A Frequency analysis of signal with unknown period

[petterg]

I was reading up on (discrete) Fourier transform when my mind started to think of an what-if scenario:

Assumed I'm sampling a signal of the form
a1*sin(b1+c1) + a2*sin(b2+c2) + a3*sin(b3+c3) + ... + aN*sin(bN+cN) + some noise
where the a's represents magnitudes, b's represents frequencies and c's represents phases.
Assumed it is not know how low the lowest frequency is. It may not even be a full period within the time frame of sampling. Is there any way to find the frequencies represented in the data set?
(As I understand the DFT requires the sample set to be one repeating period of the signal.)

 

[Dale]

In the DFT the dwell time (the time between two samples) is 1/bandwidth, so the Nyquist frequency is half of that. That limits the highest frequency which can be faithfully represented without aliasing.

In contrast the total sampling time gives the inverse of the frequency resolution and determines how close two signals may be and still be distinguished. So this would determine how close a frequency could be to DC and still be detected.

 

[petterg]

Thanks Dale
As expected this was out of range for DFT. What should I look into to solve this kind of problems?

 

[chiro]

Hey petterg.

If you are using statistical inference you could estimate the coefficients of each harmonic and make inferences on those.

 

[Dale]

Thanks Dale
As expected this was out of range for DFT. What should I look into to solve this kind of problems?

I would recommend just sampling longer. You can use model-based approaches if you know N.

 

[petterg]

Thanks
I pick statistical inference as my next reading