Signal Processing MCQ Questions & Answers | ECE

The transfer function of a discrete time LTI system is given by$$H\left( z \right) = \frac{{2 - \frac{3}{4}{z^{ - 1}}}}{{1 - \frac{3}{4}{z^{ - 1}} + \frac{1}{8}{z^{ - 2}}}}$$
Consider the following statements:
S₁ : The system is stable and causal for $${\text{ROC}}:\left| z \right| > \frac{1}{2}$$
S₂ : The system is stable but not causal for $${\text{ROC}}:\left| z \right| < \frac{1}{4}$$
S₃ : The system is neither stable nor causal for $${\text{ROC}}:\frac{1}{4} < \left| z \right| < \frac{1}{2}$$
Which one of the following statements is valid?

The approximate transition width of main lobe in Blackman window is

Consider the two different ways of cascading a decimator with an interpolator shown below
The two systems are identical if-

A signal x_n, is given by x₀ = 3, x₁ = 2, x₂ = 5, x₃ = 1, x₄ = 0, x₅ = 1, x₆ = 2, x₇ = 2, x₈ = 4, where the subscript 'n' denotes time. The peak value of the auto correlation of x_{2n - 11} is

The Causal system given by H(z) = 6 + z^-1 - z^-2 is

What is the Nyquist rate for the signal x(t) = cos2000πt + 3sin6000πt ?

What is the minimum sampling rate required to avoid aliasing for the signal $$m\left( t \right) = {\left( {\frac{{\sin \left( {2\pi t} \right)}}{{2\pi t}}} \right)^3}$$

The continuous time unit-step function is defined by

Match List-I with List-II and select the correct answer using the options given below:

List-I	List-II
a. $${\alpha ^n}u\left( n \right)$$	1. $$\frac{{\alpha {z^{ - 1}}}}{{{{\left( {1 - \alpha {z^{ - 1}}} \right)}^2}}}{\text{ROC}}:\left| z \right| > \left| \alpha \right|$$
b. $$ - {\alpha ^n}u\left( { - n - 1} \right)$$	2. $$\frac{1}{{\left( {1 - \alpha {z^{ - 1}}} \right)}}{\text{ROC}}:\left| z \right| > \left| \alpha \right|$$
c. $$ - n{\alpha ^n}u\left( { - n - 1} \right)$$	3. $$\frac{1}{{\left( {1 - \alpha {z^{ - 1}}} \right)}}{\text{ROC}}:\left| z \right| < \left| \alpha \right|$$
d. $$n{\alpha ^n}u\left( n \right)$$	4. $$\frac{{\alpha {z^{ - 1}}}}{{{{\left( {1 - \alpha {z^{ - 1}}} \right)}^2}}}{\text{ROC}}:\left| z \right| < \left| \alpha \right|$$

The positions of the poles for the Butterworth filter lie on . . . . . . . . and the positions of the poles for the Chebyshev filter lie on . . . . . . . .