Demodulation of AM Signals

Demodulation is the process of extracting the message signal from the modulated signal.
The demodulation process depends on the type of modulation employed. For
DSB-AM and SSB-AM, the demodulation method is coherent demodulation, which
requires the existence of a signal with the same frequency and phase of the carrier at
the receiver. For conventional AM, envelope detectors are used for demodulation. In
this case precise knowledge of the frequency and the phase of the carrier at the receiver

is not crucial, so the demodulation process is much easier. Coherent demodulation for
DSB-AM and SSB-AM consists of multiplying (mixing) the modulated signal by a sinusoidal
with the same frequency and phase of the carrier and then passing the product
through a lowpass filter. The oscillator that generates the required sinusoidal at the
receiver is called the local oscillator.

SSB-AM Demodulation

Matlab Coding

 1 % MATLAB script for Illustrative Problem 3.7.
 2 % Demonstration script for LSSB-AM demodulation. The message signal
 3 % is +1 for 0 < t < t0/3, -2 for t0/3 < t < 2t0/3, and zero otherwise.
 4 echo on
 5 t0=.15;                    % signal duration
 
 6 ts=1/1500;                % sampling interval
 7 fc=250;                    % carrier frequency
 8 fs=1/ts;                  % sampling frequency
 9 df=0.25;                  % desired freq.resolution
10 t=[0:ts:t0];                % time vector

11 % the message vector
12 m=[ones(1,t0/(3*ts)),-2*ones(1,t0/(3*ts)),zeros(1,t0/(3*ts)+1)];
13 c=cos(2*pi*fc.*t);            % carrier vector
14 udsb=m.*c;                    % DSB modulated signal
15 [UDSB,udsb,df1]=fftseq(udsb,ts,df);    % Fourier transform
16 UDSB=UDSB/fs;                % scaling
17 n2=ceil(fc/df1);            % location of carrier in freq. vector

18 % Remove the upper sideband from DSB.
19 UDSB(n2:length(UDSB)-n2)=zeros(size(UDSB(n2:length(UDSB)-n2)));
20 ULSSB=UDSB;                % Generate LSSB-AM spectrum.
21 [M,m,df1]=fftseq(m,ts,df);        % spectrum of the message signal
22 M=M/fs;                    % scaling
23 f=[0:df1:df1*(length(M)-1)]-fs/2;    % frequency vector
24 u=real(ifft(ULSSB))*fs;            % Generate LSSB signal from spectrum.

25 % mixing
26 y=u.*cos(2*pi*fc*[0:ts:ts*(length(u)-1)]);
27 [Y,y,df1]=fftseq(y,ts,df);        % spectrum of the output of the mixer
28 Y=Y/fs;                    % scaling
29 f_cutoff=150;                % Choose the cutoff freq. of the filter.
30 n_cutoff=floor(150/df);            % Design the filter.
31 H=zeros(size(f));
32 H(1:n_cutoff)=4*ones(1,n_cutoff);

33 % spectrum of the filter output
34 H(length(f)-n_cutoff+1:length(f))=4*ones(1,n_cutoff);
35 DEM=H.*Y;                % spectrum of the filter output
36 dem=real(ifft(DEM))*fs;            % filter output

37 pause % Press a key to see the effect of mixing.
38 clf
39 subplot(3,1,1)
40 plot(f,fftshift(abs(M)))
41 title('Spectrum of the Message Signal')
42 xlabel('Frequency')
43 subplot(3,1,2)
44 plot(f,fftshift(abs(ULSSB)))
45 title('Spectrum of the Modulated Signal')
46 xlabel('Frequency')
47 subplot(3,1,3)
48 plot(f,fftshift(abs(Y)))
49 title('Spectrum of the Mixer Output')
50 xlabel('Frequency')
51 pause % Press a key to see the effect of filtering on the mixer output.
52 clf
53 subplot(3,1,1)
54 plot(f,fftshift(abs(Y)))
55 title('Spectrum of the Mixer Output')
56 xlabel('Frequency')
57 subplot(3,1,2)
58 plot(f,fftshift(abs(H)))
59 title('Lowpass Filter Characteristics')
60 xlabel('Frequency')
61 subplot(3,1,3)
62 plot(f,fftshift(abs(DEM)))
63 title('Spectrum of the Demodulator output')
64 xlabel('Frequency')
65 pause % Press a key to see the message and the demodulator output signals.
66 subplot(2,1,1)
67 plot(t,m(1:length(t)))
68 title('The Message Signal')
69 xlabel('Time')
70 subplot(2,1,2)
71 plot(t,dem(1:length(t)))
72 title('The Demodulator Output')
73 xlabel('Time')


The effect of mixing

The effect of filtering on the mixer output

The message and the demodulator output signals

Reference,

　　1.<<Contemporary Communication System using MATLAB>> -John G. Proakis