Program Sheet for DSP Lab (EC 5102)

1. Write a function to generate a sinusoidal wave for any given frequency, amplitude and duration.
2. Write a program to compute correlation between a signal x(n) with its noisy version [x(n) + w(n)] where w(n) = random noise without using command(using equation) and compare the output with that corr/ corrcoef command.
3. Write a program to use convolution program to get correlation between two sequences, a signal x(n) with its noisy version [x(n) + w(n)] where w(n) = random noise; and compare the result with that of correlation command.
4. Write a program to use correlation program to get convolution between two sequences, a signal x(n) with its noisy version [x(n) + w(n)] where w(n) = random noise; and compare the result with that of conv command.
5. Write a program to check whether the following system is an LTI system:Numerator = [2.2403 2.4908 2.2403];Denominator = [1.0000 -0.4000 0.7500];
6. For a signal x(n) and its noisy version y(n) = αx(n)+w(n); where α=attenuation and w(n)=random noise, write a program to compute the correlated signal & its correlation coefficient.
7. For a signal x(n) and its noisy version y(n) = αx(n)+w(n); where α=attenuation and w(n)=random noise, write a program to compute the correlation coefficient for different values of α.
8. Write a program to generate the magnitude and phase response for a LTI system: for ω varying from 0 to π: h1(n)=1+2exp(-jω)+exp(-j2ω); h2(n)=1+0.5exp(-jω)+0.25exp(-j2ω);
9. For an FIR filter with b = [-6.76195 13.456335 -6.76195]; with initial condition zero filter two sinusoids of frequencies 200 Hz and 4000Hz and plot the different outputs for the same system in a single figure.
10. For an FIR filter with b = [-6.76195 13.456335 -6.76195]; with initial condition zero filter the sum of two sinusoids of frequencies 200 Hz and 3333Hz and plot the output, and the two inputs in the same figure using different legend.
11. For an IIR filter b=[2.2403 2.4908 2.2403];a=[1 -0.4 0.75]; with initial condition zero filter the sum of two sinusoids of frequencies 200 Hz and 3333Hz and plot the output, and the two inputs in the same figure using different legend.
12. For an IIR filter b=[2.2403 2.4908 2.2403];a=[1 -0.4 0.75]; with initial condition zero filter two sinusoids of frequencies 200 Hz and 4000Hz and plot the different outputs for the same system in a single figure.
13. Write a program to compute IDFT as per the equation and compare its output with that got by using the ifft command for given sequence x=[1 2 3 4].
14. Prove the linearity property of Discrete Fourier Transform and plot the error for sequences x1= [1 2 3 4]; x2= [1 2 1 2].
15. Write a program and prove that multiplication in frequency domain is { =circular convolution} in time domain averaged by the number N.
16. Design Low pass IIR Chebyshev Type-I and Type-II filters of 2KHz cut off frequency with sampling rate 10 KHz and same pass band and stop band ripples of 1 dB and 60 dB respectively and compare the magnitude and phase responses.
17. Design Low pass IIR Chebyshev Type-I and Type-II filters of 2KHz cut off frequency with same pass band and stop band ripples of 1 dB and 60 dB respectively and compute the response difference when the same random signal is filtered by both. (take any relevant sampling frequency)
18. Design High pass IIR Elliptic Type and Butterworth Type filters of 2KHz cut off frequency with sampling rate 10 KHz and same pass band and stop band ripples of 1 dB and 60 dB respectively and compare the magnitude and phase responses. (take any relevant sampling frequency)
19. Design High pass IIR Elliptic Type and Butterworth Type filters of 2KHz cut off frequency with same pass band and stop band ripples of 1 dB and 60 dB respectively and compute the response difference when the same random signal is filtered by both. (take any relevant sampling frequency)
20. Design a band pass IIR Chebyshev Type-I filter to pass the band width 3KHz to 4KHz with transition band of 500Hz. The pass band and stop band ripples are 0.5dB and 70dB.(take any relevant sampling frequency)
21. Design a band stop IIR Chebyshev Type-II filter to stop the band width 3KHz to 4KHz with transition band of 500Hz. The pass band and stop band ripples are 0.5dB and 70dB. (take any relevant sampling frequency)
22. Design a band pass IIR Butterworth Type filter to pass the band width 3KHz to 4KHz with transition band of 500Hz. Using a high pass and a low pass IIR Butterworth Type filters in cascade. And use a signal x(n) containing frequencies 2KHz, 3.5KHz and 6KHz to verify the result. (take any relevant sampling frequency and attenuation)
23. Design a High pass IIR Elliptic Type filter of cutoff frequency 3KHz and pass signal x(n) containing 2KHz and 5KHz frequencies to get output y(n) and justify your design in frequency domain. (take any relevant sampling frequency and attenuation)
24. Design a low pass IIR Elliptic Type filter for pass band and stop band deviation of 0.0559 and 0.0001 respectively; stop band and pass band frequencies 4KHz and 3.2KHz respectively and the sampling frequency is 20 KHz.
