KAUNAS UNIVERSITY OF TECHNOLOGY FACULTY OF ELECTRICAL AND ELECTRONICS ENGINEERING DEPARTMENT OF ELECTRONICS ENGINEERING Laboratory work No.

1 T121M501 Digital Signal Processing Laboratory work report Completed by Chandana Ravikumar Accepted by lekt . Andrius Solosenko KAUNAS, 2018 1. Laboratory Work Aim Learn basics of digital signal processing (DSP) using Matlab variable initialization, signal modeling and displaying, basic signal processing, writing to and reading data from the data storage media (e.g. hard disc drive). 2.

Useful MATLAB functions Some useful functions – help function name shows functionality of a certain Matlab function, operator, etc. (e.g., help plot) clear close all clc for..

.end if, else if, else…

end length() save() load() figure() plot(x, y) subplot(m, n, p) title() xlabel() ylabel() legend() hold on/off on allows multiple plots in the same figure. In order to stop, off command is applied xlimxmin xmax x-axis limits ylimymin ymax y-axis limits 3. Laboratory Assignments Preparing Matlab Start Matlab program by double-clicking the icon. Select File-New-Script Name and save the script file in a folder (note that the name can only contain alphabets, numbers and underscore). Write commands clear close all clc before any other. When the new program is run, these commands will automatically delete old variables, close all figures and clean command window.

Basic signal modeling Using for loop MATLAB is started and the commands clear close all clc are written first to close all figures, delete existing variables and clean command window. The amplitude A, signal frequency f and sampling frequency fs are initialized to the given values. The user is prompted to give a value for phase fi in degrees.

Time t is initialized to an array containing values 0 to 1 in steps of 1/fs. Then the for loop iterating over the length of t is used to calculate right-hand side of equation (1) and is assigned to y1. Thus a sine function can be computed using a for loop. The y1 is plotted against x using plot and the output is shown in Fig.1. Using vector multiplication In the same program, the right-hand side of the equation (1) is assigned to another variable y2.

This new statement is a vector multiplication as the sine function in the equation is a vector. The computed y2 is plotted against x and the output is shown in Fig.1. Refer code snippet (1). c ) Write code to detect positive peaks in the resulting waveform (write your own code, do not use standard Matlab peak detection functions) Matlab routines for locating and measuring the peaks (or valleys) in noisy ti me -series data sets .

It detects peaks by looking f or downward zero -crossi ngs (or upward zer o – crossings for valleys) in the HYPERLINK https//terpconnect.umd.edu/toh/spectrum/Differentiation.html smoothed first HYPERLINK https//terpconnect.umd.edu/toh/spectrum/Differentiation.html derivati ve then deter mines the position, height, and width of each peak by HYPERLINK https//terpconnect.umd.

edu/toh/spectrum/CurveFitting.html least – HYPERLINK https//terpconnect.umd.edu/toh/spectrum/CurveFitting.html squares cur ve -fitting of the raw data near t he detected peaks . (This is useful pri marily for signals that have several data points in each peak, not for spi kes that have onl y one or two points) .

There are both command -line and interactive versions A set of HYPERLINK https//terpconnect.umd.edu/toh/spectrum/PeakFindingandMeasurement.htmfindpeaks command -line functions for Matlab and HYPERLINK https//terpconnect.

umd.edu/toh/spectrum/SignalArithmetic.htmlOctave Octave , for finding peaks in signals and measuring their positions, heights, widths, and areas by least -squares curve -fitting, especially useful as modules to use in our own custom scrip ts and functions to automate data processing. These are listed here, each linked to its description HYPERLINK https//terpconnect.umd.edu/toh/spectrum/PeakFindingandMeasurement.

htmfindpeaksx findpeaksx, HYPERLINK https//terpconnect.umd.edu/toh/spectrum/PeakFindingandMeasurement.htmfindpeaks findpeaksG, HYPERLINK https//terpconnect.umd.

