they are used in: Separation of signals to be transmitted by shared means such as cellular telephony Recovering distorted signals Sound synthesis Audio effects: like chorus, reverb, and so on Instrumentation Image processing Seismic and geophysical signal processing Biological signal processing and electro medicine Synthesis and speech recognition Astronomy Traditional digital filters applications generate millionaire profits by new products and services, and there are many industries involved. In addition, digital filters are being applied in the financial and business area to solve problems such as; trading strategies, trading costs, industrial processes optimization, risk prediction and other type of analysis in order to improve business and industries. Therefore, the development of an application about digital filters is very useful and important. This project focused on designing a graphic user interface (GUI) application in Matlab that is capable of assisting in signal analysis and optimization of finite impulse response (FIR) filtering. II. Problem Definition The design of digital filters and their influence on filtered signals are timeconsuming and a complicated process. There are tools in Matlab that help to simplify the problem. However, there is no tool that is able to graphically modify the behavior of the filter in relation to a previously defined ideal filter, adjust it manually or automatically and save the results in memory.

6 2 The current technological requirement includes sophisticated and critical applications in design and use of filters. For example, cellular telephony, which has limited and small bandwidth requires the reuse of frequencies to provide service. In addition, these filters must be dynamic, since they must adapt to the conditions of the service area and the technology offered by the operator (GPRS, EDGE, LTE, OFDM, and so on) [4]. These filters, are of such high order that it is not feasible to attempt their design without the support of a mathematical tool that helps to perform the required calculations. An actual implementation of a digital filter can start with the design of the filter in Matlab and after finding the parameters, they are programmed into a micro controller for their physical incorporation into the devices. Matlab has developed an extensive library of functions that help in the design of filters. These functions include the calculation of filter parameters, and its Bode plot in magnitude and phase. It also includes the function diagram of poles and zeros. The source codes for these functions are not accessible or modifiable. When a design is required, the designer should often use the default functions in Matlab (trial and error) several times, resulting in waste of time and low efficiency. Matlab has also developed applications of the "toolbox" type, which help in the study of the signals subjected to filters in a more elaborate and consumption-oriented way before the design and implementation of filters. Moreover, these applications developed by Matlab, are not incorporated in the general license of use of Matlab and are sold separately. The problem can be summarized, as there is no tool or application developed in Matlab that helps in the design and study of the dynamic behavior of the filters. Finite Impulse Response Filter (FIR) The design of a digital filter [2] typically begins with a frequency specification. For example, a specification for a low pass filter might give a passband range as being 0 Hz to 200 Hz and a stopband as being 2254 Hz to half the sample frequency. The specification would also indicate the amount of ripple that is permitted in the passbands and stopband. In addition, a sample rate might be specified, or some range of sample

7 3 frequencies may be given, in which case, the design may choose the sample rate. With specification in hand, the filter designer must then decide between infinite impulse response (IIR) and finite impulse response (FIR) filters. Figure 1 is an example of this specification. Fig. 1: Specification of the filter From: There are several important methods of designing FIR filters. Matlab uses the Fourier Series Method. If the Fourier series is limited to 2N + 1 terms, we will call this approximation FN(t). In general, FIR filters are computationally less efficient than IIR filters that meet the same specifications. However, FIR filters can be designed to have linear phase, whereas IIR filters can only approximate linear phase, and often, that is over a small band. Hence, for applications where the information is encoded as part of the phase of a signal, having a filter that does not distort the phase curve is important. Zero locations for FIR linear-phase filters [2]: Real zeros must appear with their inverse. This means that they will always appear in pairs except in the case where z= +/- 1, in which case the zero is its own inverse. Complex zeros not on the unit circle must appear in sets of four (the zero plus its conjugate plus their inverse).

8 4 Complex zeros on the unit circle must appear as conjugate pairs. In this case, the conjugate (z) = inverse (z). Minimum requirements: The project will be developed in a GUI environment in Matlab language in a flexible way, easy to handle and that will serve as a tool to support in order to analyze FIR filters. Selection of the filter parameters of a menu from the GUI application. Presentation of the Bode and of the poles and zeros diagram. Online modification of the parameters and the graphics of the filter. Memorization of the states achieved in the filter settings. Automatic adjustment of parameters using the minimum error principle with reference to an ideal filter defined from the application itself. III. Solution (Design) The design starts with the development of the GUI (graphic user interface) screen, defining two areas of graphics, dynamics where the results will be presented either for the Bode and Z-Plane diagrams and their frequency spectrum. Dynamic controls are also incorporated as a slider that serve as a dynamic control of the values that the parameters of the transfer function can assume. The design techniques for FIR filters are: Parks McClellan, Window type and Frequency Sampling. I choose Frequency Sampling because has better results, and it is amenable for computer optimization. For the IIR filters the analysis use the classical Chebyshev, Butterworth and Elliptic.

