GATE EC 2021 Set 1 — Question 62
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Communications → Source Coding & Baseband Transmission → PCM & DPCM
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Question
A message signal having peak-to-peak value of 2 V, root mean square value of 0.1 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 __________.
Correct answer
30 to 34
Solution
Given:
Peak-to-peak voltage V
Root mean square value V
Bandwidth kHz
Maximum transmission rate kbps
Substituting the values:
Peak-to-peak voltage V
Root mean square value V
Bandwidth kHz
Maximum transmission rate kbps
1.For a uniform quantizer, the maximum signal voltage is half of the peak-to-peak voltage:
V2.The minimum sampling rate must be at least the Nyquist rate:
3.The bit rate is related to the number of bits per sample and the sampling rate by . To find the maximum possible , we use the minimum :
bits/sample4.For a uniform quantizer, the Signal-to-Quantization Noise Ratio (SQNR) is given by:
Substituting the values:
5.Rounded off to two decimal places, the maximum signal to quantization noise ratio is .
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