edu/toh/spectrum/PeakFindingandMeasurement.htmValleys findvalleys, HYPERLINK https//terpconnect.umd.edu/toh/spectrum/PeakFindingandMeasurement.htmfindpeaksL findpeaksL, HYPERLINK https//terpconnect.umd.edu/toh/spectrum/Integration.htmlmeasurepeaks measurepeaks , HYPERLINK https//terpconnect.

umd.edu/toh/spectrum/PeakFindingandMeasurement.htmfindpeaksG2d findpeaksG2d , findpeaksb,findpeaksb3, HYPERLINK https//terpconnect.

umd.edu/toh/spectrum/PeakFindingandMeasurement.htmfindpeaksplot findpeaksplot , HYPERLINK https//terpconnect.umd.edu/toh/spectrum/PeakFindingandMeasurement.htmfindpeaksplot findpeaksplotL, HYPERLINK https//terpconnect.umd.edu/toh/spectrum/PeakFindingandMeasurement.

htmpeakstats peakstats, HYPERLINK https//terpconnect.umd.edu/toh/spectrum/findpeaksE.m findpeaksE, HYPERLINK https//terpconnect.umd.edu/toh/spectrum/PeakFindingandMeasurement.htmPeakStartAndEnd findpeaksGSS, findpeaksLSS, HYPERLINK https//terpconnect.umd.

edu/toh/spectrum/PeakFindingandMeasurement.htmtriangle findpeaksT , HYPERLINK https//terpconnect.umd.edu/toh/spectrum/PeakFindingandMeasurement.htmfindpeaksfit findpeaksfit , HYPERLINK https//terpconnect.umd.edu/toh/spectrum/PeakFindingandMeasurement.

htmautofindpeaks autofindpeaks and HYPERLINK https//terpconnect.umd.edu/toh/spectrum/PeakFindingandMeasurement.htmautopeaks autopeaks . These can be used as components in creating your own custom scripts and functions . Dont confuse with the HYPERLINK .

./../../Tom/Dropbox/SPECTRUM/PeakFindingandMeasurement.htm23findpeaks_vs_findpeaksfi ndpeaks function i n HYPERLINK .

./../../Tom/Dropbox/SPECTRUM/PeakFindingandMeasurement.

htm23findpeaks_vs_findpeaksthe Signal Processing Toolbox . a Matlab -onl y interactive HYPERLINK https//terpconnect.umd.

edu/toh/spectrum/PeakFindingandMeasurement.htmipeak keypress – HYPERLINK https//terpconnect.umd.edu/toh/spectrum/PeakFindingandMeasurement.

htmipeak operated function HYPERLINK http//terpconnect.umd.edu/toh/spectrum/ipeak.

m iPeak , illustrated on t he right displaying si gnals from a variety of sources . Using iPeak, we can pan and zoom, adj ust each of the peak detection parameters individuall y and int eractivel y to opti mi ze peak detection and measurement , and much more . Shown in fi gure fig 3 . A set of fast customi zable functions for locating and measuring the peaks in noisy time -series si gnals . Adj ustable parameter s allow discri mination of real signal peaks from noise and background . Deter mines t he position, hei ght, and width of each peak by least -squares cur ve -fi tting. It can find and count over 10,000 peaks per second, and find and measure 1800 peaks per second, in very large si gnals .

Incl udes two interactive versions, one with mouse -controlled sliders and one with keyboar d control, for adj u sting the peak finding criter ia in real -ti me . Fig 3 positive peak detection of a sin wave without using the standard peak detection function in matlab . SHAPE MERGEFORMAT Fig.1 Sine using for and vector multiplication. Generate and display 10 s square waveform (meander) by performing summation of multiple sine (or cosine) waveforms with different frequencies (other harmonics should be the odd multiples of the waveform with main frequency f and amplitude A (2n – 1)f and (2n – 1)A, where n is no. of the harmonic). In signal processing, harmonic distortion occurs when a sine wave is sent through a memoryless nonlinear system.

Harmonic distortion adds overtones that are whole number multiples of a sound waves frequencies. The type of harmonics produced depends on the response function. This generation of square wave using the summation of odd sine or cosine harmonics is known as Gibbs Phenomenon. The MATLAB program is started with clear close all clc commands. The user is prompted to give the number of odd harmonics to be employed in the generation of the square wave and is assigned to n. The parameters of the sine function are initialized.

