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

Determines the signal's time-domain amplitude range

Answer

Defines the sampling rate required for the signal

Answer

Indicates the number of frequency components in the signal

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

A continuous frequency spectrum

Answer

An analog representation of the signal

Answer

A sequence of N real-valued time 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

Setting z = e^(−jω)

Answer

Taking the derivative of H(z) with respect to z

Answer

Setting z = jω

Question 4

An all-pass filter is characterized by:

Accepted Answer

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

Answer

Passing only high frequencies without attenuation

Answer

Blocking all frequency components equally

Answer

Constant group delay and zero phase shift

Question 5

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

Accepted Answer

X(f) · H(f)

Answer

X(f) + H(f)

Answer

X(f) − H(f)

Answer

X(f) / H(f)

Question 6

In the difference equation y[n] = b₀x[n] + b₁x[n−1] − a₁y[n−1], the term −a₁y[n−1] represents:

Accepted Answer

A feedback path using a previous output sample

Answer

A feedforward path using a previous input sample

Answer

A delay applied to the current input sample

Answer

A scaling factor applied to the current output

Question 7

The Power Spectral Density (PSD) of a signal describes:

Accepted Answer

How signal power is distributed across different frequencies

Answer

The instantaneous power at each moment in time

Answer

The total energy of a deterministic finite-duration signal

Answer

The phase angle of each frequency component