Extract Frequency, Amplitude and Phase of Logarithmic chirp

Hello,

I have two signals: both of them are logarithmic chirp but with different amplitude and normally a different phase according to the frequency. Frequency range: from 0 to 150 Hz, Sampling Rate 2000 Hz.

From those curves I would like to extract the frequency (to be sure that I have a logarithmic chirp and control the starting and ending frequency) the Amplitude and the Phase.

Here is the little code I wrote for it following the matlab help

function [f0,m,p] = myfft(x,fs)

l = length(x);          % Window length
n = pow2(nextpow2(l));  % Transform length
y = fft(x,n);           % DFT
f = (0:n-1)*(fs/n);     % Frequency range
power = y.*conj(y)/n;   % Power of the DFT

figure(1)
plot(f,power)
xlabel('Frequency (Hz)')
ylabel('Power')
title('{\bf Periodogram}')

y0 = fftshift(y);          % Rearrange y values
f0 = (-n/2:n/2-1)*(fs/n);  % 0-centered frequency range
power0 = y0.*conj(y0)/n;   % 0-centered power
m= 2*abs(y0)/l;

figure(2)
plot(f0,m)
xlabel('Frequency (Hz)')
ylabel('Magnitude (m)')
title('{\bf 0-Centered Periodogram}')

phase = unwrap(angle(y0));
p = phase*180/pi;
figure(3)
plot(f0,p)
xlabel('Frequency (Hz)')
ylabel('Phase (Degrees)')
grid on

end

I tried also to use the spectrogram function

function [f,m,a,FreqMax] = myspectrogram(Wave,SamplingRate)

      [s,f,t,p] = spectrogram(Wave,4096,4050,9192,SamplingRate,'yaxis');
      snorm = (2 * abs(s')) /sum(hamming(4096));
      [m,nd] = max(snorm); 
      m = 2*m;
      p0 = unwrap(angle(s'));
      a = p0(nd);

end

And to use the hilbert transformation.

My results are: I am able to extract the Frequency (from 0 to 1000 Hz as my sampling rate is 2000 Hz) but I have trouble to only get the frequency range of interest. I am able to measure the amplitude for the signal quite easily

BUT I don't get anything for the Phase. All three methods give me different results.

Could you tell me what is wrong ? And how can I extract the phase properly of my signal ?

Thank you !

Michael

Answer 1

[Brian Neiswander]

You can get instantaneous amplitude envelope, phase, and frequency information from a signal using the Hilbert transform. In MATLAB, the "hilbert" function returns the discrete-time analytic signal "X" for some real-valued signal "Xr":

X = hilbert(Xr);

The instantaneous amplitude envelope is the magnitude of the analytic signal:

mag = abs(X);

The instantaneous phase information can be found using the "angle" and "unwrap" functions:

phi = unwrap(angle(X));

Finally, the instantaneous frequency can be found from the derivative of the instantaneous phase:

freq = 1/(2*pi) * diff(phi) * Fs;

For a detailed example, see the page below:

http://www.mathworks.com/help/signal/ug/hilbert-transform-and-instantaneous-frequency.html

You can find more information about the MATLAB functions "hilbert", "angle", and "unwrap" below:

http://www.mathworks.com/help/signal/ref/hilbert.html

http://www.mathworks.com/help/matlab/ref/angle.html

http://www.mathworks.com/help/matlab/ref/unwrap.html