Asked by LO
on 10 May 2019

I am using the medfreq function to extract fast freq changes (few ms) in a sinewave signal. The function seems to work pretty well and better than "tfridge" (less artifacts), "sst" (faster) and instfreq (less artifacts).

however, when the source causes the signal to change in amplitude and no freq changes are present, it is when my problem starts. If one would imagine a spectrogram rapresentation of this: the signal would be a constant line, with some fast peaks occurring here and there (chirps). Using the medfreq function these are nicely detected.

Changes in amplitude are caused by movements in the signal source and cause the spectrogram trace to have gaps. In absence of freq modulations (chirps), the medfreq function detects a lot of noise - in correspondence of those gaps.

This suggests me that the medfreq function works "point to point", otherwise the gaps would be detected as "sinks" in the medfreq trace (but I could be wrong). Is there a way to impose a fixed range of freq in which the median is searched ? or somehow make it so that gaps in the main freq component are not creating artifacts which would be confused for chirps ?

Answer by Greg Dionne
on 14 May 2019

Edited by Greg Dionne
on 14 May 2019

Accepted Answer

From what I can tell your sinusoid is around ~895 Hz and has fairly clean second and third harmonics. So I took that as the starting point. The approach is to bandpass about each of the harmonics, mix down, filter and reconstruct the instantaneous frequency; if you divide each of the harmonics by its order, the overlaid results have reasonable agreement.

Anyways, this should hopefully get you started.

load seg1

Fs = 20e3;

% carrier

Fc = 895;

% choose 100 Hz (one-sided) bandwidth about carrier

bw = 100;

% attempt FM demodulation about carrier

[Finst1, Tinst] = instfreq_bb(seg1, Fs, Fc, bw);

[Finst2, Tinst] = instfreq_bb(seg1, Fs, 2*Fc, bw);

[Finst3, Tinst] = instfreq_bb(seg1, Fs, 3*Fc, bw);

% superimpose

plot(Tinst,[Finst1(:) Finst2(:)/2 Finst3(:)/3 (Finst1(:)+Finst2(:)/2+Finst3(:)/3)/3])

ylabel('Freq');

xlabel('Time');

legend('1st','2nd / 2','3rd / 3','average')

function [Finst, Tinst] = instfreq_bb(xx, Fs, Fc, bw)

%spectrogram(xx,kaiser(1024,10),1000,1024,20e3,'yaxis','power')

% pre-filter about carrier

x = bandpass(xx, Fc+[-bw bw], Fs, 'Steepness',.5);

%spectrogram(x,kaiser(1024,10),1000,1024,20e3,'yaxis','power')

t = (0:numel(x)-1)./Fs;

% mix down

z = complex(x .* cos(-2*pi*Fc*t), ...

x .* sin(-2*pi*Fc*t));

% filter

bb = lowpass(z,bw,Fs,'Steepness',0.99);

%spectrogram(bb,kaiser(1024,10),1000,1024,20e3,'yaxis','power','centered')

% fetch instantaneous frequency from angular component.

Finst = angle(bb(2:end).*conj(bb(1:end-1))).*Fs/(2*pi)+Fc;

% fetch weighted time.

Tinst = t(1:end-1)+t(2)/2;

end

LO
on 27 May 2019

thanks Greg, I have tried to change the type of analysis window (from hanning to blackmanharris). I noticed this solved the issue (it has a stronger filtering for whatever is in the surrounding of the carrier fr).

By applying at the same time a threshold on the spectrogram it is possible to visualize a cleaner signal and calculate medfreq with better results.

However still I have some issues as I am not really able to select only those points in which the power is high enough.

in the formula for medfreq calculation one can set ranges for power detection based on freq values and time values. Perhaps if one could also impose a power threshold there.. this could solve the problem (the problem now is still the same: sometimes - in correspondence of power losses in the carrier fr - some peaks are detected. this might have something to do with the 3D nature of the spectrogram and to whatever medfreq detects in those spots... at least this is what I suspect. somehow maybe the solution would be to get some 2D plane out of that 3D mess).... am I right ?

Greg Dionne
on 28 May 2019

If you are finding that changing the window has a favorable effect, you could try a parameterized window. Kaiser is often good (start with a low beta (say, 0.4) then gradually increase - but I think in your case, keep it under 10.

Eventualy though you will reach the limitations of what you can expect a median frequency method to do. It is simply looking for where the power level is split equally between the low and high frequency range. If there isn't enough discernable signal power, there's not much one can do...(the picture you posted looked like the power had completely disappeared into the noise.) I'm not sure even a reassigned spectrogram would be able to handle that case.

Perhaps other harmonics could contain enough power (or all of them together) to get a lock on your frequency? Maybe you could try computing the frequency of each harmonic separately, dividing by the harmonic number, and take weighted average by power level?

Hope this helps.

-Greg

LO
on 28 May 2019

Thanks Greg

I forgot to mention I have tried to apply your suggestion: no, considering the harmonics does not make it any better. I agree with you: there is not much to do in case of noise.

however what I want to achieve is not measauring the signal in the noisy spots. Is the opposite (exclude it). this could be achieved a little bit by changing the window and by thresholding the spectrogram (without reassignment, as it would eventually increase the noise for medfreq). I was wondering whether there is another way to apply a threshold directly on medfreq (or whether a similar function exists).

well thanks for your feedback so far ! it was helpful

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## Greg Dionne (view profile)

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## LO (view profile)

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## Greg Dionne (view profile)

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