Department of Electrical Engineering. Laboratory Manual Digital Signal Processing

Transcription

1 Department of Electrical Engineering Laboratory Manual Digital Signal Processing ABASYN UNIVERSITY ISLAMABAD CAMPUS Lab Instructor: Asim Ul Haq Abasyn University Islamabad Campus Digital Signal Processing Lab Manual Page

2 LAB No. 8 Multi-rate Digital Signal Processing Objective: The digital signal processing structures discussed so far belong to the class of singlerate systems as the sampling rates at the input and the output and all internal nodes are the same. There are applications where it is necessary and often convenient to have unequal rates of sampling at various parts of the system including the input and the output. In this laboratory exercise you will investigate first using MATLAB the properties of the up-sampler and the down-sampler, the two basic components of a multi-rate system. You will then investigate their use in designing more complex systems, such as interpolators and decimators, and filter banks. Basic Sampling Rate Alteration Devices The objective of this section is to investigate using MATLAB the operations of the upsampler and the down-sampler both in the time domain and in the frequency domain. Project. Input-Output Relations in the Time-Domain Program P_ can be used to study the operation of a up-sampler. Program_ Illustration of Up-Sampling by an Integer Factor close all; clear all; clc n=:5; x=sin(*pi*.*n); y=zeros(,3*length(x)); y([:3:length(y)])=x; subplot(,,) stem(n,x); subplot(,,) stem(n,y(:length(x))); Abasyn University Islamabad Campus Digital Signal Processing Lab Manual Page

3 InputSequence OutputSequence ProgramP_ Illustration of Down-Sampling by an Integer Factor close all; clear all; clc n = :49; m = :5*3; x = sin(*pi*.4*m); y = x([:3:length(x)]); subplot(,,) stem(n,x(:5));axis([ 5..]); xlabel(''); ylabel(''); subplot(,,) stem(n,y);axis([ 5..]); xlabel(''); ylabel(''); The Signal Processing Toolbox includes three M-functions which can be employed to design and implement an interpolator or a decimator. The three M-functions are decimate, interp, and resample. Each function is available with several options. In this section you will study the decimation and interpolation operation using these functions. Abasyn University Islamabad Campus Digital Signal Processing Lab Manual Page 3

4 Project. Decimator Design and Implementation Program P_3 illustrates the use of the M-function decimate in the design and implementation of a decimator with an integer-valued decimation factor M. In the option utilized in this program, decimate designs and uses a lowpass decimation filter with a stopband edge. ProgramP_3 Illustration of Decimation Process clear all; close all; clc M=input('Down-samplingfactor='); n=:99; x=sin(*pi*.43*n)+sin(*pi*.3*n); y=decimate(x,m,'fir'); subplot(,,); stem(n,x(:)); subplot(,,); m=:(/m); stem(m,y(:/m)); InputSequence OutputSequence Abasyn University Islamabad Campus Digital Signal Processing Lab Manual Page 4

5 Decimator and Interpolator Design and Implementation Project.3 Interpolator Design and Implementation Program P_4 illustrates the use of the M-function interp in the design and implementation of an interpolator with an integer-valued interpolation factor L. interp designs and uses a lowpass interpolation filter with a stopband edge satisfying Eq. (.). H(e jω L, ω ω ) = { c /L (.), π/l ω π ProgramP_4 Illustration of Interpolation Process clear all; close all; clc L=input('Up-samplingfactor='); Generate the input sequence n=:49; x=sin(*pi*.43*n)+sin(*pi*.3*n); Generate the interpolated output sequence y=interp(x,l); Plot the input and the output sequences subplot(,,); stem(n,x(:5)); subplot(,,); m=:(5*l); stem(m,y(:5*l)); InputSequence OutputSequence Abasyn University Islamabad Campus Digital Signal Processing Lab Manual Page 5

6 Project.4 Fractional-Rate Sampling Rate Alteration Program P_5 illustrates the use of the M-function resample in the design and implementation of an interpolator with a fractional-rate interpolation factor L/M. Resample designs and uses a lowpass interpolation filter with a stopband edge. Program_5 Illustration of Sampling Rate Alteration by a Ratio of Two Integers close all; clear all; clc L=input('Up-samplingfactor='); M=input('Down-samplingfactor='); n=:9; x=sin(*pi*.43*n)+sin(*pi*.3*n); y=resample(x,l,m); subplot(,,); stem(n,x(:3));axis([ 9 -..]); subplot(,,); m=:(3*l/m); stem(m,y(:3*l/m));axis([ (3*L/M) -..]); Lab Tasks. What is the angular frequency in radians of the sinusoidal sequence in Program P_? What is its length? What is the up-sampling factor L?. How is the up-sampling operation implemented in Program P_? 3. Modify Program P_ to study the operation of an up-sampler on a ramp sequence. 4. Program P_ can be used to study the operation of a down-sampler 5. What is the angular frequency in radians of the sinusoidal sequence Program P_? What is its length? What is the down-sampling factor M? 6. How is the down-sampling operation implemented in Program P_? 7. What are the frequencies of the two sinusoidal sequences forming the input sequence in Program P_3? What is the length of the input? Abasyn University Islamabad Campus Digital Signal Processing Lab Manual Page 6

7 8. What are the type and order of the decimation filter? 9. Run Program P_3 for M = 4 and comment on the results.. Change the frequencies of the two sinusoidal sequences in Program P_3 in the input signal to.45 and.9, and the length of the input to. Run the modified Program P 5 for M = 3. Comment on your results.. What are the frequencies of the two sinusoidal sequences in Program P_4 forming the input sequence? What is the length of the input? What are the type and order of the interpolation filter?. Run Program P_4 for L = and comment on the results. 3. Change the frequencies of the two sinusoidal sequences in the input signal to.45 and.9, and the length of the input to 4. Run the modified Program P_4 for L = 3. Comment on your results. 4. What are the frequencies of the two sinusoidal sequences in Program P_5 forming the input sequence? What is the length of the input? What are the type and order of the bandlimiting filter? 5. Change the frequencies of the two sinusoidal sequences in the input signal to.45 and.9, and the length of the input to 4. Run the modified Program P 7 for L = 3 and M = 5. Comment on your results. Checked By: Date: Abasyn University Islamabad Campus Digital Signal Processing Lab Manual Page 7