Spectral Density and Autocorrelation Questions and Answers

Digital Communications Questions and Answers – Spectral Density and Autocorrelation

This set of Digital Communications Multiple Choice Questions & Answers (MCQs) focuses on “Spectral Density and Autocorrelation”.

1. How can power spectral density of non periodic signal be calculated?
a) By integrating
b) By truncating
c) By converting to periodic
d) None of the mentioned

Explanation: Typically, a power signal is a periodic signal. However, by truncating the signal and viewing it in the range of (-T/2,T/2), the power spectral density of a non periodic signal can be computed.

2. What is Wiener-Khinchin theorem?
a) Spectral density and auto-covariance makes a fourier transform pair
b) Spectral density and auto-correlatioon makes a fourier tranform pair
c) Spectral density and variance makes a fourier tranform pair
d) None of the mentioned

Explanation: According to the theorem, a fourier transform pair is formed by the spectral density of a signal x(t) and the auto correlation function.

3. According to Parseval’s theorem the energy spectral density curve is equal to?
a) Area under magnitude of the signal
b) Area under square of the magnitude of the signal
c) Area under square root of magnitude of the signal
d) None of the mentioned

Explanation: The energy spectral density function can be written as the square of the signal’s magnitude x, according to Parseval’s theorem (t).

4. Spectogram is the graph plotted against?
a) Frequency domain
b) Time domain
c) Frequency & Time domain
d) None of the mentioned

Explanation: A spectogram is a graph that is plotted against time domain and a spectral density function is a graph that is plotted against frequency domain.

5. Autocorrelation is a function which matches
a) Two same signals
b) Two different signal
c) One signal with its delayed version
d) None of the mentioned

Explanation: Autocorrelation is a function that matches a signal with its delayed version.

6. Autocorrelation is a function of
a) Time
b) Frequency
c) Time difference
d) Frequency difference

Explanation: Because it compares the signal to its delayed form, autocorrelation is a function of time difference.

7. Autocorrelation is maximum at _______
a) Unity
b) Origin
c) Infinite point
d) None of the mentioned

Explanation: According to its properties autocorrelation is maximum at origin.

8. Autocorrelation function of periodic signal is equal to _______
a) Energy of the signal
b) Power of the signal
c) Its area in frequency domain
d) None of the mentioned

Explanation: The autocorrelation function of a real-valued signal equals the signal’s energy, while the autocorrelation function of a periodic signal equals the signal’s average power.

9. Autocorrelation is a _______ function.
a) Real and even
b) Real and odd
c) Complex and even
d) Complex and odd

Explanation: When the frequency value f is real, the autocorrelation function is an even function, according to its characteristics.

10. Autocorrelation function of white noise will have?
a) Strong peak
b) Infinite peak
c) Weak peak
d) None of the mentioned

Explanation: Autocorrelation function curve of continuous time white noise signal has a strong peak.

11. Power spectral density function is a?
a) Real and even function
b) Non negative function
c) Periodic
d) All of the mentioned

Explanation: According to the definition, a power signal is a periodic signal with a real even and non negative function.

12. Energy spectral density defines
a) Signal energy per unit area
b) Signal energy per unit bandwidth
c) Signal power per unit area
d) Signal power per unit bandwidth

Explanation: The signal energy is equal to the area under the waveform energy spectral density vs frequency curve when using energy spectral density.

13. Power spectrum describes distribution of _________ under frequency domain.
a) Mean
b) Variance
c) Gaussian
d) None of the mentioned

Explanation: The variance distribution of a signal in the frequency domain, sampled into spectral components, is known as the power spectrum.

The energy spectral density of a signal is a measurement of how much energy is distributed across frequencies. An energy signal’s autocorrelation function gauges signal self-similarity vs delay and can be utilised for synchronisation. The autocorrelation and ESD of a signal are Fourier transform pairs. The signal’s power spectral density (PSD) describes the signal’s power as a function of frequency, per unit frequency. Watts per hertz (W/Hz) is a typical unit of measurement for power spectral density. For random vibration analysis, the PSD of acceleration is commonly expressed in g2 Hz1.

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