In a Hilbert transform, the phase angle of all components of the signal are shifted by 90 degrees.
Yes, Hilbert transform can be used in Demodulation (example is phase Demodulation).
In the case of phase demodulation, the Hilbert transform can be used to find the instantaneous phase of the signal and then removing the carrier signal to find the message signal which is represented as phase.
For Example, Let’s assume
x(t)= Acos[2πfct+β+αsin(2πfmt+θ)]
where
fc = Carrier frequency,
A = amplitude of carrier,
m(t) = message signal = αsin(2πfmt+θ)
MATLAB Code for Demodulation:
c = 240; %carrier frequency
fm = 10; %frequency of modulating signal
alpha = 1; %amplitude of modulating signal
theta = pi/4; %phase offset of modulating signal
beta = pi/5; %constant carrier phase offset
fs = 8*fc; %sampling frequency
duration = 0.5; %duration of the signal
t = 0:1/fs:1-1/fs; %time base
m_t = alpha*sin(2*pi*fm*t + theta); %modulating signal
x = cos(2*pi*fc*t + beta + m_t ); %modulated signal
%Add AWGN noise to the transmitted signal
nMean = 0; %noise mean
nSigma = 0.1; %noise sigma
n = nMean + nSigma*randn(size(t)); %awgn noise
r = x + n; %noisy received signal
%Demodulation of the noisy Phase Modulated signal
z= hilbert(r); %form the analytical signal from the received vector
inst_phase = unwrap(angle(z)); %instaneous phase
offsetTerm = 2*pi*fc*t+beta;
demodulated = inst_phase - offsetTerm;