9 5 Digital filters are achieved using the bilinear transform. Both FIR and IIR filters are designed and analyzed using graphic user interface and functions of Matlab. FIR FILTERS Parks McClellan Algoritm Window Type Frequency Sampling Frequency sampling: Better results Amenable to computer optimization Filter Design Techniques Project based in Matlab using GUI resources and functions IIR FILTERS IIR CLASSIC FILTERS: Butterworth Chebyshev I & II Elliptic Good templates for creating Digital Filters, using mapping functions such as Bilinear Transform. Figure 2: Design techniques The application is divided into multipurpose functional routines that can be used in various scenarios. The definition of routines and functions follow the logic established by the GUI application of Matlab. When the dynamic variables are defined, they respond immediately to the changes made and modify online the diagrams of Bode, Z plane and time and spectrum of the analyzed signals. Other controls, such as a pop-up menu for selection and presentation of parameters, are included; additionally, static and dynamic text windows are added to show the results of the process. Taking into account that the adjustment is manual and graphic, it is necessary to have a memory system that stores the parameters of a simulation and that can be retrieved later. At least three memory vectors will be defined to store historical data in the filter analysis. The design (figure 3), begins with a main page in which the user can get some information about the project and can select design FIR filters. The application allows the adjustment of parameters in order to get the best results. Another function is to test the filter with an audio record, comparing the time and spectrum diagram before and after the

10 6 FIR Application. For IIR filters, it is possible to choose the type of filter, frequency and ripple parameters. When the Bode diagram and Z plane diagram are displayed, it is possible to move poles and zeros from Z plane with the mouse. Time Domain & Spectrum Audio signals (test) Test Signal (WAV File) FIR Filtering GUI Signal Analysis and Filtering Design IIR Filtering Dynamic Adjust Automatic Adjust Fig. 3 Design 3.1 FIR FILTERS Frequency sampling is a filter design technique that is related to the Fourier series method. Its advantage is that can provide better results and it is amenable to compute optimization [2]. It begins with an ideal frequency response for a filter, which is sampled at regular intervals. Applying DFT and IDFT it is possible to get the impulse response and thereby arrive at a transfer function. Some restrictions apply. Since we want to a filter that has real coefficients and a linear phase response.

11 GUI DESIGN Fig 4: GUI Screen for FIR Filters The GUI screen has been divided into three work areas. The first shows the instantaneous numerical value of the filter parameters and the frequencies used. The second one shows the functions of RESET and PRESET, which are two pushbuttons that when activated load the data by default (RESET) or the selected values (PRESET). The third area shows the memory commands that allow memorize the analysis status and also allows to load the previously saved data to present them at any time. The fourth is the graphic work area, where the diagrams of Bode and Z plane (axes 1 and axes 2) are presented Functions The functions include parameter selection as well the frequency parameters. Also allows to manual or automatic adjust and memorization. Figure 3 shows the Functions for this module.

12 8 Manual Adjust Automatic Adjust Reset Memory Reload from memory GUI Filter Design FIR filter Test with an audio signal and compare Parameter selection a0, a1,. an fs, fstop, fpass Figure 5: Functional Block Diagram of the project a) Reset function Load basic parameters by default to the system and present the ideal filter and its best design approach. These are shown in figure 4. Reset Parameters of the filter: a0=1; a1=1; a2=1; a3= a4= ; a5=0; a6=0; a7=0; a8=0; a9=0; a10=0; fs=1000; % fs = frequency sample fpass=125; % fpass = passband frequency fstop=200; % fstop = Stopband frequency

13 9 Fig. 6 Results from Reset function b) Preset function Preset allows changing the values of the working frequencies of the filter. For this, a control window is used, where the value of the frequencies can be written. The graphic display includes the representation of the ideal filter (PRESET) and the actual filter, with the last parameters used. The PRESET function only affects the values of the working frequencies and not the filter parameters. Fig. 7 Results from Preset function