Variable y1 is used to compute and display square wave using only 5 harmonics. Output y1 is plotted against x. Then using a for loop, square wave using n harmonics is computed and assigned to y2. Output y2 is plotted against x. As shown in Fig.2, the influence of number of odd harmonics is proportional to the shape of the square wave. The more harmonics used, the better looking the square wave is.

Refer code snippet (2). Calculate spectrum of the resulting square waveform(s) and plot it. Use the following code to calculate spectrum SHAPE MERGEFORMAT Fig.2 Square wave generation using odd sine harmonics.

L length(SquareWaveform) Y fft(SquareWaveform) P2 abs(Y/L) P1 P2(1L/21) P1(2end-1) 2P1(2end-1) f Fs(0(L/2))/L The frequency -domai n representation of a signal reveals i mportant si gnal characteristics that are difficult to anal yze in the ti me domain . Spectral analysis lets us characterize the frequency content of a signal . Perfor m real -ti me spectral analysis of a dynamic signal using the HYPERLINK https//www.mathworks.com/help/dsp/ref/dsp.spectrumanalyzer-system-object.

html dsp . Spectrum Anal yzer System obj ect in MATLA B and the HYPERLINK https//www.mathworks.com/help/dsp/ref/spectrumanalyzer.html Spectrum Anal yze r bl ock in Si mulin k . The spectrum anal yzer uses the We lchs method of averaging modified periodogram or the filter bank method to compute the spectral dat a . Both these methods are FFT -based spectr al estimation methods that make no assumptions about the input data and can be used with any kind of si gnal .

For m ore infor mation on the algorithm the spectr um anal yzer uses, see HYPERLINK https//www.mathworks.com/help/dsp/ug/spectral-analysis.html Spectral Anal ysis . In addition to viewing the spectrum, you can also view the spectrogram of the si gnal in the spe ctrum anal yzer . If we want to acquire this data for post processing in MATLAB, call HYPERLINK https//www.

mathworks.com/help/dsp/ref/dsp.spectrumanalyzer.isnewdataready.html isNewDataReady and HYPERLINK https//www.mathworks.com/help/dsp/ref/dsp.spectrumanalyzer.

getspectrumdata.html getSpectrumData obj ect functions on the spect rum anal yzer obj ect . By calling these functions in the streaming loop, you can acquire the entire spectral data . In Si mulink, to acquire t he spectral data, creat e a HYPERLINK https//www.mathworks.com/help/dsp/ref/spbscopes.spectrumanalyzerconfiguration.html Spectrum Anal yzer Confi guration obj ect and run the HYPERLINK https//www.

mathworks.com/help/dsp/ref/dsp.spectrumanalyzer.getspectrumdata.html getSpectr umData function on this obj ect . We should Note that in Si mulink, we can acquire only the l ast frame of the spectr al data shown on the spectrum anal yzer .

Alternately, we can use the HYPERLINK https//www.mathworks.com/help/dsp/ref/dsp.spectrumestimator-system-object.html dsp . SpectrumEsti mator System obj ect and HYPERLINK https//www.mathworks.

com/help/dsp/ref/spectrumestimator.html Spectrum Esti mato r block to compute the power spectrum and acquire the spectral data for further processing . To view the spectral data computed by the spectrum esti mator , use an array plot . Fig 4 spectrum of a square waveform Generate and display square wave by using transition from low to high or vice versa using for loop and if else statements In this program, conditional statements are used to generate a square wave that has transitions from high to low. First, the user is prompted to enter the frequency of the square wave to be generated and is assigned to f. Using for loop f cycles of the square wave are generated. The counter c is reset to 0 after every cycle. The loop is iterated over the length of x times to generate square wave of given frequency.

The variable y contains the values of the square and is plotted against x to display the square wave. The output is shown in Fig.4. Refer code snippet (3).

