Digital Signal Processing — Summer 2022

Draw and explain the following sequences:

Unit sample sequence ii) Unit step sequence iii) Unit ramp sequence iv) Sinusoidal sequence and v) Real exponential sequence

List the merits and demerits of Digital signal processing.

Determine if the system described by the following input-output equations are linear or non-linear.

y(n) = x(n) + (1 / (x(n-1)) ii) y(n) = x2(n)

State and prove the following properties of z-transform. i) Time shifting ii) Time reversal iii)Differentiation iv) Scaling in z-domain

Explain the principle of operation of analog to digital conversion with a neat diagram.

Find the inverse z-transform of x(z) x(z) = z-1/(2-3z-1+z-2) ROC: z > 1.

Describe the different types of discrete time signal representation.

What is the advantage of radix-2 FFT algorithm in comparison with the classical DFT method?

Explain the design of FIR filters using windows.

Find the z-transform and ROC of the causal sequence. X(n) = {1,0,3,-1,2} ↑

Describe the window sequences generally used and compare their properties

What is ROC?State properties of ROC.

Using a rectangular window technique design a lowpass filter with pass band gain of unity,cutoff frequency of 1000 Hz and working at a sampling frequency of 5 kHz. The length of the impulse response should be 7.

Determine the z-transform of x(n) = cos (ω n)u(n)

Explain any two properties of Discrete Fourier Transform.

State and prove any two properties of z-transform.

Write short notes about the applications of DSP.