MATLAB Fourier Synthesis: Create Signal from Spectrum

[Branny12000]

Hi I wanted to check how to do a Fourier synthesis to recreate a signal from a frequency spectrum. So I basically have the frequency spectrum so I have the power of the fundamental frequency and the harmonics. Is there a way I can do a synthesis to create a time signal?

 

[f95toli]

If you have the spectra you should be able to just do an inverse transform (ifft).
There are a few things that can cause problems (read up on the fftshift command in the manual); but it should not be very difficult.

Have a look at some examples in the manual.

 

[Branny12000]

is there are a way I can do it from Fourier synthesis using a version of the code
for i =1:n (N = no of harmonics)
y = y + p(n)*cos(2*pi*n*f*t)

end

where P(n) is the power and f is the fundamental frequency

 

[f95toli]

Only if the original Fourier transform was done using a discrete cosine transform and the signal had some unusual properties(I think?); the inverse transform fir the cosine transform is as far as I know more complicated than what you have in your program
Hence, I guess the answer is perhaps yes for some signals but not in general.

Have a look at the wiki for discrete cosine transforms if this is really what you need. If your spectra was calculated from the usual FFT you need to use the IFFT function.

 

[alphy]

Hello,

Thank you for your question. MATLAB has a built-in function called "ifft" which stands for inverse fast Fourier transform. This function can be used to reconstruct a time signal from a frequency spectrum. The steps to perform a Fourier synthesis using MATLAB are as follows:

1. Create a vector of frequencies corresponding to the frequency spectrum you have. This can be done using the "linspace" function.

2. Use the "ifft" function to perform the inverse Fourier transform on the frequency spectrum. This will give you a complex-valued vector.

3. Take the real part of the complex vector to get the time signal.

4. Plot the time signal using the "plot" function to visualize the reconstructed signal.

It is important to note that the frequency spectrum should be in the form of a complex vector with the first element representing the power of the fundamental frequency and subsequent elements representing the harmonics.

I hope this helps. Best of luck with your Fourier synthesis!