14 10 c) Parameter setting function This function allows the user to modify the parameters of the filter transfer function. For this, the user must choose from a POP UP menu, the parameter that he wants to modify. The selection includes the parameters a0, a1, a2,... a10. Once the parameter has been selected, it can be varied by entering a specific value in the presentation window or by controlling a "slider", which was defined to vary between values from 0 to 10. The adjustment of the parameters produces instantaneous changes in the Bode and Z-Plane graphs. Fig.8 Parameter setting function For the example, the parameters a3 and a4 of their original values have been modified. The graph shows the immediate update of the table showing the parameter vector and the graph resulting from that modification. d) Memory function Fig. 9 Memory and recall functions

15 11 The memory function provides a working window where the user can record up to three sets of data associated with the analysis of a filter. The work window has a couple of buttons for each memory. The first has the function of recording and the second that of loading the data stored in that memory position. e) Test with an audio signal This function loads a sound file in WAV format, reproduces it in its original audio, presents it in the temporal domain and also graphs its frequency spectrum. The function also has the option of comparing the original state of the audio signal with the one it has after being subjected to a type of filter chosen by the user. The comparison includes the reproduction of sound, re-representation in the time domain and its frequency spectrum Program Description Fig. 10 Test with an audio signal The software was developed in Matlab. Begins loading parameters, then the Bode and Z plane diagram are presented. Routines for adjust manually or automatically parameters were developed. Memory routine allows to keep values. The adjust routine allows to get the best conditions and Audio test routines compare a record after and

16 12 before the filter. The program is divided into subroutines and functions that are activated graphically from the GUI screen. Start Load frequencies Fs, Fpass, Fstop Preset? Reload Reset Load Default Parameters Load Parameters from Memory Adjust Auto? Yes No Show Bode Diagram, Z Plane and error Adjust minimizing error Memorize? No Save Parameters in Memory (1,2,3) Start Fig. 11 Software Block Diagram The program starts by calling the GUI application from the Matlab program. Initially a GUI screen is presented, without data and without graphs, so the next step is to load the predefined values (RESET) a) Filter analysis program: The equation for IDFT is: Where L is the length of the filter. The design process for frequency sampling filters can be summarized as follows [2]:

17 From the frequency response plot for an ideal filter, choose L equally spaced samples. These are H[k]. 2.- Use h(n) to find the impulse response of the filter. 3.- Use H[z] to find the transfer function for the FIR filter. The program shown below is developed in Matlab and illustrates the necessary operations to find the filter parameters that meet the specifications. [2]. This program calculates the filter parameters using the resources of the Matlab. It also calculates the error between the designed filter and the ideal filter, presents the Bode plot and the poles, and zeros diagram of the function in the Z plane. Code program %% FIR design Program %% The program was proposed by Dr. Blandford, %% The plot of Z plane was added %% Definition of the parameters: a0=1; a1=1; a2=1; a3= a4= ; a5=0; a6=0; a7=0; a8=0; a9=0; a10=0; fs=1000; fpass=125; fstop=200; L = 21; N = L-1; A2 = [a0 a1 a2 a3 a4 a5 a6 a7 a8 a9 a10]; h = zeros(1,l); for n = 1:L for k=2 : ((L-1)/2+1) h(n) = h(n) + 2* (-1)^(k-1)*A2(k)*cos(((2*(n-1)+1)*pi*(k- 1))/L); h(n) = (A2(1) + h(n))/l;

18 14 [H f] = freqz(h, 1, 4096, fs); plot(f, abs(h), 'r'); xlabel('frequency'); ylabel('amplitude'); title ('Bode Diagram'); grid on; m = -1/(fstop - fpass); b = -m*fstop; HId = m*f + b; % Ideal filter HId(HId > 1) = 1; HId(HId < 0) = 0; hold on; plot(f, HId, 'b'); %Plot Z Plane axes(handles.axes2); zplane(h); ylabel('imaginary part'), xlabel('real part'); grid on title ('Z Plane'); error = sqrt(sum((abs(h) - abs(hid)).^2)) disp(['original error = ' num2str(error)]); set(handles.text5,'string',error); b) Program of change of parameters Figure 12: Diagrams of the filter The change of parameters starts with the selection of the parameter that is carried out with a POP UP window, from which the parameter is selected, afterwards, each one is assigned a "case", which will be used to make modification decisions later. %************ Function: Select the paramerter ai ********* function selector_callback(hobject, eventdata, handles) %each case defines a parameter for transfer function val = get(hobject,'value')

