fourier analysis of quasi periodic signal

[shomikc]

Can anybody please give me the algorithm or procedure to find the Fourier series or transform of a quasiperiodic signal. Thankyou.

I need this for homework that I would like to give my students. I am not able to proceed as the signal is not a regular signal like a triangular or square where the function of the signal is defined.

This is what the signal looks like.

There are 5 periods of 400 points each, a total of 2000 points, and I need to find the coefficients upto 20th harmonic. I also have to identify the dc component and the 4 largest frequency components. Please help.

The complete question is given here.

 

[wwfeldman]

microsoft excel spreadsheet will do FFT
(and i expect other comparable spreadsheets will also)
select data tab
select data analysis on far right side of ribbon
select FFT

i have never used it
you may have to activate an add-in
file, options, add-ins, analysis toolpack

 

[c_mitra]

Can anybody please give me the ahttps://en.wikipedia.org/wiki/Cooley%E2%80%93Tukey_FFT_algorithmlgorithm or procedure to find the Fourier series or transform of a quasiperiodic signal.

The definition is simple; the algorithm is messy to describe but the most common subroutine is a modified Cooley Tukey algorithm. See for details: https://eng.libretexts.org/Bookshel...Cooley-Tukey_Fast_Fourier_Transform_Algorithm

You can also refer for the mathematically inclined: https://en.wikipedia.org/wiki/Cooley–Tukey_FFT_algorithm

Remember that there are subtle differences between a FT and DFT. FFTs are DFT (discrete Fourier transform) and you may lose some information. Better to consult a regular text book on Fourier Transformation.

Excel has built in FFT and so has many other spreadsheets.

You need to put these 2000 points in a suitable col in the spreadsheet. FFT expects your data in equal intervals. The x-axis is assumed to be time.

Do the FFT the usual way; use the whole array of 2000 points. Your result will be a complex transformation (2000 real and 2000 imaginary) array.

You can make a power spectrum with simple analysis.

The new x-axis is now frequency. Scale them appropriately.

I use libre office and all these can be done without leaving the spreadsheet. It should be same for excel.

 

[KlausST]

Hi,

I used excel to generate FFT... there are "how to" descriptions around.

There also are documents on how to use FFT, like:
* Usually an FFT needs 2^n input samples, n is an integer number.
* Within this 2^n samples you need to have all frequencies to be multiples of 1/tsamplewindow
* if you can't guarantee this you need to perform a windowing funktion before running the FFT

Plese read those documents.

Klaus

 

[c_mitra]

* Usually an FFT needs 2^n input samples, n is an integer number.

This is no more a requirement; N just has to be a composite number.

See, for example, https://mathworld.wolfram.com/FastFourierTransform.html

You can also see https://en.wikipedia.org/wiki/Fast_Fourier_transform and some code in the talk page is illustrative.

I personally do not believe that we should discard good data (2^n is 1024 with n=10 and that means we ignore 2000-1024 data points).

I also do not want to pad real data with fake data (2^n with n=11 is 2048 and that means we pad the sequence with 48 zeros or replicate with start of the sequence 48 number) but the error in the present case is likely to be small.

However, some of the modern applications in signal processing, apart from the classical applications in X-ray diffraction, NMR spectroscopy and FT-IR, are really impressive (although I do not understand much of the underlying mathematics)

 

[KlausST]

Hi,

This is no more a requirement; N just has to be a composite number.

Thus I wrote "usually". It depends on algorithm. The OP needs to read the documentation
The last time I used the Excel FFT, I think 2^n was a requirement. Not 100% sure.

I agree that discarding data is not the way to go. I did not recommend it. Discarding valid data means discarding information, thus your FFT result will contain errors.
The same is with adding fake data (zeros). It will cause errors, too.
A useful way is to adjust sampling frequency.

Klaus