33. The sequence x(n) = \(\frac{sin ω_c n}{πn}\) does not have both z-transform and Fourier transform.
A. True
B. False
Answer: B
The given x(n) does not have Z-transform. But the sequence has finite energy. So, the given sequence x(n) has a Fourier transform.
34. If x(n) is a stable sequence so that X(z) converges on to a unit circle, then the complex cepstrum signal is defined as ____________
A. X(ln X(z))
B. ln X(z)
C. X-1(ln X(z))
D. None of the mentioned
Answer: C
Let us consider a sequence x(n) having a z-transform X(z). We assume that x(n) is a stable sequence so that X(z) converges on to the unit circle. The complex cepstrum of the signal x(n) is defined as the sequence cx(n), which is the inverse z-transform of Cx(z), where Cx(z) = ln X(z)
= > cx(z) = X-1(ln X(z))
35. If cx(n) is the complex cepstrum sequence obtained from the inverse Fourier transform of ln X(ω), then what is the expression for cθ(n)?
A. \(\frac{1}{2π} \int_0^π \theta(ω) e^{jωn} dω\)
B. \(\frac{1}{2π} \int_{-π}^π \theta(ω) e^{-jωn} dω\)
C. \(\frac{1}{2π} \int_0^π \theta(ω) e^{jωn} dω\)
D. \(\frac{1}{2π} \int_{-π}^π \theta(ω) e^{jωn} dω\)
37. If a power signal has its power density spectrum concentrated about zero frequency, the signal is known as ________
A. Low-frequency signal
B. Middle-frequency signal
C. High-frequency signal
D. None of the mentioned
Answer: A
We know that, for a low-frequency signal, the power signal has its power density spectrum concentrated at about zero frequency.
38. What are the main characteristics of an Anti-aliasing filter?
A. Ensures that the bandwidth of the signal to be sampled is limited to the frequency range
B. To limit the additive noise spectrum and other interference, which corrupts the signal
C. All of the mentioned
D. None of the mentioned
Answer: C
The anti-aliasing filter is an analog filter that has a twofold purpose. First, it ensures that the bandwidth of the signal to be sampled is limited to the desired frequency range. Using an anti-aliasing filter is to limit the additive noise spectrum and other interference, which often corrupts the desired signal. Usually, additive noise is wideband and exceeds the bandwidth of the desired signal.
39. In general, a digital system designer has better control of tolerances in a digital signal processing system than an analog system designer who is designing an equivalent analog system.
A. True
B. False
Answer: A
Analog signal processing operations cannot be done very precisely either, since electronic components in analog systems have tolerances and introduce noise during their operation. In general, a digital system designer has better control of tolerances in a digital signal processing system than an analog system designer who is designing an equivalent analog system.
40. The term ‘bandwidth’ represents the quantitative measure of a signal.
A. True
B. False
Answer: A
In addition to the relatively broad frequency domain classification of signals, it is often desirable to express quantitatively the range of frequencies over which the power or energy density spectrum is concentrated. This quantitative measure is called the ‘bandwidth’ of a signal.