19 15 switch val case 1 S.temp = 1 case 2 S.temp = 2 case 3 S.temp = 3 case 4 S.temp = 4 case 5 S.temp = 5 case 6 S.temp = 6 case 7 S.temp = 7 case 8 S.temp = 8 case 9 S.temp = 9 case 10 S.temp = 10 case 11 S.temp = 11 otherwise set(handles.selector, 'UserData', S); % of parameter slection from Pop Up menu *********** After selecting the parameter, we proceed to vary its value with the use of the "slider": %******************* Function: Slider ***************** %Assign slider value to a ai %temp is a output parameter from pop up table (VARIES FROM 0 TO 11) temp = get(handles.selector, 'Value'); % Selecting ai if temp == 1 a0=ax elseif temp == 2 a1=ax elseif temp == 3 a2=ax elseif temp == 4 a3=ax elseif temp == 5 a4=ax elseif temp == 6 a5=ax elseif temp == 7 a6=ax elseif temp == 8 a7=ax elseif temp == 9 a8=ax elseif temp == 10 a9=ax elseif temp == 11

20 16 a10=ax else a10=ax set(handles.text2,'string',ax); c) Memory and loading program The memory function uses a vector in which it stores the data and loads it again when needed. The vector includes, in addition to the parameters, the frequency values used. The parameters to be saved are taken from the dynamic table of instantaneous presentation of the data: A33=get(handles.uitable2,'Data'); A44_mem1=A33([ ]) fs_mem1=a33([12]) fpass_mem1=a33([13]); fstop_mem1=a33([14]); The loading of the data in memory: A_mem1=A44_mem1([ ]) fs=a44_mem1([12]) fpass=a44_mem1([13]) fstop=a44_mem1([14]) After loading the vector, the filter analysis, presentation and modification program is invoked. In addition to the graphical presentation, the calculation of the error is executed instantaneously and all the time, because it is the decision parameter for the adjustment of the filter. This calculation is made with: error = sqrt(sum((abs(h) - abs(hid)).^2)) Fig.13: GUI Screen example of results for FIR Filters

21 IIR FILTERS IIR filters have feedback, which results in a transfer function that has poles at locations other than the origin [2]. The poles, deping on how close they are to the unit circle, cause the gain to increase at a particular frequency. In the design of IIR filters, we need to figure out where to place the zeros to decrease the gain and where to place the poles to make it increase. This is the reason for which the interaction with poles and zeros in Z plane was choose as a technique for analysis of IIR filters. Using IIR, the design results with narrower transition bands than comparable FIR filters. Because IIR filters have a feedback, it is possible that they can be unstable, whereas with FIR, the stability is a given. The feed back causes other problems indirectly tied to stability that has to do with noise. FIR filters are always linear phase. For a IIR filter linear phase across the 0 to fs/2 frequency band is impossible GUI DESIGN Fig 14: GUI Screen for IIR Filters The GUI screen has been divided into four work areas: The first shows the setting for the filter. This allows to choose type of filter, kind of filter, frequency sample, band pass frequency, band stop frequency, band pass ripple, band stop ripple. The second shows instantaneous numerical value of the filter parameters (poles and zeros). The third shows the functions of RESET and PRESET, which are two pushbuttons that when

22 18 activated load the data by default (RESET) or the selected values (PRESET), and the insert/delete poles and zeros commands that allow to add or erase poles or. The fourth is the graphic work area, where the diagrams of Bode and Z plane (axes 1 and axes 2) are presented Functions The functions allow the selection of the type of filters, parameters and frequencies. They also allow to move poles and zeros from Z plane, as well as add or delete them. Select LowPass or BandPass Select: Chebyshev I, Butterworth, Chebyshev II or Elliptic Preset Reset Move Poles And Zeros Add And Remove Poles and Zeros GUI Filter Design IIR filter Parameter Selection: fs, fstop, fpass, Ripple Fig. 15 IIR functions a) Preset function Load basic parameters by default to the system and present the ideal filter and its best design approach. Type of filter: Low pass Frequency Sample = fs = Hz Band Pass: 2 KHz Band Stop: 3 KHz Pass Band Ripple: 0.01 Band Stop Ripple: 0.01

