Digital Signal Processing — Summer 2021

State merits and demerits of Analog signal processing v/s Digital Signal processing.

State and prove the properties of discrete time sinusoids.

Discuss from the location of poles, time domain behavior of causal signals.

Derive the power of unit step signal in discrete time domain.

Check whether the following system is 1) Linear/Non-linear 2) Static/Dynamic 3) Time variant/Time invariant 4) Causal/anti-causal y(n) = Ax(n) + B

Determine the total solution y(n), n ≥ 0, to the difference equation y(n) – 3 y(n-1) – 4 y(n-2) = x(n) + 2 x(n-1) when the input sequence is x(n) = 4n u(n).

Calculate the linear convolution for the LTI system h(n) = {1, 2, 1, -1} and input signal x(n) ={ 1,2 ,3 1}

Prove the convolution property of Ztransform.

Derive the z transform for 1) X(n) = an u(n) + bn u(-n-1)

Derive the closed form expression for the nth term of Fibonacci sequence.

Prove the multiplication of two sequence propertiy in Zdomain.

Derive the necessary and sufficient condition for a system to be stable in Zplane.

Using partial fraction expansion, for the following system. (3−4z−1) H (z)= (1−3.5z−1 +1.5z−2) Specify the ROC of H(z) and determine h(n) for following system. 1) The system is stable. 2) The system is causal. 3) The system is anti-causal.

Determine the signal having following Fourier transform X(w) = cos2w.

Compute and plot energy density spectra for the signal x(n) = u(n) – u(n-4).1

Derive and explain symmetry properties for DTFT.

Obtain circular convolution of two sequences x (n) = { 1,2,3,4} and x (n) = {0,1,0,-1}.12

State and prove following properties of DTFT. 1) Convolution 2) Time reversal

Derive and explain symmetry properties for DFT.

Explain in brief about windowing method for FIR filter design.

Draw cascade and parallel FIR filter structure for the system described by difference equation, y(n) – 3 y(n-1) – 4 y(n-2) = x(n) + 2 x(n-1)

Using decimation in frequency (DIF) radix-2 algorithm, compute 8 point DFT for the sequence x(n) = cos2 л n

Explain in brief about impulse invariance method for IIR filter design.

Draw form-Iand form-II FIR filter structure for the system described by difference equation, y(n) – 3 y(n-1) – 4 y(n-2) = x(n) + 2 x(n-1)

Using decimation in time (DIT) radix-2 algorithm, compute 8 point DFT for the sequence x(n) = cos2 л n