A lowpass signal mt with a 3 kHz bandwidth and an amplitude

A low-pass signal m(t) with a 3 kHz bandwidth and an amplitude range from -5 volts to +5 volts is sampled at the Nyquist rate. It is then converted to an eight-bit code using uniform quantization. The mean-squared value of the message signal So is 2 volts-squared. Calculate the normalized power for quantization noise N_q. Calculate the signal-to-quantization noise ratio (S_0/N_q) in decibels (dB).

Solution

VH= 5 v, VL=-5 v

Fs= sampling frequency=2*3= 6 khz

n= 8 bit

M= number of levels= 2^8

S= step size=(VH-VL)/M=10/2^8

a) e^2= mean square quantization error

= S^2/12

=1.29*10^-4

Nq= quantization noise power

=(fs)^2*e^2

=36*1.29*10^2

=46.44*20^2

b) So= Ouput signal power= M^2*S^2*(2fs)^2/12

So/Nq= M^2=2^16