23 19 Fig. 16 Preset function for IIR Filters b) Setting function This allow to choose: Type of filter: Low Pass Filter Band Pass Filter Kind of filter: Chebyshev I Butterworth Chebyshev II Elliptic Frequency selection: Frequency Sample Band Pass Auxiliary Band pass (for Pass Band filter) Band Stop Auxiliary Band stop (for Pass Band filter) Pass Band Ripple Band Stop Ripple

24 20 c) Visualizing Poles and zeros function There is a table in which poles and zeros are presented (numerical values). The table has a push button in order to actualize values when and adjust is made. d) Execute or leave function Pushbuttons were implemented in order to execute the program taking in account the parameters, leave the program or return to the home page. The execution uses Matlab resources for the filters. e) Modify Pole and zeros function This function allows to modify poles and zeros from the graph in a flexible and dynamic way. The functions allow to use the mouse/cursor in order to catch a pole or zero and move it along the z plane. Whenever a pole or zero is moving its conjugates moves as well. The movement of poles or zeros in the z plane immediately produce a modification of the Bode diagram. f) Insert Poles or Zeros Function This function allows to insert poles or zeros in the z plane. Whenever a pole is inserted, a single pole appears in the right plane on the axis. If the pole is moved in the z plane it will generate its conjugate in an automatic mode. Whenever a Zero is added, it will appear in the left-hand axis and as the poles, it can be moves along the z plane generating its conjugate. g) Reset Function This function has a pushbutton in order to clear all values and graphics Program Description The program is divided into subroutines and functions that are activated graphically from the GUI screen. The program starts by calling the GUI application from

25 21 the Matlab program. Initially a GUI screen is presented, without data and without graphs, so the next step is to load the predefined values (RESET) Start Select Type of filter Select Parameters No Preset? Yes Load Preset parameters Draw Poles and Zeros diagram and Bode Diagram Show Poles & Zeros roots Modify Poles or Zeros Position? No Yes Modify the transfer function and parameters Insert Poles or Zeros? Yes No Figure 17: Software Block Diagram for IIR Filters a) Filter analysis program: This program (appix A), calculates the filter parameters using the resources of the Matlab program. It also allows to modify the poles and zeros from z plane, presents the Bode plot and the poles, and zeros diagram of the function in the Z plane.

26 22 Fig.18: GUI Screen example of results for IIR Filters Safety Designing Filters The Safety Standard [5] IEC defines the requirements for safety systems in the plant safety indepently of application. It is inted for the basis of all safety related electrical, electronic and programmable electronic systems, in order to apply it in safely critical applications. The safety concept ensures that the filter work with the predefined characteristics. Like medical technology, it is important that a filter work with high reliability. For this reason, the design of a filter must be done in a way that the safely is guaranteed in the application environment. Digital filters take an important role in this world which are most controlled by electronics. The filter designed must be analyzed as a simulation in a mathematical model. These models must be implemented in real models. V. Costs For the cost estimation, the following items will be taken: Cost of the Matlab license, which includes simulink and 10 applications or toolboxes. The student license will be quoted as having a reduced price.

27 23 Table 1: Cost of the project Item Description Quantity Unit Cost ($) Total Cost 1 Student Licence (Matlab + Simulink + 10 applications) Total $ 99 VIII. Conclusions Digital filters have a wide variety of applications and their use will increase in the immediate future, including social and financial fields. For the development of the project, it was necessary to know in detail, Matlab, GUI and theory and management of digital filters. The application is useful for digital signal processing analysis and telecommunications. From several methods, "frequency sampling filters" has been chosen for FIR filters and the variation of poles and zeros from the Z plane to analyze IIR filters. For FIR filters, it is possible to analyze in a practical way, how the filter designed, influences a specific audio record. The minimum requirements not only were achieved, but also another tool for IIR filters was developed. The contribution of the project, allows manual and automatic adjustment of parameters in the case of FIR filters and the graphically manipulation of poles and zeros for the IIR filters. These facilities were not developed in Matlab tools or in other applications for filter design.