SHAPE MERGEFORMAT Fig.5 Square wave using loop and conditional statements. 2 IV. Gradually decrease the sampling frequency of previously generated sine wave, plot few examples of those waveforms at different sampling frequencies in the same figure and write your observations. The parameters of the sine are initialized to the given values. Four variables y1, y2, y3, y4 are computed with descending sampling frequencies. The sampling frequency is halved each time.

Each variable is plotted against t using stem() and two cycles are displayed for better understanding. It is clear from Fig.4 that, as the sampling rate goes down the reconstruction of the signal is hard to achieve correctly because of less number of samples obtained. Refer code snippet (4).

SHAPE MERGEFORMAT Fig.6 Signals with descending sampling frequencies. ADDITIONAL TASK Generate cosine waveform (sampling frequency Fs 5000 Hz, amplitude A (10 x student no. in the list) V, signal frequency f (10 x student no. in the list) Hz) and perform the following tasks a) Clip the positive half-periods by 1 / (student no. in the list 1) of the amplitude A.

Save clipped values in .mat file. Load .

mat file containing clipped values of the cosine waveform and plot them This MATLAB program is used to generate and display a chopped cosine wave. The parameters of the cosine function are initialized to the given values. The sampling frequency is 5000 Hz. Variable y is assigned with the resulting value of the cosine after computation. Loop and conditional statements are used to chop the positive half cycles of the wave by 2/3 of its amplitude. The chopped values are saved to a .mat file using save() and it can be loaded using load() command. Chopped cosine is then displayed, shown in Fig.

5. Refer code snippet(5). SHAPE MERGEFORMAT Fig.7 chopped cosine wave. 2.

Generate an exponentially damped sine/cosinewaveform Note that the chopped values from the previous program is loaded here and can be seen in the workspace. The damping of the cosine can be clearly seen in the Fig.6. Refer code snippet (6). Conclusion The Laboratory work 1 introduced MATLAB basics and signal modeling.

The tasks contained generation and manipulation of discrete time sine and cosine waves. The influence of sampling frequency on discrete time signals was understood. The Gibbs effect in signal processing was explored i.e. summation of odd harmonics of a sinusoid resulting in a square wave. Generation of the Square wave without using the built-in function was successful.

Generation of damped cosine waves with different phase shift was also completed successfully. The decay constant and frequency of the wave was the factors in damping. A cosine wave chopped by 2/3rd of its amplitude was generated. Many basic MATLAB functions like plotting continuous and discrete signals, signal modeling, read and write from memory were successfully performed. SHAPE MERGEFORMAT Fig.

8 Damped cosine waves with a different phase. Appendix Code Snippet (1) clear close all clc Generate and display discrete sine wave A 28 Amplitude f 50 Signal frequency fs 8000 Sampling frequency t 01/fs1-1/fs fi input(Enter the phase shift – ) Using for loop for i 1length(t) y1(i)Asin(2pifi/fsfi) end using vector multiplication y2 Asin(2piftfi) figure subplot(2,1,1) stem(t,y1) title(Sine wave with 50Hz frequency and 20V amplitude using for,fontsize,18) xlabel(Time in seconds —,fontsize,18) ylabel(Amplitude in Volts — ,fontsize,18) xlim(0 0.1) subplot(2,1,2) stem(t,y2) title(Sine wave with 50Hz frequency and 20V amplitude using vector multiplication,fontsize,18) xlabel(Time in seconds —,fontsize,18) ylabel(Amplitude in Volts — ,fontsize,18) xlim(0 0.1) Code snippet (2) clear close all clc generation of square wave with summation of sine promptEnter the number of harmonics n – ninput(prompt) j1 A20 f50 Fs8000 fi0 t01/Fs0.1 x2piftfi figure(1) subplot(2,1,1) y1 A(sin(x) sin(3x)/3 sin(5x)/5 sin(7x)/7 sin(9x)/9 ) summation of 5 harmonics plot(t,y1,color,black) title(Square wave using 5 harmonics,color,blue,FontSize,18) xlabel( t —,fontsize,18) ylabel( A —,fontsize,18) y2 sin(x) while j(n-1) k2j1 while is used to generate summation of n harmonics y2 y2 (sin(kx)/k) jj1 end y2Ay2 subplot(2,1,2) plot(t,y2,color,red) title(Square wave using ,num2str(n), harmonics,color,b,FontSize,18) xlabel( t —,fontsize,18) ylabel( A —,fontsize,18) Code snippet (3) clear close all clc f input(Enter the frequency of the square wave – ) x 00.

