Reference no: EM132297226

Digital Signal Processing

Question 1. Realize signal processing systems described by the difference equation:
y1(n) = 1/2 [x(n) + x(n - 1)]
and y2(n) = 1/2 [x(n) - x(n - 1)] using Matlab. Assuming same input signal x(n)=sin(ωn)
for various values of ω ={0,Π/6, 3Π/2, 1.9Π/2} applied to both systems find the following:

a. Obtain stem plots of y1(n) and y2(n) in each case.

b. Critically analyze y1(n) and y2(n) in terms of type of filter, maximum gain and cut off frequency. (Hint : The system can be tested by computing frequency response of the system).

Question 2. A discrete system is characterized by the difference equation

y(n) = x(n) - x(n - 1) - 0.5 y(n - 1)

a. If the output of the system before applying the input is 0.8, calculate the first six samples system output when an input signal x(n) = [ ↑^0.5, 3, 2, 1] is applied as the input.

b. By plotting outputs, compare the output obtained in part i with that when there is no initial condition.

Question 3. Realize the system which generates the output y1(n) = 1/2[x(n) + x(-n)] and y2(n) = 1/2 [x(n) - x(-n)] using matlab. By generating signals x1(n)=sin(ωn) and x2(n)=cos(ωn) for various values of ω ={0,Π/6, ,3Π/2, 1.9Π/2} obtain:

a. Output y1(n) and y2(n).

b. Critically analyze the system outputs y1(n) and y2(n) and find out the type of filter obtained.

Question 4. a. FFT is used to represent a signal in frequency plane. If frequency spectrum of a signal is taken by FFT and multiply the spectrum by a desired frequency response of a FIR filter, whether we can implement filters efficiently? Justify your answer in terms of merits and demerits of this system.

b. Calculate FFT of a signal x(n)= [7, 3+j, 2, 5, 9, 6,0,0] using the signal flow graph given in figure 2. Show the intermediate values at every nodes of the flow graph.