B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

6.9 MATLAB Exercises 313
Figure 6.40
Reconstructed
signal spectrum
and waveform
from applying
the ideal impulse
sampling and
ideal low-pass
filter reconstruction.
Spectrum of ideal filtering (reconstruction)
300 .--------,,------., -------., ------,------,.--------,
250
200
1 50
100
50
0 ----'-----'------/ -----' -----'----
-150 -100 -50 0
50 100 150
Frequency, Hz
-
-
Original signal versus ideally reconstructed signal
2.-----.----,---,_._,--,---.-- ----.--- -.- -- -. --- -,- -- ---, --- -,
Original signal
Reconstructed signal
0
- 1
-2 '- -- .J____ __t____ ,___ -1....__ _1___ ..,_____ _L-:......JL.___ .J____ _j
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Time, second
recovered signal is still very close to the original signal g(t). This is because we have chosen
a high sampling rate such that T p
= T s is so small that the approximation of Eq. ( 6.17) holds.
Certainly, based on our analysis, by applying the low-pass equalization filter of Eq. (6.16), the
reconstruction error can be greatly reduced.
PCM Illustration
The uniform quantization of an analog signal using L quantization levels can be implemented
by the MATLAB function uniquan . m.
% (uniquan .m)
function [q__out ,Delta , SQNR] =uniquan (sig_in,L)
% Usage
% [q__out ,Delta , SQNR] =uniquan (sig_in,L)
% L number of uniform quantization levels
% sig_in - input signal vector
% Function outputs:
% q__out - quantized output
% Delta - quantization interval
% SQNR actual signal to quantization noise ratio
sig_pmax=max (sig_in) ; % finding the positive peak
sig_nmax=min (sig_in) ; % finding the negative peak
Delta= (sig_pmax-sig_nmax) /L; % quantization interval