I am trying to convert random wave into number of uniform sine waves (frequency spectrum) using FFT in MATALB. My concern is to optimize the selection of the best 3-5 sine waves and create the initial wave (90-99%) back. 1) Whether I need to do zero padding (time domain data should be in 2 power numbers)? Will it affect the resultant sine waves? 2) whether i should include Nyquist theorem in determining bins. whats the purpose of setting frequency bins. Why not the frequency domain length is as same as the time domain length? Kindly clarify these issues regarding to the objective of my work.
Without these two also, I am getting fft of the original wave and if i include all the sine waves (frequency spectrum) and do ifft, i can get back the original wave. So what is the influence of these two 1) converting data in form of 2 power 2) setting the number of bins in frequency domain?
Whether I really need to those steps? How will it improvize my work's output?
You would use zero padding if you wanted to interpolate between frequency bins, i.e. to artificially increase your frequency resolution.
You may also want to do it if you were auto-correlating your signal or cross-correlating two signals, to remove the assumed cyclical boundary condition.
I wouldn't worry about using data lengths that are a power of two. That is just for computational efficiency.
If you are confident that your signal is stationary then you could get away with using a long window (for improved freq resolution).
If you are interested in the phase of your signal components, then don't try averaging the spectra of multiple data blocks (to reduce noise variance).
You may want to apply a tapered window function to the sampled data, to reduce the impact of high side-lobes caused by the rectangular time window.
Nyquist sampling theorem is used to determine the sampling rate which is used to traslate analogue signal to digital signal. If you already got digital signal there is no need to worry about that.
DFT is used to analyze periodic signals in theory. There is no need to padding zeros If your data length is the integral multiple of the wavelength. Hamming window (like tapered window)can be used when the signal is not periodic or the wavelength is not easy to be determined. Padding zeros introducing artifacts in frequency domain and is not a best choice.
How the FFT works
Dear, please check this link:
http://www.dspguide.com/ch12/2.htm
Actually i want to represent a random signal into a series of regular sine waves as in figure. I used fft function and converted the data from time domain to frequency domain. Is there any functions in matlab to get all the sine waves in a series from fft frequency domain output?
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