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1 Student number: Name: Student number: Name: Date: Passed(signature): SGN-1650 Signaalinkäsittelyn työkurssi SGN-1656 Signal processing laboratory Filter Structures Background and Goals DSPtoolboxforMATLABiscreatedbyAss. Prof.OscarGustafssonandhisteam,Electronic Systems, Linköping University, Sweden to simulate signal flow graphs. The Goals aretousedsptoolboxtosimulateandcomparetheperformanceofsignalflowgraphsand investigate scaling and overflow problems using finite word-lengths. Prerequisites The student should have some background in digital linear filters and working experience with MATLAB. 1 Preparations 1.ReadChapters1and5inLecturenotesofcoursesSGN-2010orSGN Read Introduction to the DSP toolbox below. 3.NB:YouneedtogetanaccountinLintula slinuxcomputersforthework.thedsp toolbox is only available in Lintula environment. Return your report to Raija Lehto room TE421 or raija.lehto@tut.fi(pdf-document or postscript-file). The report must contain(at least) the following items: Answers the questions given in the work. Return all the plots and graphs with titles. Return your Matlab codes. Youcaneitheranswerthequestionsbyusingthisformorcopytheformassuchinyour own word-processor. The report returned should look like this form regarding tasks, task numbers etc... see section Tasks. 1

2 2 Introduction to the DSP toolbox The DSP toolbox consists of MATLAB functions and provides a way to manipulate and simulate signal flow graphs, and to evaluate properties of signal flow graphs. 2.1 Howtocreateasignalflowgraph(SGF) The signal flow graph is constructed by adding operations connected to nodes, as in e.g. analog circuit simulator SPICE. Although, in MATLAB, the SFG is presented as an array. TherearefunctionstomanipulatetheSFG,sothereisnoneedtohavedeepknowledgeof theformat.aninitialsfgisobtainedbyusinganemptymatrix: sfg=[] To add an operation, the function addoperand can be used as follows: sfg = addoperand(sfg, operandname, id-number, innodes, outnodes, operanddata, operandtype) whereparametersareasfollows: sfgisthesfgtoaddtheoperandto, operandnameis the name of an operand(see Appendix for available operands), id-number is an identifyingnumberfortheoperation, innodesisoneormorenodestoconnecttotheinput(s), outnodes similarly for the output(s), operanddata is an optional data for certain operations(e.g. the coefficient for a multiplier etc...), and operandtype is used for certain operands which may have several different types(e.g. different types of quantization). More on possible operanddata and operandtype is available in the Appendix. ToseehowwecancreateanSFG,letususethesimplefilterbelow,wherewehavenumberedthenodes1to4. Eachoperandalsohasanidentifyingnumber. Note:sinceonly operands of the same type must have different identifying numbers all operands are using 1 as the identifying number. To create the corresponding SFG we can use the following in 1 3 out Z -1 4 MATLAB code: sfg = []; sfg = addoperand(sfg, in, 1, 1); sfg = addoperand(sfg, add, 1, [1 2], 3); sfg = addoperand(sfg, delay, 1, 3, 4); sfg = addoperand(sfg, mult, 1, 4, 2, 0.5); sfg = addoperand(sfg, out, 1, 3); ToobtaintheSFGinreadableformwecanusethecommand printsfgas 2

