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Assignment 1

The document outlines an assignment focused on digital communication concepts, including calculations for Nyquist sampling rates, quantization noise, and PCM system parameters. It includes various problems related to sinusoidal signals, quantization characteristics, and signal transmission using PCM and DM systems. Additionally, it requires the calculation of transmission bandwidth and signal-to-noise ratios in different scenarios.

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Soumitra Bhowmik
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57 views1 page

Assignment 1

The document outlines an assignment focused on digital communication concepts, including calculations for Nyquist sampling rates, quantization noise, and PCM system parameters. It includes various problems related to sinusoidal signals, quantization characteristics, and signal transmission using PCM and DM systems. Additionally, it requires the calculation of transmission bandwidth and signal-to-noise ratios in different scenarios.

Uploaded by

Soumitra Bhowmik
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Digital communication (TIU-UEC-T312)

(Assignment 1)
1) Calculate the nyquist sampling rate and nyquist sampling interval of the
signal m(t)= 6 sin(2𝜋(400)𝑡).
2) Calculate the nyquist sampling rate and nyquist sampling interval of the
signal m(t)= 6 sin(2𝜋(400)𝑡)+8 sin(2𝜋(800)𝑡).
3) A sinusoidal signal m(t)= 6 sin(2𝜋𝑡) is transmitted using 4 bit binary PCM.
The quantizer used in PCM system is midrise type. Draw the quantizer
characteristics (input vs output). In this problem what is the value of
quantization noise (error) power.
4) An analog signal of bandwidth 4 KHz is transmitted using 8 bit binary PCM.
The signal is sampled at nyquist rate. Calculate the transmission bandwidth
and signal to quantization noise (error) ratio (in dB) of the PCM system.
5) An analog signal is sampled at the nyquist rate 𝑓𝑠 and quantized using L
level quantizer. Find the time duration of a 1 bit of binary encoded signal.
6) A sinusoidal signal m(t)= 6 sin(500𝜋𝑡) is transmitted using 7 bit binary
PCM.
a) Calculate the step size.
b) How many PCM bits are required to maintain the minimum value of
signal to quantization noise (error) ratio at 60 dB.
7) Let a signal having uniformly distributed amplitude in the interval (-2, +2)
volt is transmitted using 8 bit binary PCM. Calculate signal to quantization
noise (error) ratio (in dB).
8) An analog signal m(t)=𝛽𝑡 is transmitted using DM system, where 𝛽 is a
constant. Determine the minimum step size for DM system, which is
required to avoid the slope overload distortion.
9) An analog signal m(t)= 5 sin(2𝜋(1000)𝑡) is sampled at 56000 Hz.
Determine the minimum step size for DM system, which is required to avoid
the slope overload distortion.

10) Calculate the signal to quantization noise (error) ratio (in dB) in a DM
system for a 1 KHz sinusoid which is sampled at 32 KHz, without slope
overload and followed by 4 KHz reconstruction filter (Low pass). Compare
the result with the signal to quantization noise (error) ratio obtained without
reconstruction filter.

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