# 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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### Whitening signal vs. whitening its DFT

A whitening transformation (PCA) is simply a rotation into a space in which variables become uncorrelated. Because a DFT is a transformation into a coordinate space of orthogonal frequency components,...
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### Understanding LPC for Formant Estimation

I went through the Matlab tutorial on Formant Estimation using LPC Coefficients. Though I vaguely understand the details, it's not entirely clear why we need to do this. From http://person2.sol.lu.se/...
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### Expression for discrete fourier transform of linear ramp

I am trying to compute a single coefficient of the DFT of a linearly ramping sequence, $x[n]=an$ where $a$ is a constant that changes from sequence to seqeunce. I have looked at loads of DFT transform ...
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### non-uniform sampling on the unit circle - applications

If there is an N-point sequence, it has a Fourier Transform. DFT of this sequence is the sampling of the Fourier Transform at N equally spaced points on the unit circle. What happens if we take some ...
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### Difference between 2D DFT's and 1D DFT's of Linearized Matrices

I have recently left the safe and easy MATLAB environment and begun to use CUDA-C/C++ for image processing. Since CUDA doesn't allow 2D arrays to be passed into kernels I am now used to linearizing ...
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### Exercise Related to Frequency Resolution and SNR

I'm studying a book about DSP and trying to make exercises. Here is one I'm interested in: A scientist acquires 65,536 samples from an experiment at a sampling rate of 1 MHz. He knows that the signal ...
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### Sliding DFT: I think my results are accurate, but I can't buy a swap-swap IDFT

I've got a sliding DFT implementation that appears to be working (judging from an output plot). I would like to be able to invert this implementation using the standard tricks of swapping the real and ...
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### Does chirp have constant magnitude frequency response?

Pg. 223 claims so, yet my results via DFT differ: Is the textbook wrong? My attempted explanations: (code) DFT vs DTFT: "frequency response" is computed via latter. Still, DFT should ...
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### Cross Domain Equivalent to Nyquist Sampling Theorem?

In attempting to answer this question by @Oliver here: What characterizies 'causality' for a finite FFT? I have considered the minimum requirement to avoid time domain aliasing in the Discrete ...
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### 2D DFT in image processing in python

I try to compute 2D DFT in a greyscale image with this formula: I write the code bellow with python ...
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### Leakage in power spectral density estimation

What does it mean for a power spectral density exhibiting leakes from one frequency bin to other. I am reading a book which states the following: "Often the time series we use as input for our ...
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### What is the DFT of a pure cosine wave cos(Īø)

I want to find a DFT of a pure cosine wave cos(Īø) sampled at N equally spaced points on the interval $[0, 2\pi)$ so for our cosine wave, I put my $x$ like this $x=cos(\phi)$ then I just put it in ...
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### Performed the Danielson-Lanczos shuffling for FFT, but I don't know what to do next

I'm writing an audio analysis program and need to do some FFT to frames of the data. I've got some code (rather verbose so I'll leave out the details) that successfully performs the shuffling of the ...