28 24 Appix A: Code for FIR Filters Analysis %Axel Daniela Campero Vega %IIR Filter design and analysis %University of Evansville function varargout = Axel_IIR5(varargin) clc; 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{:}); function Axel_IIR5_OpeningFcn(hObject, eventdata, handles, varargin) handles.output = hobject; guidata(hobject, handles); function varargout = Axel_IIR5_OutputFcn(hObject, eventdata, handles) varargout{1} = handles.output; %********************************************************* function sel1_callback(hobject, eventdata, handles) global contador fun = get(handles.sel1,'value'); switch fun case 1 contador=1 case 2 contador=2 case 3 contador=3; case 4 contador=4;

29 25 guidata(hobject, handles); function sel1_createfcn(hobject, eventdata, handles) if ispc && isequal(get(hobject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hobject,'backgroundcolor','white'); %************************************************ function edit3_callback(hobject, eventdata, handles) Val=get(hObject,'string'); NewVal=str2double(Val); handles.edit3=newval; guidata(hobject,handles); function edit3_createfcn(hobject, eventdata, handles) if ispc && isequal(get(hobject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hobject,'backgroundcolor','white'); %***************************************************** function edit4_callback(hobject, eventdata, handles) Val=get(hObject,'string'); NewVal=str2double(Val); handles.edit4=newval; guidata(hobject,handles); function edit4_createfcn(hobject, eventdata, handles) if ispc && isequal(get(hobject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hobject,'backgroundcolor','white'); %*************************************************** function edit5_callback(hobject, eventdata, handles) Val=get(hObject,'string'); NewVal=str2double(Val); handles.edit5=newval; guidata(hobject,handles); function edit5_createfcn(hobject, eventdata, handles) if ispc && isequal(get(hobject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hobject,'backgroundcolor','white'); %****************************************************** function edit6_callback(hobject, eventdata, handles) Val=get(hObject,'string'); NewVal=str2double(Val);

30 26 handles.edit6=newval; guidata(hobject,handles); function edit6_createfcn(hobject, eventdata, handles) if ispc && isequal(get(hobject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hobject,'backgroundcolor','white'); %******************************************************* function edit7_callback(hobject, eventdata, handles) Val=get(hObject,'string'); NewVal=str2double(Val); handles.edit7=newval; guidata(hobject,handles); function edit7_createfcn(hobject, eventdata, handles) if ispc && isequal(get(hobject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hobject,'backgroundcolor','white'); %************************************************ function edit8_callback(hobject, eventdata, handles) Val=get(hObject,'string'); NewVal=str2double(Val); handles.edit8=newval; guidata(hobject,handles); function edit8_createfcn(hobject, eventdata, handles) if ispc && isequal(get(hobject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hobject,'backgroundcolor','white'); %********************************************************** function edit9_callback(hobject, eventdata, handles) Val=get(hObject,'string'); NewVal=str2double(Val); handles.edit9=newval; guidata(hobject,handles); function edit9_createfcn(hobject, eventdata, handles) if ispc && isequal(get(hobject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hobject,'backgroundcolor','white'); %*********************************************************** function pushbutton1_callback(hobject, eventdata, handles)

31 27 global zh ph b a z rety p pt zr global ax1 ax2 global contador2 contador fs=handles.edit3 fps1=handles.edit6 fst1=handles.edit7 Rp=handles.edit4 Rs=handles.edit5 fps2=handles.edit9 fst2=handles.edit8 [m1,n1]=size(contador2) [m2,n2]=size(contador) %Seleccion de tipos de filtros if (m1==0 & n1==0) contador2=1; if contador2==1 RsDB=-20*log10(Rs); RpDB=-20*log10(1-Rp); Wp=fps1/(fs/2) Ws=fst1/(fs/2) elseif contador2==2 fps=[fps1 fps2] fst=[fst1 fst2] RsDB=-20*log10(Rs) RpDB=-20*log10(1-Rp) Wp=fps/(fs/2) Ws=fst/(fs/2) if (m2==0 & n2==0) contador=1; if contador==1 [Nc,Wnc] = cheb1ord(wp,ws,rpdb,rsdb); [num den]=cheby1(nc,rpdb,wnc) elseif contador==2 [Nc,Wnc] = buttord(wp,ws,rpdb,rsdb); [num den]=butter(nc,wnc); elseif contador==3 [Nc,Wnc] = cheb2ord(wp,ws,rpdb,rsdb); [num den]=cheby2(nc,rpdb,wnc); elseif contador==4 [Nc,Wnc] = ellipord(wp,ws,rpdb,rsdb); [num den]=ellip(nc,rpdb,rsdb,wnc);