3 printsfg(sfg) which will give the output 1. in id: 1 out: 1 2. add id: 1 in: 1, 2 out: 3 3. delay id: 1 in: 3 out: 4 4. mult id: 1 in: 4 out: 2 coeff: out id: 1 in: 3 AlwaysmakesurethatthecreatedSFGisvalid,i.e.,thatnonodeshavemultipledrivers and no dangling(unconnected) nodes are included, by using the function errorlist = checknodes(sfg) ForacorrectSFGtheresult,errorlist,isempty,otherwiseadescriptionoftheerror(s)is printed at the prompt. 2.2 Simulation For the simulation, the function simulate is available for this purpose. The basic form of simulateisas output = simulate(sfg, inputvalues) where inputvalues is the sequence of samples to be used as input. Two commonly used input data are an impulse and random data(uniformly distributed ontheinterval[-1,1])whichcanbeobtainedas impulse = [1, zeros(1,n-1)]; random = 2*rand(1,N)-1; More complex way to use simulate is as: [outputs, outputids, registers, registerids, nodes,nodeids] = simulate(sfg, inputvalues, inputids, initialregister, registerids, wordlength) where it has support for multiple inputs and outputs, initializing registers, and tracking values in registers and nodes. General description of input parameters: If the wordlength input value is specified, the simulator will use finite wordlengths for the nodes. The wordlength input can be either [WiWf],whereWidenotesthenumberofintegerbitsandWffractionalbits,orWf,where itisassumedthatwiis1.notethat initialregisterand registeridscanbesetto anemptyvector[]iftheyarenotneeded,butyouwanttosetthewordlength. 3

4 General description of output parameters: For multiple outputs, the outputs variable containsa2darray,whereeachrowcontainstheoutputvaluesoftheoutputwithidentifying number given at the same row of outputids. Similarly, registers-registerids and nodes-nodeids have the same structure. To obtain the values of a certain output/register/node the function getnodevalues can be used as values = getnodevalues(outputs, outputids, outputidentifier) values = getnodevalues(registers, registerids, registeridentifier) values = getnodevalues(nodes, nodeids, nodenumber) Inthisworkweuseonlyasingleinputandoutput. The functions impulseresponse and stepresponse are available for computing the impulse response and step response, respectively. They are used as output = impulseresponse(sfg, numberofsamples) where numberofsamples is the number of samples of the impulse response to be computed. 2.3 SFGmodifications For scaling and other modification purposes it is possible to insert a single input-single output operation at a node. This is done with insertoperand as sfg = insertoperand(sfg, operandname, idnumber, node, operanddata, operandtype) ToinsertamultiplierattheinputofourpreviousSFGwewouldtype sfg = insertoperand(sfg, mult, 2, 1) Notethat insertoperandaddsanewnodetothesfgfortheinputofthenewoperand. IfyouneedtochangetheSFG,youcanusethefunctions removeoperand(oppositeto addoperand) or changeoperand, which are used as sfg = removeoperand(sfg, operandname, idnumber) sfg = changeoperand(sfg, operandname, idnumber, operanddata, operandtype) 2.4 The precedence form To see the precedence relations between operands there are two functions available, printprecedence and plotprecedence. They return an SFG sorted in precedence order. 4

5 Applying the printprecedence to our SFG example gives the following output: 1.1 in id: 1 out: mult id: 1 in: 4 out: 2 coeff: add id: 1 in: 1, 2 out: out id: 1 in: delay id: 1 in: 3 out: 4 3 Tasks This work uses the DSP toolbox commands and additionally some MATLAB s own commands e.g. freqz, etc... Write all commands in a textfile using MATLAB s own editor using format filename.m andrunthatfile. 1.StartMATLABandaddthepathtotheDSPtoolboxinMATLAB.Thiscanbedone using addpath /share/sgncourses/sgn-1650/dsptoolbox Tosavethepathforlaterlaborationsyoucanuse savepath 2. Simulate and plot the impulse response of the example in Chapter 2 Introduction to the DSP toolbox above. Also plot the frequency response. Attach it in your report. 3.Givetheexactvalueofallsamplesintheimpulseresponsethatarelargerthan Whatisasignalflowgraph? 5.Whatisaprecedencegraph? 5

