Demodulation of Standard AM with Hilbert Transform in Matlab

Standard AM signal also called conventional AM signal carries message signal or information signal in a carrier signal. There are three types of AM modulation: DSB-SC AM, standard AM and SSB-SC AM signal. The difference between them lies in what frequency part of the signal is sent. In standard AM, the full signal frequency of the modulated signal is transmitted. That is the carrier signal frequency, upper and lower signal frequency are transmitted. If the message bandwidth is W then the transmission bandwidth of standard AM is twice the message bandwidth, that is, 2W. In case of DSB-SC AM, both the upper and lower sideband are transmitted but the carrier signal is suppressed, that is, carrier signal is not transmitted. However the transmission bandwidth is equal 2W just as in standard AM. In SSB-SC AM, only either upper or lower sideband is transmitted and the transmission bandwidth is just W. 

In the earlier blog post Standard AM signal generation in Matlab it was shown how to generate standard AM signal and in the blog post Generate DSB-AM Signal in Matlab it was show how to generate DSB-SC AM signal in Matlab. Similarly in the tutorial post SSB-SC AM signal generation in Matlab it was shown how to generate SSB-SC AM signal. Here it is shown how to demodulate standard AM signal with Hilbert transform method.

There are two methods of demodulation of standard AM signal- one is the square law demodulation and the other is Hilbert transform demodulation. In square law demodulation method, the AM signal is passed through a square law device such as a diode and the output of the diode is then low pass filtered. In the Hilbert transform demodulation method, the signal is first passed through a Hilbert transformer and then the output of the Hilbert transformer is then low pass filtered.

Here it is illustrated how to demodulate standard AM signal using Hilbert Transform  method. A Hilbert transformer is a filter that shifts all the phase of the input signal by 90 degree. That is why it is also called broadband 90 degree phase shifter.

The following shows DSB-SC demodulation with Hilbert Filter circuit diagram.

The Matlab code for demodulation of AM signal using the Hilbert filter transformer is below.

Ac=0.8;
Am=0.5;    
fc=1000;
fm=100;
ka=0.8; 

fs = 10*fc;      % sampling frequency
ts = 1/fs;     % sampling time

% Generate message signal
t = (0:ts:500*ts).';  % time vector
m = Am*cos(2*pi*fm*t); % message signal

% Generate carrier signal
c = Ac*cos(2*pi*fc*t); % carrier signal

% Perform DSB-SC AM modulation
stx = (1+ka*m).*c;

% Add channel noise
SNR = 30; % signal-to-noise ratio in dB
stx_noisy = awgn(stx, SNR, 'measured');

% Demodulate using envelope detection
envelope = abs(hilbert(stx_noisy));
m_demod = (envelope./Ac-1)/ka;

% Plot the signals
subplot(4,1,1); plot(t,m); title('Message signal');
xlabel('Time (s)'); ylabel('Amplitude');

subplot(4,1,2); plot(t,stx); title('Carrier signal');
xlabel('Time (s)'); ylabel('Amplitude');

subplot(4,1,3); plot(t,stx_noisy); title('Noisy Standard AM signal');
xlabel('Time (s)'); ylabel('Amplitude');

subplot(4,1,4); plot(t,m_demod); title('Demodulated Standard AM signal');
xlabel('Time (s)'); ylabel('Amplitude');