25. Design a low pass IIR Elliptic Type filter for pass band and stop band deviation of 0.0559 and 0.0001 respectively; cutoff frequency of 3KHz; order=30 and the sampling frequency is 20 KHz.
26. Design an FIR equiripple Low pass filter of pass band and stop band deviation of 0.0559 and 0.0001 respectively; pass band, stop band and sampling frequencies of 2KHz, 3KHz and 15KHz respectively and pass a signal x(n) containing 1.5KHz and 4KHz and get the output in both time and frequency domain.
27. Design an FIR equiripple Band pass filter of pass band and stop band deviation of 0.5dB and 80dB respectively; pass bands, stop bands and sampling frequencies of 3KHz-4KHz, 2.5KHz, 4.5KHz and 15KHz respectively.
28. Design an FIR equiripple High pass filter of pass band and stop band deviation of 0.0559 and 0.0001 respectively; pass band, stop band and sampling frequencies of 2KHz, 3KHz and 15KHz respectively and compare its response with an IIR Butterworth type filter of same characteristics.
29. Design a Hamming window based Low pass FIR filter of order 35; with cutoff frequency of 4KHz for sampling at 20KHz and plot the response.
30. Design a Kaiser window based Band pass FIR filter of order 50; with pass band frequency of 4KHz-5KHz for sampling at 20KHz and plot the response.
31. Write a program to generate all possible available inbuilt windows (at least 10) of MATLAB® for order 70 in a single figure and mark with proper legend.
32. Write a program to generate 9 different mesh-grid 3D windows in a single figure with proper legend and demarcation in a single figure window.
33. Design an FIR lowpass filter & an IIR lowpass filter for sampling frequency 4000Hz and pass and stop bands 800Hz & 1000Hz; & pass and stop band attenuations 0.5dB and 70dB. Then pass any signal x(n) through both and plot the difference between the outputs yFIR(n) and yIIR(n)
34. Design an analog Butterworth filter of order 4. Then get both the s (Laplace) domain and z domain response of the same filter.
35. Design a Parks-McClellan optimal filter for stopping the power line noise (48-52Hz) signal from disturbing the ECG signal which is being sampled at 500Hz.
36. Generate a sinusoidal signal containing frequencies 151Hz; 1500Hz and 15Hz and plot its frequency domain representation. In the frequency domain remove the frequencies below 1KHz and perform the IDFT to get back the sinusoidal wave.
37. Design a Low pass IIR filter of order 20 and another of order 18 for the same cut off frequency 0.5 with pass band & stop band being 1dB and 80dB. Then pass signal x(n) and plot the differences in their responses.
38. Design a High pass IIR filter of order 20 and another of order 18 for the same cut off frequency 0.5 with pass band & stop band being 1dB and 80dB. Then pass a sinusoidal signal x(n) and plot the differences in their responses.
39. Design two Band pass IIR filters of orders 18 & 20 for the same cut off frequency [0.4 0.6] with pass & stop attenuations 1dB and 80dB. Pass a sinusoidal signal x(n) (in pass band)and plot the differences in their responses.
40. Design two Band pass IIR filters of orders 18 & 20 for the same cut off frequency [0.4 0.6] with pass & stop attenuations 1dB and 80dB. Pass a sinusoidal signal x(n) (in stop band)and plot the differences in their responses.
41. Design two Band stop IIR filters of orders 18 & 20 for the same cut off frequency [0.4 0.6] with pass & stop attenuations 1dB and 80dB. Pass a sinusoidal signal x(n) (in stop band)and plot the differences in their responses.
42. Design a Low pass IIR Butterworth with order 15 and cutoff frequency 0.5 & pass a signal x(n) through it to get output y1(n); now making this filter more sensitive get y2(n). Plot the difference between y1(n) and y2(n).
43. Write a program to compute 8 point real DFT using 4 point DFT