6 3.1 Simulations Inthistaskwesimulateandscaleadirect-formIIIIRfilters A direct-form IIR filter 1.Considerthefollowingthird-orderdirectformIIIIRfilter,whereb 1 = , b 2 = , b 3 = , a 0 = , a 1 = ,a 2 = anda 3 = in a 0 out Z -1 a 1 b 1 b 2 Z -1 a 2 b 3 Z -1 a 3 2.Numberthenodesandoperationsandcreatethesignalflowgraph.Attachittoyour report. a) Print and plot the precedence graph. b) Simulate the filter using an impulse. Plot the impulse response. c) What kind of filter is this(lowpass, highpass etc...)? 3. How large is the stopband attenuation? 4. Plot the discrete values of all interesting nodes. 5. Identify nodes that are possibly badly scaled under the worst-case(safe) scaling criteria,i.e.,criticalnodeswherethesumoftheabsolutevaluesofthenodesaregreater than one. 6

7 6. Scale all the critical nodes using the worst-case scaling coefficients. Indicate where you introduce scaling. 7.Simulatethefilteragain. Arethenodescorrectlyscaled? Whatisthesumofthe absolute values of the nodes in the critical nodes? 8.a)Simulatetheoriginalandscaledfiltersusingthesamerandomdataforboth.Use first 1 integer bit and 8 fractional bits and compare the discrete outputs by plotting them in the same figure with different markers. Comments? b)simulatetheoriginalandscaledfiltersusingthesamerandomdataforboth.use 1 integer and 15 fractional bits. Compare the discrete outputs by plotting them in the same figure with different markers. Comments? c) Compare also quantized simulations with each other. Comments? 9. How does scaling affect the magnitude response? A direct-form IIR filter as a cascade of a first-order block and a second-order block 1.CascadetheIIRfilterintheprevioustaskasafirst-orderblockandasecond-order block. 2. Give the coefficients of the first order section. 7

8 3. Give the coefficients of the second-order section. 4. Draw the cascaded structure. Nowdoasforthestructureinsection Number the nodes and operations and create the signal flow graph. a) Print and plot the precedence graph. b) Simulate the filter using an impulse. c) Plot the impulse response. Check signs on your filter poles. 6. How large is the stopband attenuation? 7. Plot the discrete values of all interesting nodes. 8. Identify nodes that are possibly badly scaled under the worst-case scaling criteria, i.e.,criticalnodeswherethesumoftheabsolutevaluesofthenodesaregreaterthan one. 8

9 9. Scale all critical nodes using worst-case scaling coefficients. Indicate where you introduce scaling. 10.Simulatethefilteragain.Arethenodescorrectlyscaled?Whatisthesumofabsolute node values in the critical nodes? 11.Simulatetheoriginalandscaledfiltersusingthesamerandomdataforboth.Use1 integer bit and 15 fractional bits. Compare the discrete outputs by plotting them in the same figure with different markers. Comments? 12. How does scaling affect the magnitude response? Comparisons Now we compare the structures in and Whatisthepassbandedgeforthebothstructures,doesitdiffer? 2. How large is the stopband attenuation? Does it differ? 3.Comparewithallthepointsabove.Doesthestructuresdifferinanyways?Ifitdoes, explain why? 9

10 A DSP TOOLBOX Functions The following operations are available and can be used as an input to addoperand: in InputofSFG,oneoutputnode. out Output of SFG, one input node. add Addition of two inputs. sub Subtraction of the second input from the first input. mult Multiplication with coefficient operanddata. delay Register delaying the signal one sample. quant Quantization to operanddata fractional bits. Uses operandtype: truncation, rounding, or magnitudetruncation. overflow Overflow detection. Uses operandtype: twosc or saturation. invert Multiplication by 1. 10

LABORATION 1 TSTE87 ASIC for DSP

LABORATION 1 TSTE87 ASIC for DSP Name:... Personal ID:... Date:... Passed (signature):... LABORAION 1 SE87 ASIC for DSP 2008 Oscar Gustafsson, Kenny Johansson Goals o get an overview of the DSP toolbox for MALAB. Use the DSP toolbox to