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# 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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### Zero Padding in Implementing FFT from scratch

I'm trying to implement an FFT algorithm from scratch. I'm using the recursive algorithm where if N is a power of 2, then I have M = N/2. The algorithm is divided into even and odd parts and I have ...
28 views

### Strided unpadding energy relationship?

If x1 = x0[::2] is unaliased subsampling, then $E(x_1) = E(x_0)/2$, which can be proven via Parseval's theorem. For same $x_0, x_1$, however, ...
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### Phase extraction from Fourier transform

Is it possible in principle to correctly extract the phase from Fourier transform? I just tried to do so using Python, here some attempts: ...
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### FFT of a gaussian signal in Python

I've been trying to get the FFT of a gaussian in Python. When I use the following parameters, the FFT goes hand in hand with the theoretical FT of the gaussian, but if I increase $\sigma$ they rapidly ...
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1 vote
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### Can anyone explain how dft works as a filter bank?

When we take the fft of input signal, the fft formulas say us to down convert the 2pik/N frequency content of input signal and sum one period interval. This gives us a just one complex number,not an ...
74 views

### Bandwidth visualization in frequency domain

Consider some signal in frequency domain: the maximum length of which corresponds to the half of the original signal ($N/2$), here $N=32$. It is known that the bandwidth of each sample is $2/N$, so ...
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102 views

### What is going wrong with the plot of 2D spatial spectrum at a specific frequency?

I've a set of 09 sensors in the following arrangement and the script for the sensor positions as follows: ...
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1 vote
53 views

### Lowering Spectral Resolution of FFT

I find myself in the position of having to lower the FFT resolution. Basically I have a signal of length M and I would like to make an FFT with N<M frequency bins. I cannot simply make several FFT'...
1 vote
39 views

1 vote
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### Entropy Loss in Linear Filters

I've been trying to figure out the result for the entropy loss/entropy gain in linear systems derived in "The Mathematical Theory of Communication" by Claude Shannon. Claude Shannon states ...
1 vote
73 views

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### How to interpret a 1D-DFT of an image with a sinus grating/gradient compared to its 2D-DFT outcome?

For getting a better and more intuitive understanding on how the 2D-DFT works I was playing around with sinus gratings in grayscale. I tried to compute the 1D-FFT first and compare it with the 2D-DFT ...
67 views

### Why does the 2D-DFT of a sinus gradient not show energy along the diagonal straigh lines and only vertical/horizontal from the diagonal point?

I have been experimenting a little bit with simple examples of the 2D DFT to get a better sense for it's interpretation. For this purpose I have been using sinus gratings with the following code: <...
1 vote
45 views

### Scaling of FFT2 magnitude in image-processing

I got the following code: ...
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