# GATE Questions & Answers of Digital communications: PCM, DPCM, digital modulation schemes, amplitude, ASK, PSK, FSK, QAM, MAP and ML decoding, matched filter receiver, calculation of bandwidth, SNR and BER for digital modulation

## What is the Weightage of Digital communications: PCM, DPCM, digital modulation schemes, amplitude, ASK, PSK, FSK, QAM, MAP and ML decoding, matched filter receiver, calculation of bandwidth, SNR and BER for digital modulation in GATE Exam?

Total 36 Questions have been asked from Digital communications: PCM, DPCM, digital modulation schemes, amplitude, ASK, PSK, FSK, QAM, MAP and ML decoding, matched filter receiver, calculation of bandwidth, SNR and BER for digital modulation topic of Communications subject in previous GATE papers. Average marks 1.75.

Consider binary data transmission at a rate of 56 kbps using baseband binary pulse amplitude modulation (PAM) that is designed to have a raised-cosine spectrum. The transmission bandwidth (in kHz) required for a roll-off factor of 0.25 is ________

An analog pulse $s(t)$ is transmitted over an additive white Gaussian noise (AWGN) channel. The received signal is $r(t) = s(t) + n(t)$, where $n(t)$ is additive white Gaussian noise with power spectral density $\frac{{N}_{0}}{2}$. The received signal is passed through a filter with impulse response $h(t).$ Let $E_s$ and $E_h$ denote the energies of the pulse $s(t)$ and the filter $h(t)$ respectively. When the signal-to-noise ratio (SNR) is maximized at the output of the filter (SNRmax), which of the following holds?

A speech signal is sampled at 8 kHz and encoded into PCM format using 8 bits/sample. The PCM data is transmitted through a baseband channel via 4-level PAM. The minimum bandwidth (in kHz) required for transmission is ________

An ideal band-pass channel 500 Hz - 2000 Hz is deployed for communication. A modem is designed to transmit bits at the rate of 4800 bits/s using 16-QAM. The roll-off factor of a pulse with a raised cosine spectrum that utilizes the entire frequency band is ________

A binary baseband digital communication system employs the signal

$p\left(t\right)=\left\{\begin{array}{l}\frac1{\sqrt{{\mathrm T}_\mathrm s}},\;0\leq\mathrm t\leq{\mathrm T}_\mathrm s\;\;\;\\0,\;\;\;\;\;\;\;\;\;\;\;otherwise\;\end{array}\right.$

for transmission of bits. The graphical representation of the matched filter output y(t) for this signal will be

The bit error probability of a memoryless binary symmetric channel is 10−5. If 105 bits are sent over this channel, then the probability that not more than one bit will be in error is __________

A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. The sampling rate and step-size $\triangle$ of the delta modulator are 20,000 samples per second and 0.1 V, respectively. To prevent slope overload, the maximum amplitude of the sinusoidal signal (in Volts) is

The input X to the Binary Symmetric Channel (BSC) shown in the figure is ‘1’ with probability 0.8. The cross-over probability is 1/7. If the received bit Y = 0, the conditional probability that ‘1’ was transmitted is _______.

The transmitted signal in a GSM system is of 200 kHz bandwidth and 8 users share a common bandwidth using TDMA. If at a given time 12 users are talking in a cell, the total bandwidth of the signal received by the base station of the cell will be at least (in kHz) _______.

A source emits bit 0 with probability $\frac{1}{3}$ and bit 1 with probability $\frac{2}{3}$ . The emitted bits are communicated to the receiver. The receiver decides for either 0 or 1 based on the received value $R$. It is given that the conditional density functions of $R$ are as

The minimum decision error probability is

A sinusoidal signal of amplitude A is quantized by a uniform quantizer. Assume that the signal utilizes all the representation levels of the quantizer. If the signal to quantization noise ratio is 31.8 dB, the number of levels in the quantizer is __________.

Consider a binary, digital communication system which uses pulses g(t) and – g(t) for transmitting bits over AWGN channel. If the receiver uses a matched filter, which one of the following pulses will give the minimum probability of bit error?

