# 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.