00001f time axis x y zeros(1,length(x)) generate square wave cycle of frequency f k 0 a 0.5 c 1 for i1length(x) if ka y(i) 1 c c1 else y(i) -1 c c1 end k k0.00001 if c 100001 a a1 c 1 counter c is used to increment…. ..

..checking point to flip value of.

… ….

y from high to low or vice versa end end x x/f rescaling x plot(x,y,color,red) title(Square wave of frequency ,num2str(f), Hz using for and if…else,color,blue,fontsize,18) xlabel(time in s —,fontsize,18) ylabel(amplitude in v —,fontsize,18) Code snippet (4) clear close all clc Generate and display discrete sine wave 6 A 20 Amplitude f 50 Signal frequency fs 2000 Sampling frequency t 01/fs0.

04 y1 Asin(2pift) figure (1) subplot(4,1,1) stem(t,y1) title(signal with fs ,num2str(fs),color,red,fontsize,18) xlabel(Time in seconds —,fontsize,12) ylabel(Amplitude in Volts —,fontsize,12) Decreasing Fs by half fs fs/2 fs1000 t 01/fs0.04 y2 Asin(2pift) figure(1) subplot(4,1,2) stem(t,y2) title(signal with fs ,num2str(fs),color,red,fontsize,18) xlabel(Time in seconds —,fontsize,12) ylabel(Amplitude in Volts —,fontsize,12) Decreasing Fs by half again fs fs/2 fs500 t 01/fs0.04 y3 Asin(2pift) figure(1) subplot(4,1,3) stem(t,y3) Decreasing Fs by half again fs fs/5 fs100 t 01/fs0.

04 y4 Asin(2pift) figure(1) subplot(4,1,4) stem(t,y4) title(signal with fs ,num2str(fs),color,red,fontsize,18) xlabel(Time in seconds —,fontsize,12) ylabel(Amplitude in Volts —,fontsize,12) Code snippet (5) clear close all clc operations on cosine wave. A50 Amplitude f30 frequency Fs5000 sampling frequency t01/Fs1 k1 yAcos(2pift) 7 for i1length(t) if y(i)(A/3) chop y if greater than A/3 c(k)y(i) store chopped values in c y(i)(A/3) kk1 end end save chop.mat c save c in chop.mat file figure(1) stem(t,y) xlabel(time in seconds —,fontsize,18) ylabel(amplitude in volts —,fontsize,18) title(Chopped Cosine Wave with 50Hz frequency and 50V amplitude,color,r,fontsize,18) xlim(0 0.

1) Code snippet (6) clear close all clc load chop.mat load chop.mat c A 58 a 0.7 decay constant f 1 T 1/f fi1 input(Enter the phase shift for the first wave in degrees – ) fi2 input(Enter the phase shift for the second wave in degrees – ) t 00.00110T y1 A.(exp(-at).

cos(2piftfi1)) damped sine wave equation plot(t,y1) hold on y2 A.(exp(-at).cos(2piftfi2)) plot(t,y2,color,k) xlabel( time in seconds —-,fontsize,18) ylabel( amplitude in volts —-,fontsize,18) title(Damped cosine waves,color,red,fontsize,18) legend(phase shift ,num2str(fi1), degrees,phase shift ,num2str(fi2), degrees) hold off WFzoRWGPgi4eb2ayy.piyoAN4EQMDo-mvprHOIeAFvvB9ogMDtkQkDTT6QTwRZ.jXXzhksWMpFPBKPU(BBF9buBQXz/[email protected])5HMwu12JW_fkD3_sh4eVl5V969y4CeHHM /UICKW)afFzoRDD6H ZPqhaMDDTG hX/[email protected],oC6aVGJXGsGCDGZK.

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