32 28 [z,p,k] = tf2zp(num,den); p=p'; z=z'; A=[num den]; axes(handles.axes1); bl=roots(num); %los zeros al=roots(den); %los polos ax=[]; %creamos un vector de N dimensiones para los zeros bx=[]; %creamos un vector de N dimensiones para los polos k=1; i=1; var1=length(bl); while (k~=var1) if (bl(k)==conj(bl(k+1))) ax(1,i)=bl(k); ax(2,i)=bl(k+1); k=k+2; %Incremento para el salto de dos i=i+1; if (k>var1) break; else ax(1,i)=bl(k); ax(2,i)=nan; k=k+1; %Incremento para el salto de uno i=i+1; if (k>var1) break; k=1; i=1; var2=length(al); while (k~=var2) if (al(k)==conj(al(k+1))) bx(1,i)=al(k); bx(2,i)=al(k+1); k=k+2; %Incremento para el salto de dos i=i+1; if (k>var2) break; else

33 29 bx(1,i)=al(k); bx(2,i)=nan; k=k+1; i=i+1; if (k>var2) break; %Incremento para el salto de uno [zh,ph]=zplaneplot(ax,bx); grid on ax1 = gca; ylabel('imaginary Part') xlabel('real Part') rety = handles.axes2; axes(rety); p=p'; z=z'; [b,a]=zp2tf(z,p,k); [H f]=freqz(b,a,1024,fs); global Hz; global az; global bz; Hz=H; az=a; bz=b; plot(f,abs(h)); grid on ax2 = gca; xlabel('frequency (Hz)') ylabel('magnitude (db) ') set(zh,'buttondownfcn','filtros(''zeroclick'')',... 'markersize',8,'linewidth',1) set(ph,'buttondownfcn','filtros(''poleclick'')',... 'markersize',8,'linewidth',1) function pushbutton2_callback(hobject, eventdata, handles) global zh ph b a z rety p pt zr global ax1 ax2 global contador3 contador4 [m11,n11]=size(contador3) [m22,n22]=size(contador4)

34 30 if (m11==0 & n11==0 & m22==0 & n22==0) contador3=1; contador4=1; size(contador4) if (contador3==1 & contador4==1) %Opcion POLO SIMPLE if length(ph)>0 ph(+1) = line([0.5 NaN],[0 0], 'parent', ax1, 'buttondownfcn', 'FILTROS(''poleclick'')',... 'markersize',8,'linewidth',1,'marker','x','linestyle','none'); else ph = line(.5,0,'parent',ax1,'buttondownfcn','filtros(''poleclick'')',... 'markersize',8,'linewidth',1,'marker','x','linestyle','none'); set(findobj('string','borrar POLO'),'enable','on') FILTROS('recompute') elseif (contador3==1 & contador4==2) %Opcion POLO CONJUGADO if length(ph)>0 ph(+1) = line([ ],[ ], 'parent', ax1, 'buttondownfcn', 'FILTROS(''poleclick'')',... 'markersize',8,'linewidth',1,'marker','x','linestyle','none'); else ph = line(.5,0,'parent',ax1,'buttondownfcn','filtros(''poleclick'')',... 'markersize',8,'linewidth',1,'marker','x','linestyle','none'); set(findobj('string','borrar POLO'),'enable','on') FILTROS('recompute') elseif (contador3==2 & contador4==1) %Opcion ZERO SIMPLE if length(zh)>0 zh(+1) = line([-0.5 NaN],[0 0], 'parent',ax1, 'buttondownfcn', 'FILTROS(''zeroclick'')',... 'markersize',8,'linewidth',1,'marker','o','linestyle','none'); else zh = line(.5,0,'parent',ax1,'buttondownfcn','filtros(''zeroclick'')',... 'markersize',8,'linewidth',1,'marker','o','linestyle','none'); set(findobj('string','borrar CERO'),'enable','on') FILTROS('recompute') elseif (contador3==2 & contador4==2) %Opcion ZERO CONJUGADO if length(zh)>0 zh(+1) = line([ ],[ ], 'parent',ax1,'buttondownfcn','filtros(''zeroclick'')',... 'markersize',8,'linewidth',1,'marker','o','linestyle','none'); else

