# 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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### Spectral Leakage in layman's terms

I'm trying to understand the concept of spectral leakage for the DFT, without going deep to the mathematical intricacies (it's for practical purposes). I've read from the book "Introduction to Digital ...
189 views

### 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 ...
334 views

### Why Is the DFT of a Signal Symmetric About Its Central Bin?

When i take an N point DFT of a signal, it comes out to be conjugate symmetric about the point N/2 . Could someone please tell how to understand this intuitively or mathematically ?
1k views

### DFT - Removing window effect in spectral domain with convolution

I was thinking about the DFT windowing subject and a thought came to my mind. A DFT will yield the spectrum of a signal convoluted with spectrum of the window used, therefore having a main lobes and ...
2k views

### Implementation of Wikipedia Equation for the DFT

I was writing a simple fourier transform implementation and looked at the DFT equation on wikipedia for reference, when I noticed that I was doing something differently, and after thinking about it ...
144 views

### dft of sampled sine using python

I'm trying to write a python script to perform a 100-point DFT over a finite length sample of a sinewave at 1/8 the sampling frequency. I'm curious why my DFT magnitude plot has two spikes in it when ...
56 views

### Anyone explain to me this video?

I was watching a video in time 24:48 I would like to know where you got the value .9 (1.14z + .941) and 1.0232 + .757 Does anyone explain how he got those numbers?
2k views

### Shift in Time Domain After DFT Based Convolution

To my understanding, multiplying a signal in the frequency-domain is equal to a convolution in the time-domain. I wrote a small python program, but i always end up with a shift in the time domain. ...
56 views

### When to Apply Circular Convolution Formulas?

Context I am studying the family of Discrete Trignometric Transforms (DTT): Discrete Cosine Transforms (DCT) and Discrete Sine Transforms (DST). And trying to understanding more their properties, I ...
1k views

### Circular Convolution of Length L of Sequences of Length Greater Than L

I'm trying to understand how may I obtain the circular convolution of length L when the sequences I'm trying to convolve are of length greater than L. For instance this Matlab code using sequences ...
700 views

### The Number of Sine and Cosine Waves in an $N$ Point DFT

This is bound to be an embarrassingly simple question, but here it goes... I was reading the chapter on discrete Fourier transforms (DFT) of this really didactic online book, The Scientist and ...
5k views

### Calculating the Spectral Centroid of a Signal

Here is the equation: $$C_i=\frac\sum_{k=1}^{W_{f_L}}kX_i(k)}{\displaystyle\sum_{k=1}^{W_{f_L}}X_i(k)}$$ The MATLAB code for the equation is: ...
123 views

### Scaling of the PWELCH function in MATLAB

I am trying to compute the power spectral density of a random signal using the PWELCH function in MATLAB. Since I think have not understood properly how Pwelch scales the PSD, I wrote a sample ...
59 views

### DFT from Fourier transform

I always studied the DFT starting from his formula, but for some reasons I need to do comparison between the FT and the DFT. I found the pdf in this link very useful http://www.robots.ox.ac.uk/~sjrob/...
24 views

### Proof that module of FT of 2 independent signals is sum of modules

I found on these posts (PSD subtraction and PSD of a sum of two stationary real signals) what I expected : that, just like the variance of the sum of 2 independent signals is the sum of the variances ...
31 views

### SciPy - Distinguish between two group of periodic samples [closed]

First of all, I'm sorry for my bad English writing, plus, I'm new to DSP. Background We have got motion data of 20 cows. 10 cows are healthy and 10 cows are slightly lame. Lameness is an abnormal ...
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### DFT and integer valued basis functions'sf requencies

In Matlab the function W=dftmtx(N) gives the DFT matrix of size N. Each row is computed for an integer frequency k. $W_{k,n} = e^{-i2\pi kn/N}$, k-th frequency, ...