The modulation scheme commonly used for transmission from GSM mobile terminals is

In a baseband communications link, frequencies upto 3500 Hz are used for signaling. Using a raised cosine pulse with 75% excess bandwidth and for no inter-symbol interference, the maximum possible signaling rate in symbols per second is

A BPSK scheme operating over an AWGN channel with noise power spectral density of N0/2, uses equiprobable signals ${s}_{1}\left(t\right)=\sqrt{\frac{2E}{T}}\mathrm{sin}\left({\omega }_{c}t\right)$ and ${s}_{2}\left(t\right)=-\sqrt{\frac{2E}{T}}\mathrm{sin}\left({\omega }_{c}t\right)$ over the symbol interval (0, T). If the local oscillator in a coherent receiver is ahead in phase by 45$°$ with respect to the received signal, the probability of error in the resulting system is

A binary symmetric channel (BSC) has a transition probability of 1/8. If the binary transmit symbol X is such that P(X=0) = 9/10, then the probability of error for an optimum receiver will be

An analog signal is band-limited to 4 kHz, sampled at the Nyquist rate and the samples are quantized into 4 levels. The quantized levels are assumed to be independent and equally probable. If we transmit two quantized samples per second, the information rate is

A four-phase and an eight-phase signal constellation are shown in the figure below.

For the constraint that the minimum distance between pairs of signal points be d for both constellations, the radii r1, and r2 of the circles are

A four-phase and an eight-phase signal constellation are shown in the figure below.

Assuming high SNR and that all signals are equally probable, the additional average transmitted signal energy required by the 8-PSK signal to achieve the same error probability as the 4-PSK signal is

Consider the pulse shape s(t) as shown. The impulse response h(t) of the filter matched to this pulse is

The Nyquist sampling rate for the signal $s\left(t\right)=\frac{\mathrm{sin}\left(500\mathrm{\pi t}\right)}{\mathrm{\pi t}}×\frac{\mathrm{sin}\left(700\right)\mathrm{\pi t}}{\mathrm{\pi t}}$ is given by

The amplitude of a random signal is uniformly distributed between -5V and 5V

If the signal to quantization noise ratio required in uniformly quantizing the signal is 43.5dB, the step size of the quantization is approximately

The amplitude of a random signal is uniformly distributed between -5V and 5V

If the positive values of the signal are uniformly quantized with a step size of 0.05 V, and the negative values are uniformly quantized with a step size of 0.1 V, the resulting signal to quantization noise ratio is approximately

Consider a Binary Symmetric Channel (BSC) with probability of error being P. To transit a bit, say 1, we transmit a sequence of three 1s. The receiver will interpret the received sequence to represent 1 if at least two bits are 1. The probability that the transmitted bit will be received in error is

Four messages band limited to W, W, 2W and 3W respectively are to be multiplexed using Time Division Multiplexing (TDM). The minimum bandwidth required for transmission of this TDM signal is

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

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

In delta modulation, the slope overload distortion can be reduced by

The raised cosine pulse p(t) is used for zero ISI in digital communications. The expression for p(t) with unity roll-off factor is given by $p\left(t\right)=\frac{\mathrm{sin}4\pi Wt}{4\pi Wt\left(1-16{W}^{2}{t}^{2}\right)}$. The value of p(t) at $t=\frac{1}{4W}$ is

During transmission over a certain binary communication channel, bit errors occurs independently with probability p. The probability of AT MOST one bit in error in a block of n bits is given by

In a GSM system, 8 channels can co-exist in 200 KHz bandwidth using TDMA. A GSM based cellular operator is allocated 5 MHz bandwidth. Assuming a frequency reuse factor of $\frac{1}{5}$, i.e. a five-cell repeat pattern, the maximum number of simultaneous channels that can exist in one cell is

In a Direct Sequence CDMA system the chip rate is 1.2288 × 106 chips per second. If the processing gain is desired to be AT LEAST 100, the data rate

Two 4-ray signal constellations are shown. It is given that $\phi_1$ and $\phi_2$ constitute an orthonormal basis for the two constellations. Assume that the four symbols in both the constellations are equiprobable. Let $\frac{{N}_{0}}{2}$ denote the power spectral density of white Gaussian noise.

The ratio of the average energy of constellation 1 to the average energy of constellation 2 is:

Two 4-ray signal constellations are shown. It is given that $\phi_1$ and $\phi_2$ constitute an orthonormal basis for the two constellations. Assume that the four symbols in both the constellations are equiprobable. Let $\frac{{N}_{0}}{2}$ denote the power spectral density of white Gaussian noise.

If these constellations are used for digital communications over an AWGN channel, then which of the following statements is true?

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: