GATE ECE Digital communications PYQs & Answers — Page 2

Questions 11–20 of 26. Imported answers require independent review unless marked reviewed.

Consider a real valued source whose samples are independent and identically distributed random variables with the probability density function,

, as shown in the figure.

Consider a 1 bit quantizer that maps positive samples to value

and others to value

. If

and

are the respective choices for

and

that minimize the mean square quantization error, then

________ (rounded off to two decimal places).

Diagram for Electronics and Communication Engineering question 64

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A speech signal, band limited to 4 kHz, is sampled at 1.25 times the Nyquist rate. The speech samples, assumed to be statistically independent and uniformly distributed in the range −5 V to +5 V, are subsequently quantized in an 8-bit uniform quantizer and transmitted over a voice-grade AWGN telephone channel. If the ratio of transmitted signal power to channel noise power is 26 dB, the minimum channel bandwidth required to ensure reliable transmission of the signal with arbitrarily small probability of transmission error (rounded off to two decimal places) is ______ kHz.

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A 4 kHz sinusoidal message signal having amplitude 4 V is fed to a delta modulator (DM) operating at a sampling rate of 32 kHz. The minimum step size required to avoid slope overload noise in the DM (rounded off to two decimal places) is ______ V.

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A digital transmission system uses a (7, 4) systematic linear Hamming code for transmitting data over a noisy channel. If three of the message-codeword pairs in this code

, where

is the codeword corresponding to the

message

, are known to be (1100; 0101100), (1110; 0011110) and (0110; 1000110), then which of the following is a valid codeword in this code?

Your answerChoose one option.

1101001

1011010

0010111

0110100

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A message signal having peak-to-peak value of 2 V, root mean square value of 1 V and bandwidth of 5 kHz is sampled and fed to a pulse code modulation (PCM) system that uses a uniform quantizer. The PCM output is transmitted over a channel that can support a maximum transmission rate of 50 kbps. Assuming that the quantization error is uniformly distributed, the maximum signal to quantization noise ratio that can be obtained by the PCM system (rounded off to two decimal places) is ______.

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Consider a polar non-return to zero (NRZ) waveform, using +2 V and −2 V for representing binary ‘1’ and ‘0’ respectively, is transmitted in the presence of additive zero-mean white Gaussian noise with variance 0.4 V

. If the a priori probability of transmission of a binary ‘1’ is 0.4, the optimum threshold voltage for a maximum a posteriori (MAP) receiver (rounded off to two decimal places) is _____ V.

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A digital communication system transmits a block of

bits. The probability of error in decoding a bit is

. The error event of each bit is independent of the error events of the other bits. The received block is declared erroneous if at least one of its bits is decoded wrongly. The probability that the received block is erroneous is

Your answerChoose one option.

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In a digital communication system, a symbol S randomly chosen from the set {s₁, s₂, s₃, s₄} is transmitted. It is given that s₁ = −3, s₂ = −1, s₃ = +1 and s₄ = +2. The received symbol is Y = S + W. W is a zero-mean unit-variance Gaussian random variable and is independent of S. P_i is the conditional probability of symbol error for the maximum likelihood (ML) decoding when the transmitted symbol S = s_i. The index i for which the conditional symbol error probability P_i is the highest is ______.

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A single bit, equally likely to be 0 and 1, is to be sent across an additive white Gaussian noise (AWGN) channel with power spectral density

. Binary signaling, with

and

, is used for the transmission, along with an optimal receiver that minimizes the bit-error probability. Let

form an orthonormal signal set. If we choose

and

, we would obtain a certain bit-error probability

. If we keep

, but take

, for what value of

would we obtain the same bit-error probability

Your answerChoose one option.

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A voice signal

is in the frequency range 5 kHz to 15 kHz. The signal is amplitude-modulated to generate an AM signal

, where

kHz. The AM signal

is to be digitized and archived. This is done by first sampling

at 1.2 times the Nyquist frequency, and then quantizing each sample using a 256-level quantizer. Finally, each quantized sample is binary coded using

bits, where

is the minimum number of bits required for the encoding. The rate, in Megabits per second (rounded off to 2 decimal places), of the resulting stream of coded bits is ______ Mbps.

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GATE ECE Digital communications PYQs

Question 64

Question 23

Question 24

Question 34

Question 52

Question 53

Question 12

Question 48

Question 34

Question 46