Frequency analysis of signal with unknown period

In summary, the conversation discusses the use of discrete Fourier transform to analyze a signal with multiple frequencies and unknown lowest frequency. It is mentioned that the sampling time and frequency resolution play a role in accurately detecting the frequencies in the signal. Statistical inference is suggested as a potential solution and sampling longer is recommended.
  • #1
petterg
162
7
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.)
 
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  • #2
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.
 
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  • #3
Thanks Dale
As expected this was out of range for DFT. What should I look into to solve this kind of problems?
 
  • #4
Hey petterg.

If you are using statistical inference you could estimate the coefficients of each harmonic and make inferences on those.
 
  • #5
petterg said:
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.
 
  • #6
Thanks
I pick statistical inference as my next reading
 

What is frequency analysis of a signal with unknown period?

Frequency analysis is a mathematical technique used to determine the frequency components present in a signal with an unknown period. It involves examining the signal to identify its dominant frequencies and their amplitudes.

Why is frequency analysis important in signal processing?

Frequency analysis helps in understanding the underlying patterns and characteristics of a signal. It can provide valuable information about the behavior and structure of a signal, and can be used for tasks such as filtering, noise reduction, and feature extraction.

How is frequency analysis performed on a signal with unknown period?

Frequency analysis can be performed using various methods such as Fourier transform, wavelet transform, and autocorrelation. These methods involve transforming the signal into the frequency domain, where the frequencies and their amplitudes can be easily identified and analyzed.

What challenges are involved in frequency analysis of a signal with unknown period?

One of the main challenges in frequency analysis is the presence of noise or interference, which can affect the accuracy of the results. Additionally, the choice of the appropriate method and parameters for the analysis can also impact the results.

How is the period of a signal determined through frequency analysis?

The period of a signal can be determined by identifying the dominant frequency component in the signal. This can be done by finding the peak in the frequency spectrum or by using methods such as autocorrelation to estimate the signal's period.

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