DSP Practical

1) Generate the basic functions like unit impulse, unit step, ramp, exp, sin, cos etc.

2) Generate the signal given bellow, plot the magnitude and phase response. Also plot the frequency content of it.

a. sn = 3.5 * sin(2 * pi * (0.15) * n) + sin(2 * pi * (0.4) * n);b. sn = 3 + 5.657 * cos(2*pi*(0.1)*n)

where n = 0,1,2…..256

3) Compute the z-transform of the following using partial fraction method.

a. X(z) = z-1/pow((z – 0.7071),2)b. X(z) = pow(z,4) - 1/pow(z,4) + 1c. X(z) = pow(z,3) - pow(z,2) + z – 1/ pow((z + 0.9),3)

4) Compute the N-point DFT of the following, vary the value of N and visualize the effect. Try N = 8,16,24,64,128,256 etc

a. s(n) = 3 * pow(e,-0.1 * n)b. s(n) = 2 * cos(2 * pi * (0.15) * n) + sin(2 * pi * (0.4) * n)c. s(n) = 4 * sin(4 * pi * (0.4) * n) + sin(2 * pi * (0.2) * n)

5) Compute 4-point DFT using Twiddle matrix, except the input sequence x(n) from the user and calculate the output sequence y(n). Compute N-point DFT without using Twiddle matrix. Except N and input sequence x(n) from the user and calculate the output sequence y(n).

6) Write a program for Linear Convolution of the sequence x = [1 1 1 1] and h = [1 2 3 4 5 6 7 8]. Except the sequences x and h from the user. Calculate the output sequence. Plot the all three sequences.

7) Write a program for Circular convolution of the sequence x = [1 2 4] and h = [1 2]. Except the sequences x and h from the user. Calculate the output sequence. Plot the all three sequences.

8) Design a N-point FIR low-pass filter with cutoff frequency 0.2 * pi using rectangular, hamming, Blackman, hanning, Kaiser windows. Where N may vary from 16 to 256. Try N = 1024. Also try to vary the cutoff frequency and see the effect.Plot its magnitude and phase response.

9) Design a N-point high-pass filter using above windows. Where N may vary from 16 to 256. Try N = 1024. Also try to vary the cutoff frequency and see the effect.Plot its magnitude and phase response.

10) Use 2.a, 4.b, 4.c as input to the above design filters and find the output of the filter. Plot the input and output.

11) Design a Band-Pass and Band-Stop FIR filter using Chebyshev window to meet the following specification.

Passband frequency:- 900 – 1100 HzPassband ripple: - < 0.87 dBStopband attenuation: - > 30 dBSampling frequency: - 15 kHzStopband frequency: - 4500 HzPlot the filter spectrum. Magnitude and phase response.

12) Design ButtorWorth Lowpass, Highpass, Bandpass and BandStop digital IIR filters. Except passband ripple, stopband ripple, passband frequency, stopband frequency and sampling frequency from the user. Plot the magnitude and phase response of the filters.