GATE E&C Engineering Communications Syllabus

Communications syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Communications in GATE E&C Engineering, not a summary of it.

1. 1

   Random Processes

   2 topics

   • Auto Correlation and Power Spectral Density
   • Properties of White Noise
2. 2

   Analog Communications

   4 topics

   • Amplitude Modulation and Demodulation
   • Angle Modulation and Demodulation
   • Spectra of AM and FM
   • Super Heterodyne Receivers
3. 3

   Information Theory

   2 topics

   • Entropy
   • Mutual Information and Channel Capacity Theorem
4. 4

   Digital Communications

   8 topics

   • PCM
   • DPCM
   • Digital Modulation Schemes
     • ASK (Amplitude Shift Keying)
     • PSK (Phase Shift Keying)
     • FSK (Frequency Shift Keying)
     • QAM (Quadrature Amplitude Modulation)
   • Bandwidth
   • Inter-Symbol Interference
   • MAP (Maximum A Posteriori) and ML (Maximum Likelihood) Detection
   • Matched Filter Receiver
   • SNR (Signal-to-Noise Ratio) and BER (Bit Error Rate)
5. 5

   Fundamentals of Error Correction

   2 topics

   • Hamming Codes
   • CRC (Cyclic Redundancy Check)

Communications flashcards for GATE E&C Engineering

18 of 51 cards from the Communications deck — real questions with worked answers.

1. Define the autocorrelation function $R_X(\tau)$ of a wide-sense stationary (WSS) random process $X(t)$.

   $$R_X(\tau) = E[X(t)X(t+\tau)]$$ It measures the correlation of the process with a time-shifted version of itself and depends only on the lag $\tau$, not on absolute time $t$.

2. State the Wiener-Khinchin theorem relating autocorrelation and power spectral density (PSD).

   For a WSS process, the PSD is the Fourier transform of the autocorrelation function: $$S_X(f) = \int_{-\infty}^{\infty} R_X(\tau)\, e^{-j2\pi f \tau}\, d\tau$$ and conversely $R_X(\tau) = \int_{-\infty}^{\infty} S_X(f)\, e^{j2\pi f \tau}\, df$.

3. How is the total average power of a WSS process obtained from $R_X(\tau)$ and from $S_X(f)$?

   $$P = R_X(0) = E[X^2(t)] = \int_{-\infty}^{\infty} S_X(f)\, df$$ The power is the autocorrelation at zero lag, equal to the area under the PSD.

4. List three key properties of the autocorrelation function $R_X(\tau)$ of a real WSS process.

   1) It is even: $R_X(\tau)=R_X(-\tau)$. 2) It is maximum at the origin: $|R_X(\tau)|\leq R_X(0)$. 3) $R_X(0)=E[X^2(t)]\geq 0$ equals the total average power.

5. Define white noise in terms of its power spectral density.

   White noise has a constant (flat) PSD over all frequencies: $$S_X(f) = \frac{N_0}{2}$$ (two-sided), independent of frequency, analogous to white light containing all colors equally.

6. What is the autocorrelation function of white noise with PSD $S_X(f)=\frac{N_0}{2}$?

   $$R_X(\tau) = \frac{N_0}{2}\,\delta(\tau)$$ An impulse at $\tau=0$, meaning any two distinct time samples (however close) are uncorrelated.

7. Why is ideal white noise physically unrealizable?

   Its total power is infinite: $P=\int_{-\infty}^{\infty}\frac{N_0}{2}\,df=\infty$. Real systems have band-limited noise; white noise is an idealization valid over the bandwidth of interest.

8. For an AM (DSB-LC) signal $s(t)=A_c[1+\mu m(t)]\cos(2\pi f_c t)$, what does $\mu$ represent and what is its allowed range?

   $\mu$ is the modulation index. For distortionless envelope detection $0 < \mu \leq 1$. If $\mu > 1$ overmodulation occurs, causing envelope distortion.

9. Derive the modulation index for a single-tone AM signal in terms of $A_{max}$ and $A_{min}$ of the envelope.

   $$\mu = \frac{A_{max}-A_{min}}{A_{max}+A_{min}}$$ where $A_{max}$ and $A_{min}$ are the maximum and minimum envelope amplitudes.

10. For single-tone AM, what is the total transmitted power and the fraction in the sidebands?

    Total power: $$P_t = P_c\left(1+\frac{\mu^2}{2}\right)$$ Sideband fraction (efficiency): $$\eta = \frac{\mu^2}{2+\mu^2}$$ At $\mu=1$, $\eta=\frac{1}{3}$ (33.3%), so at most one-third of power is in the information-bearing sidebands.

11. Compare transmission bandwidth and power efficiency of DSB-LC (AM), DSB-SC, and SSB.

    DSB-LC (AM): BW $=2W$, carries carrier (low efficiency, simple envelope detection). DSB-SC: BW $=2W$, carrier suppressed (higher efficiency, needs coherent detection). SSB: BW $=W$ (half), most spectrum/power efficient, requires coherent detection.

12. What demodulation technique is used for conventional AM and why is it preferred?

    Envelope detection (a diode, RC low-pass filter). Preferred because it is simple, cheap, and noncoherent (needs no carrier phase recovery), which is why broadcast AM transmits the carrier.

13. In a coherent (synchronous) detector for DSB-SC, what happens if the local oscillator has a phase error $\phi$?

    The recovered output is scaled by $\cos\phi$: $$v_o(t) \propto \frac{1}{2}A_c m(t)\cos\phi$$ A constant phase error attenuates the signal (zero at $\phi=90^\circ$); a frequency offset causes a beat distortion.

14. Write the expression for an FM signal and define the frequency deviation.

    $$s(t)=A_c\cos\!\left(2\pi f_c t + 2\pi k_f\int_{-\infty}^{t} m(\lambda)\,d\lambda\right)$$ The instantaneous frequency deviation is $\Delta f = k_f\, |m(t)|_{max}$, where $k_f$ is the frequency sensitivity (Hz/V).

15. Define the modulation index $\beta$ for FM and PM (single tone).

    FM: $\beta = \dfrac{\Delta f}{f_m} = \dfrac{k_f A_m}{f_m}$. PM: $\beta = k_p A_m$ (peak phase deviation). $\beta$ is dimensionless.

16. State Carson's rule for the transmission bandwidth of an FM signal.

    $$B_T = 2(\Delta f + f_m) = 2(\beta + 1) f_m$$ where $\Delta f$ is the peak frequency deviation and $f_m$ is the highest modulating frequency.

17. Distinguish narrowband FM (NBFM) from wideband FM (WBFM) using $\beta$.

    NBFM: $\beta \ll 1$ (typically $\beta < 0.3$), BW $\approx 2f_m$ similar to AM. WBFM: $\beta \gg 1$, BW $\approx 2\Delta f$, occupying much larger bandwidth but giving better noise immunity.

18. How are the instantaneous frequency and phase related in angle modulation?

    $$f_i(t) = f_c + \frac{1}{2\pi}\frac{d\theta(t)}{dt}$$ Instantaneous frequency is the derivative of the total phase (divided by $2\pi$); FM modulates frequency proportional to $m(t)$, PM modulates phase proportional to $m(t)$.

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