# Questions tagged [dft]

The Discrete Fourier Transform (DFT) is a mapping between a finite set of discrete points in a (primal) domain (time, space) and the dual frequency domain. DFT requires an input sequence which is discrete, such as a sampling from an analogue audio signal.

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### Extracting Peak Frequencies Using FFT vs. Time Domain Peak Finding

I am trying to compare two processing algorithms that I believe should be producing very similar results. I am processing acceleration signals over the course of the day and we expect to see a ...
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### Estimate Filter Coefficients from the Result of Linear Convolution with a Known Signal

If I have samples of input say x(1:500) and it passes through FIR filter with 9 taps and some unknown coefficients. The output y(1:508) is also known. The aim is to estimate the filter response in ...
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### How can I take a fixed number of bins after N-point DFT when N is unknown?

I am working with machine learning for time series classification. I am trying to extract features from the amplitude spectrum. My current concern is that I cannot tell the length of the signal in ...
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### How to “scale” the FFT when using it to calculate discrete convolution?

As you probably know, the discrete convolution $H = F \ast G$ of some $F \left[ x \right]$ and some $G \left[ x \right]$ can be calculated using the Fast Fourier Transform (FFT). To do this, ...
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### Analysis frequency of the DFT?

So I'm reading Richard G. Lyons' book "Understanding Digital Signal Processing" and I've just started to make my way through the DFT chapter. While most of his examples and explanations make sense, I ...
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### Independence of Noise at Each DFT Output

My math may be a little rusty, so I would like confirmation or correction or my calculations here. Given white noise samples, $x_i$, which are IID and zero-mean, and variance $\sigma^2_x$. I want to ...
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### What is the physical significance of the Fourier coefficients in the DFT of audio signals and how can they be best displayed in a spectrogram?

I am trying to display the spectrogram of an input audio signal (a newcomer to all things spectral here). The amplitudes of my audio signal can be assumed to be normalized between -1 and +1. Suppose ...
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### Accuracy of IFFT(FFT(X)) unit transformation

I want to use FFTs to do seriously accurate interpolation on band-limited data. To do that, I need to get a handle on the fundamental accuracy of the FFT() and IFFT() algorithms available. My idea ...
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### Using Goertzel Algorithm in under-sampling

I plan to calculate a signal's phase using Goertzel Algorithm. I have 2 signals coming to microcontroller's ADC. Need to measure the phase difference between them. Signals are 15MHz sinusoids. Sample ...
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### Where does homomorphic filtering stand in regards to DSP applications?

I am studying my Oppenheim and Shaffer book, (New Edition), and the last chapter deals with something called homomorphic filtering. I have read the wiki and some other websites about it, but they do ...
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### Phase Correlation and Negative Shifts

I am implementing phase correlation algorithm to determine shift between two images. It generally works, but I am not sure how to interpret the resulting shift. Pseudocode: ...
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### How to calculate the power of a discrete signal? / Clarification on PSD estimates

I want to calculate the channel power $P_\mathrm{x}$ of a given discrete and complex signal $x[n]$ (with a length of N) in a given bandwidth $B$. I'm aware, that I could probably apply a sharp ...
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### Correlation between real and imaginary parts of a Fourier transform of zero mean Gaussian

From this previous post, the real and imaginary parts of the Fourier transform of a zero mean Gaussian are uncorrelated (and i.i.d. Gaussians) This some how seems counter-intuitive. It seems if the ...
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### retrieving original data from phase and magnitude of Fourier transform

I use this snippet of python code to transform data to Fourier phase and magnitude and then retrieving original data. ...
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### Time domain interpolation using FFT with zero padding on the end

I've got a situation where I'd like to use an FFT to do interpolation in time on some complex data (I need to go to the frequency domain anyways to window my data). The notional way of doing this ...