B CompE Bachelor of Computer Engineering Signals and Systems 3

Question 1

The Region of Convergence (ROC) of the Z-transform is significant because it:

Accepted Answer

Specifies where the Z-transform converges and determines causality and stability

Answer

The ROC defines where the Z-transform sum converges; its location relative to poles determines whether the system is causal, anti-causal, and whether it is stable.

Question 2

The N-point Discrete Fourier Transform (DFT) of a sequence of N samples produces:

Accepted Answer

N complex coefficients at equally spaced discrete frequencies

Answer

The N-point DFT produces exactly N complex frequency coefficients at N equally spaced frequencies from 0 to 2π, mirroring the N input samples.

Question 3

The frequency response H(e^jω) of a discrete-time LTI system is obtained from H(z) by:

Accepted Answer

Setting z = e^(jω)

Answer

The frequency response is evaluated on the unit circle of the z-plane by substituting z = e^(jω), where ω is the normalized digital frequency.

Question 4

An all-pass filter is characterized by:

Accepted Answer

Unity magnitude response for all frequencies while introducing frequency-dependent phase shifts

Answer

An all-pass filter has |H(e^jω)| = 1 for all ω but alters the phase, making it useful for phase equalization without affecting signal magnitude.

Question 5

According to the Fourier Convolution Theorem, F{x(t) * h(t)} equals:

Accepted Answer

X(f) · H(f)

Answer

The Convolution Theorem states that the Fourier Transform of a convolution equals the product of the individual Fourier Transforms: F{x(t)*h(t)} = X(f)·H(f).

B CompE Bachelor of Computer Engineering Practice Test

B CompE Bachelor of Computer Engineering Practice Test

B CompE Bachelor of Computer Engineering Signals and Systems 3