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When do you take the FFT of a signal?
If I have a signal that is time limited, say a sinusoid that only lasts for T seconds, and I take the FFT of that signal, I see the frequency response. In the example this would be a spike at the sinusoid’s main frequency. Now, say I take that same time signal and delay it by some time constant and then take the FFT, how do things change?
Is there a phase offset in the FFT vector?
This relationship only applies to the DFT since it is finite in time; it’s does not apply to the classic Fourier transform or discrete-time Fourier transform. This simply means that there will be a phase offset in your FFT vector. When you FFT your (real) signal, your answer will be complex, so you will have real, and imaginary part.
When to use fractional sample for delay estimation?
Remaining delay is fractional-sample. This approach will fail, if frequency-dependent group delay variations cause the phase to wrap at some frequency. This may happen for example when dealing with a multipath radio channel: “Determining the delay” is not a well-defined problem, once the group delay varies with frequency.
How to get the phase of a delay?
(In matlab you can also get the phase by simply “angle(fft_result)”). By the way if you do a correlation of your signal with delay and without delay and pick the peak, you can get the delay in that way.
Which is Fourier transform maps time domain to frequency domain?
The discrete Fourier transform (DFT), commonly implemented by the fast Fourier transform (FFT), maps a finite-length sequence of discrete time-domain samples into an equal-length sequence of frequency-domain samples.
How is Fourier deconvolution used in signal processing?
Fourier deconvolution is used here to remove the distorting influence of an exponential tailing response function from a recorded signal (Window 1, top left) that is the result of an unavoidable RC low-pass filter action in the electronics.