# Questions tagged [fourier-transform]

The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.

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### Understanding the FFT phase spectrum with a simple example

I'm trying to compute the DFT using scipy's functions. I don't understand why the phase spectrum of a simple sine wave with 2 Hz frequency doesn't show $\pm\pi/2$ at the $\pm 2Hz$ frequencies. Instead,...
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### Is it possible to reduce the complexity of radix-2 FFT if the input vector contains identical elements?

my question is about reducing the complexity of radix-2 FFT when the input vector has a specific structure. For an input vector of x with N elements, the complexity is given by O(N log2 N). My input ...
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### Orthogonal Basis for a 2D Signals (Compressive Sensing)

I have a 2-D signal that is (1536x128) and that is sparse in the Fourier domain (after applying fft2). I want to apply compressive sensing to recover the signal using fewer random elements, but I am ...
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### Complex output after inverse FFT of a real signal

I have a real one dimensional signal s (light absorbance in a flow cell), which has significant noise and some periodic noise after performing a deconvolution of $S$ from $S_o$. Basically fft($S$) was ...
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### Advantages of the Rotation Translation Operation Before Doing FT Smoothing

I was reading a relatively old paper from the 1970s on smoothing by FT methods (chemistry applications), where the authors show that if we do rotation translation operation on the signal (y- values) ...
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### Finding the impulse response of a system

I have the following transfer function. $$H(j\omega) = \frac{1+0.5 e^{-j\omega}}{1-1.8 \cos(\frac{\pi}{16}) e^{-j\omega}+0.81 e^{-j2\omega}}$$ I'm trying to find the impulse response of the system. ...
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### Is it possible to recover the time-domain signal after manipulating it in the frequency-domain? [duplicate]

I've worked a fair amount with EEG signals, though I've never had formal training in signal processing, so please excuse my ignorance. The problem is this: my signal has noise at many, many ...