Principles of Communication Engineering

Answer

Correct Option: (ii) Improve signal-to-noise ratio (high-frequency boost)

Explanation

Pre-emphasis in FM is high-pass filtering (75 µs, cutoff ~2.1 kHz) at transmitter that boosts high-frequency components of $m(t)$ before modulation.

• FM noise PSD at detector output ∝ $f^2$ (parabolic) → high frequencies noisier.
• Boosting highs before TX → de-emphasis (low-pass) at receiver restores flat response while suppressing high-freq noise.

Result: SNR improvement ~10 dB. Complementary to de-emphasis at receiver.

Final Answer

Improve SNR → Option (ii) (high-frequency noise reduction). If option (i) “reduce low-frequency noise” is opposite.

Answer

Correct Option: (ii) $1$

Explanation

Variance $\sigma^2 = E[(X-\mu)^2]$. Standard deviation $\sigma =\sqrt{\text{variance}}$.

Given $\sigma =1$ → variance $\sigma^2 =1^2=1$.

Mean 0 irrelevant.

Final Answer

$1$ → Option (ii).

Answer

Correct Option: (ii) Constant

Explanation

White noise $n(t)$ PSD $S_n(f)=N_0/2$ flat over $-\infty$ to $\infty$, autocorrelation $R(\tau)=N_0/2\delta(\tau)$. Zero mean Gaussian.

Not zero, exponential, parabolic.

Final Answer

Constant → Option (ii).

Answer

White noise $n(t)$ PSD $N_0/2$ flat, $R(\tau)=N_0/2\delta(\tau)$.

In AM, received $y=A_c[1+\mu m(t)]\cos\omega_c t + n(t)$. After envelope detection, noise in-phase $n_I$ and quadrature $n_Q$.

Input SNR $\gamma_i=(A_c^2/2)/(N_0B)$, $B=2f_m$.

Output SNR $\gamma_o = \frac{\mu^2P_m}{1+\mu^2P_m}\gamma_i$, figure $\gamma<1$ (AM wastes carrier). DSB-SC $\gamma=1$.

Derivation: noise power $N_0B$, signal $A_c^2/2+\overline{m^2}/2$, LPF extracts baseband. Threshold ~10dB.

Answer

PDF $f_X(x)$: $P(x<X\le x+dx)=f_X(x)dx$, $\int f=1$, $F_X(x)=\int_{-\infty}^x f$. CDF $F_X(x)=P(X\le x)$: monotonic 0→1, $f=dF/dx$. Gaussian $f=(1/\sqrt{2\pi}\sigma)e^{-(x-\mu)^2/2\sigma^2}$, $F=\Phi((x-\mu)/\sigma)$. Use for BER via $Q$.

Answer

**Probability $P(A)\in[0,1]$, $P(A|B)=P(A\cap B)/P(B)$. RV $X$, PDF $f_X$, CDF $F_X$, process $X(t)$ ensemble, mean $\mu(t)=E[X]$, $R(t_1,t_2)=E[X_1X_2]$. Stationary: stats independent shift, WSS mean const $R(\tau)$. Ergodic time=ensemble. AWGN zero-mean Gaussian $N_0/2$. Use for BER via $Q$.

Answer

Pre-emphasis: High-pass at transmitter boosting highs ($75\mu$s) before FM, high-freq noise dominates. De-emphasis low-pass at receiver restores flat and suppresses high-freq noise. Improves SNR ~10dB. Block $m$→HPE→FM→chan→FM demod→LPF→$m$.