**DSP LAB QUESTIONS**

- Write a MATLAB program so that output signal is sampled with a rate a) greater than twice the max frequency content in the input signal and b) for equal to maximum frequency content in the input signal. Given input signal is a cos function and the spacing between the samples is 50µs and total time duration is 0.05 seconds.
- Write a MATlAB program to find the system function of the causal LTI system with input x(z)= 1+2z
^{-1}+2z^{-2}+z^{-3}and output y(z)= 1+z^{-1}+2z^{-2}+z^{-3}so plot input, output and impulse response. - Write a MATLAB program to find convolution of unit imulse function with X(z)= 1+3z
^{-1}+4z^{-2}and convoluted output length is equal to sum of two input lengths-1. - Write a MATLAB program to find the output of given system whose frequency response is Y(z)= X(z).H(z) and given x(n)= (1,2,3,4), h(n)= (1,2,3,4) and output length is equal to maximum length of x(n) and h(n).
- Write a MATLAB program to find convolution of two given sequences in time domain X
_{1}(z)= 1+2z^{-1}+3z^{-2}& X_{2}(z)= 2+z^{-1}+4z^{-2}and convoluted output length is equal to sum of two input lengths minus one. - Write a MATLAB program to find the similarities between the given sequence x(n)= Sin(2*pi*n/N) for N=4 and the time shifted version of same sequences in terms of convolution and write and verify a) Energy property b) periodicity property and draw the graph for the same.
- Write a program using MATLAB code for the received signal replected from the target is the delayed uerreon of the transmitted signal. Assume delay in two time units. Assume transmitted signal is {3, -1, 2, 1}.
- Write a MATLAB program to find the similarities between the two given sequence X
_{1}(n)= [1 3 -2 1 2 -1 4 4 2] and X_{2}(n)= [2 -1 4 1 -2 3] is its time shifted version which is shifted by two units, in terms of convolution and prove i) ϒ_{xy}[l]= ϒ_{xy}[-l] and 2) cross correlation of two sequences x(n) and y(n)= x(n-k) is having peak at the value of k. - Write a MATLAB program to find the steady state response for the given difference equation y(n)-0.8y(n-1)=x(n) and x(n)= cos(0.05*pi*n); n=0 to N-1 where N=20 and plot the respective graph.
- Write a MATLAB program to find the first 8 samples of the complete response y(n) for the difference equation y[n]= 1/3 {x[n]+x[n-1]+x[n-2]}+0.95y[n-1]-0.9025y[n-2]; n>=0 where x(n)=cos(n*pi/3)u(n) and initial conditions are y[-1]=-2, y[-2]=-3, x[-1]=1, x[-2]=1.
- Write a MATLAB program to find the impulse response of a given difference equation y(n)+0.8y(n-2)+0.6y(n-3)=x(n)+0.7x(n-1)+0.5x(n-2). Plot the graph for N=20.
- Find steady state response using MATLAB for the difference equation y(n)-0.8y(n-1)= x(n) and x(n)= Cos(wn); n=0 to N-1 where N=20.
- Write a MATLAB program to find the multiplication of two frequencies domain aperiodic signals in the domain x1=[1 1 1 1] and x2=[1 2 3 4].
- Write a MATLAB program to find the multiplication of the two frequency domain periodic signals in time domain x1=[1 1 1 1] and x2=[1 2 3 4].
- Design an FIR filter for the given order of filter is 33 and cut-off frequency is 150Hz and sampling frequency is 1KHz and having stop band attenuation 21dB. Implement the same filter with assumed sinusoidal input.
- Write a MATLAB program to design an FIR filter is 2 and cut-off frequency is 150 and sampling frequency is 1KHz and having minimum stop band attenuation 44dB, Write a MATLAB program to implement the same filter with assumed sine input.
- Design an IIR filter for the pass band edge frequency w1=800 and stop band edge frequency w2=1200. sampling frequency ws=3600, passband ripple 1dB and stopband attenuation 40dB by using butterworth filter and maps it with bilinear transform. Find and plot the magnitude and frequency response. Implement with 3 various sinusoidal input signals of your own specification.

**CCS PROGRAM:**

- Linear convolution of a given sequence.
- Circular convolution of two sequences.
- Computation of N-point DFT for given value of N.
- Impulse response of given first order or second order filter.

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