35 31 zh = line(.5,0,'parent',ax1,'buttondownfcn','filtros(''zeroclick'')',... 'markersize',8,'linewidth',1,'marker','o','linestyle','none'); set(findobj('string','borrar CERO'),'enable','on') FILTROS('recompute') %********************************************* function pushbutton3_callback(hobject, eventdata, handles) global zh ph b a z rety p pt zr global ax1 ax2 global contador3 if contador3==1 %Opcion para eliminar POLOS delete(ph()) ph()=[]; if length(ph)==0 set(gco,'enable','off') FILTROS('recompute') elseif contador3==2 %Opcion para eliminar ZEROS delete(zh()) zh()=[]; if length(zh)==0 set(gco,'enable','off') FILTROS('recompute') function uipanel1_selectionchangefcn(hobject, eventdata, handles) global contador2 if (hobject==handles.uno) contador2=1 elseif (hobject==handles.dos) contador2=2 else contador2=1 function sel2_callback(hobject, eventdata, handles) global contador3 fun = get(handles.sel2,'value'); switch fun case 1 contador3=1 case 2 contador3=2

36 32 guidata(hobject, handles); function sel2_createfcn(hobject, eventdata, handles) if ispc && isequal(get(hobject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hobject,'backgroundcolor','white'); function uipanel2_selectionchangefcn(hobject, eventdata, handles) global contador4 if (hobject==handles.tres) contador4=1 elseif (hobject==handles.cuatro) contador4=2 function pushbutton6_callback(hobject, eventdata, handles) global contador contador2 opc=questdlg('do you want to leave the program?','leave','yes','no','no'); if strcmp(opc,'no') return; contador=1; contador2=1; delete(hobject); clear,clc,close all function pushbutton7_callback(hobject, eventdata, handles) global datax dataxt global datbx datbxt set(handles.uitable1,'data',dataxt); set(handles.uitable2,'data',datbxt); function uitable1_celleditcallback(hobject, eventdata, handles) function edit10_callback(hobject, eventdata, handles) clc global fs fps1 fst1 Rp Rs; fs=11025; fps1=2000; fst1=3000; Rp=0.01; Rs=0.01; set(handles.edit3,'string',fs);

37 33 set(handles.edit4,'string',rp); set(handles.edit5,'string',rs); set(handles.edit6,'string',fps1); set(handles.edit7,'string',fst1); handles.edit3 =fs; handles.edit4 =Rp; handles.edit5 =Rs; handles.edit6 =fps1; handles.edit7 =fst1; guidata(hobject, handles) function edit10_createfcn(hobject, eventdata, handles) if ispc && isequal(get(hobject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hobject,'backgroundcolor','white'); % --- Executes on button press in pushbutton8. function pushbutton8_callback(hobject, eventdata, handles) gui1; % --- Executes on button press in pushbutton9. function pushbutton9_callback(hobject, eventdata, handles) clc global fs fps1 fst1 Rp Rs; fs=11025; fps1=2000; fst1=3000; Rp=0.01; Rs=0.01; set(handles.edit3,'string',fs); set(handles.edit4,'string',rp); set(handles.edit5,'string',rs); set(handles.edit6,'string',fps1); set(handles.edit7,'string',fst1); guidata(hobject, handles) handles.edit3 =fs; handles.edit4 =Rp; handles.edit5 =Rs; handles.edit6 =fps1; handles.edit7 =fst1; guidata(hobject, handles)

38 % --- Executes on button press in pushbutton10. function pushbutton10_callback(hobject, eventdata, handles) close Axel_IIR5 open Axel_IIR5 clearvars run Axel_IIR5 % of the program 34

39 35 References [1] Matlab - Matworks Documentation: Digital Filters [Online]. Available: [2] Dick Blandford, Jhon Parr, Introduction to Digital Signal Processing. PEARSON, 2013 [3] Alexander D. Poularikas, Signals and Systems Primer with MATLAB, CRC Press, Technology & Engineering [4] Julius Orion Smith, Spectral Audio Signal Processing, Contributors Stanford University. Center for Computer Research in Music and Acoustics, Stanford University, Publisher W3K, 2011 [5] Tomasz Nowakowski, Marek Młyńczak,, Safety and Reliability: Methodology and Applications, CRC Press, Sep 18, Technology & Engineering