Test 4 - Communication Systems | Electronics and Communication (ECE4

A carrier is phase modulated (PM) with frequency deviation of 10 kHz by a single tone frequency of 1 kHz. If the single tone frequency is increased to 2 kHz, assuming that phase deviation remains unchanged, the bandwidth of the PM signal is

Two sinusoidal signals of same amplitude and frequencies 10 kHz and 10.1 kHz are added together. The combined signal is given to an ideal frequency detector. The output of the detector is

X(t) is a stationary random process with autocorrelation function R_x(^_$\tau$) = exp ^{$(\pi r^2)$}. This process is passed through the system shown below. The power spectral density of the output process Y(t) is

A sinusoidal signal with peak-to-peak amplitude of 1.536 V is quantised into 128 levels using a mid-rise uniform quantiser. The quantisation noise power is

The Nyquist sampling rate for the signal s(t) = ^{$\dfrac{sin(500 \pi t)}{\pi t}$ _$\times$ $\dfrac{sin(700 \pi t)}{\pi t}$} is given by

In the following figure, the minimum value of the constant “C”, which is to be added to y₁ (t) such that y₁ (t) and y₂ (t) are different, is

A signal m(t )with bandwidth 500 Hz is first multiplied by a signal g (t ) where
g (t) = $\displaystyle \sum_{R = - \infty}^\infty (-1)^k \delta (t - 0.5 \times O^{-4}k )$
The resulting signal is then passed through an ideal low pass filter with bandwidth 1 kHz. The output of the low pass filter would be

Match the following:

A random variable X with uniform density in the interval 0 to 1 is quantized as follows :
If 0$\le$x$\le$ 0.3, x_q = 0
If 0.3 < X$\le$1, x_q = 0.7
where xq is the quantized value of X.
The root-mean square value of the quantization noise is

If E_b, the energy per bit of a binary digital signal, is 10^-6 watt-sec and the onesided power spectral density of the white noise, N₀ = 10^-5 W/Hz, then the output SNR of the matched filter is

A message signal with bandwidth 10 kHz is Lower-Side Band SSB modulated with carrier frequency f_c1 = 10⁶ Hz. The resulting signal is then passed through a Narrow-Band Frequency Modulator with carrier frequency f_c2 = 10⁹ Hz.
The bandwidth of the output would be

The input to a linear delta modulator having a step-size ^$\Delta$ = 0.628 is a sine wave with frequency f_m and peak amplitude E_m. If the sampling frequency f_s = 40 kHz, the combination of the sine wave frequency and the peak amplitude, where slope overload will take place, is

A speed signal, band limited to 4 kHz and peak voltage varying between + 5 V and - 5 V, is sampled at the Nyquist rate. Each sample is quantized and represented by 8 bits.

If the bits 0 and 1 are transmitted using bipolar pulses, the minimum bandwidth required for distortion free transmission is

A symmetric three-level midtread quantizer is to be designed assuming equiprobable occurrence of all quantization levels.

The quantization noise power for the quantization region between -a and +a in the figure is

A device with input x(t) and output y(t) is characterized by: y(t) = x²(t). An FM signal with frequency deviation of 90 kHz and modulating signal bandwidth of 5 kHz is applied to this device. The bandwidth of the output signal is

A speed signal, band limited to 4 kHz and peak voltage varying between + 5 V and - 5 V are sampled at the Nyquist rate. Each sample is quantized and represented by 8 bits. What is the number of quantization levels required to reduce the quantization noise by a factor of 4?

A symmetric three-level midtread quantizer is to be designed assuming equiprobable occurrence of all quantization levels.

If the input probability density function is divided into three regions as shown in figure, the value of a in the figure is

In a Direct Sequence CDMA System, the chip rate is 1.2288 ^$\times$ 10⁶ chips per second. If the processing gain is desired to be at least 100, then the data rate

The minimum sampling frequency (in samples/sec) required to reconstruct the following signal x (t) = 5 ^{$\left(
\dfrac{sin2\pi 1000 t}{\pi t}
\right) ^ 3
$} + 7^{$\left(
\dfrac{sin2\pi 1000 t}{\pi t}
\right) ^ 2
$} from its samples without distortion would be

An input to a 6-level quantizer has the probability density function f(x) as shown in the figure. Decision boundaries of the quantizer are chosen so as to maximize the entropy of the quantizer output. It is given that 3 consecutive decision boundaries are -1, 0 and 1.

The values of a and b are

Consider a system shown in the figure. Let X (f) and Y( f) denote the Fourier transforms of x (t) and y (t) respectively. The ideal HPF has the cutoff frequency 10 kHz.

The positive frequencies, where Y (f) has spectral peaks are

If S represents the carrier synchronization at the receiver and ^_$\rho$ represents the bandwidth efficiency, then the correct statement for the coherent binary PSK is

A speed signal, band limited to 4 kHz and peak voltage varying between + 5 V and - 5 V, is sampled at the Nyquist rate. Each sample is quantised and represented by 8 bits.

Assuming the signal to be uniformly distributed between its peak to peak value, the signal to noise ratio at the quantiser output is

Three analog signals, having bandwidths 1200 Hz, 600 Hz and 600 Hz, are sampled at their respective Nyquist rates, encoded with 12 bit words, and time division multiplexed. The bit rate for the multiplexed signal is

A signal is sampled at 8 kHz and is quantized using 8-bit uniform quantizer. Assuming SNRq for a sinusoidal signal, the correct statement for PCM signal with a bit rate of R is

Consider the following Amplitude Modulated (AM) signal, where fm < B :
$X_{AM}(t) = 10 (1+0.5 sin 2\pi f_m t) cos2\pi f_ct$

The average side band power for the AM signal given above is:

Consider the following Amplitude Modulated (AM) signal, where fm < B:

$X_{AM}(t) = 10 (1+0.5 sin 2\pi f_m t) cos2\pi f_ct$

The AM signal gets added to a noise with Power Spectral Density S_n (f) given in the figure below. The ratio of average sideband power to mean noise power would be