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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5
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3answers
733 views

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 ...
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4answers
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 ...
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2answers
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 ?
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4answers
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 ...
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3answers
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 ...
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3answers
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 ...
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1answer
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?
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1answer
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. ...
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2answers
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 ...
2
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2answers
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 ...
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4answers
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 ...
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3answers
5k views

Calculating the Spectral Centroid of a Signal

Here is the equation: $$C_i=\frac{\displaystyle \sum_{k=1}^{W_{f_L}}kX_i(k)}{\displaystyle\sum_{k=1}^{W_{f_L}}X_i(k)} $$ The MATLAB code for the equation is: ...
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1answer
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 ...
2
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1answer
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/...
2
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1answer
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 ...
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0answers
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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1answer
62 views

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, ...
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2answers
1k views

Convolution in Spatial Domain Is Multiplication in Frequency Domain

I have to prove convolution in spatial domain is equivalent to multiplication in frequency domain using two matrices. $$ x(m, n) = \begin{bmatrix} 1 && 2 \\ 3 && 4 \end{bmatrix} $$ $...
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1answer
131 views

Spatial spectrum of EEG data: non-uniform DFT?

I want to compute the spatial spectrum of EEG data collected using a non-uniformly sampled grid of sensors (as in the figure below). One way to do this would be to interpolate the data on a ...
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2answers
92 views

Fourier Like Spectral Analysis with Uneven Intervals and Redesigned DFT Matrix

I intended to use a discrete Fourier transform (DFT) on a time series sampled at uneven intervals. What I did was to calculate a DFT matrix where the elements are the values at the uneven locations ...
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2answers
472 views

Interpolate DFT Coefficient of a Frequency That Is Not in the DFT Bin

I'm using the Jacobsen interpolation to get a more precise frequency of my signal. To get the corresponding DFT coefficient I'm doing: $$X_{f} = \sum_{n=0}^{N}{x_{n} e^{-2\pi ifn}}$$ Where $x_{n}$ ...
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2answers
9k views

Frequency resolution and timestep in DFT

I am learning DFT and I am not sure I understand it correctly. I am just going to write out the process of DFT and I am asking you to tell me if I am thinking the right way. Suppose we have a signal ...
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1answer
96 views

Inverse FFT - synch the phase

Is there any way to synchronise phase of output of inverse DFT in each buffer? When I send the output of inverse DFT to the speaker it sounds nasty. Of course I know the „windowing functions” but it ...
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1answer
161 views

Precompute parts of an FFT on streamed data inputs

I've implemented Radix-2 & Radix-4, DIT & DIF variants of the cooley-tukey FFT algorithm and they perform well on test data. Now for a project, my algorithms will be applied to a real-time ...
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1answer
115 views

resilient codes to phase shift

I need to define an encoding to beacon IDs. The codes are going to be periodic but in the receiver side I can have phase shifts so I' wondering the best way to decode: - 8 bits code groups that ...
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1answer
32 views

Question based on scaling property of dft

Can you please tell how use the scaling property to solve this question?? i am new to dsp subject
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2answers
959 views

harmonics of a signal and FFT

Consider that we have a discrete signal of finite length. How can we find the amplitude and phase corresponding to different harmonics of this signal in Matlab? Thanks.
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3answers
1k views

Correct magnitude spectra of a cosine DFT?

I've just started my course on DSP and haven't laid my hands on MATLAB yet. I was wondering if the plot of the magnitude spectra was correct for the below shown $x(n)$:
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3answers
253 views

Finding the time domain equation corresponding to a given DFT

I'm stuck with the following exercise while self-studying the Discrete Fourier Transform: Consider sampling exactly three cycles of a continuous $x(t)$ sinusoid resulting in an 8-point $x(n)$ time ...
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2answers
25 views

How do you get FFT for negative $k$ values?

I am reading a book (am a programmer so I suck at math) and it states that for a number of $k$-values that are symmetric around 0 (for example $k = -3, -2, -1, 0, 1, 2, 3$), we need to calculate $$\...
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2answers
90 views

Why padding zeros in the middle of a DFT spectrum improves original signal reconstruction?

I'm experimenting with the Inverse Discrete Fourier Transform. Starting from the two-cycles continuous $x(t)$ signal below: I have the discrete signal $x(n) = \{ 1, 0, -1, 0, 1, 0, -1, 0 \}$ leading ...
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3answers
758 views

How do I calculate peak amplitude of the signal components after zero padding and FFT?

I am learning about DFT and trying to apply it to some audio processing. I am new to DSP but experienced in programming and have some background in math and physics. The FFT algorithm I use (lomontFFT)...
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1answer
4k views

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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1answer
267 views

Question About Linear and Circular Convolution - 1D and 2D

We know that applying a filter on an image is called correlation or convolution depending on the filter angle. In Gonzalez I have read that we can apply linear convolution on an image. Here I have a ...
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1answer
289 views

How to Combine 8 N/8 FFT's into one N FFT

I need to make in FPGA (using Verilog) an FFT. Input data is N=8192 points at 1 GSPS. However, the FPGA operates at 125 MHz, therefore the data is split into 8 channels (each one at 125 MHz). This ...
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1answer
27 views

Bin sizes for non-uniform discrete Fourier transforms

For a non-uniform discrete Fourier transforms, do the specified frequencies – i.e., $f_k$ in – refer to the midpoint of the bin or the lower bound? I read the answer here, but that stated that ...
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1answer
116 views

Use samples of Fourier transform as DFT?

Consider the LTI system given by: $H(z) = 1 - \frac{1}{2}z^{-1}+\frac{3}{4}z^{-2}$ Let $x[n] = (\frac{1}{2})^nu[n]$ be the input to the system. We want to find the output for $n = 0,1,...,N_a$, using ...
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1answer
49 views

Proof that DFT does not require more than N points

I'm trying to show how the discrete Fourier transform (DFT) arises from the equation for the continuous-time Fourier Transform. I've run into an interesting caveat which I can't seem to find an ...
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2answers
38 views

Length of DFT defines whether I see the harmonic or the dominant frequency

I have a number of signals that are periodic. I use an fft transformation to obtain the dominant frequency of each signal. In order to increase the frequency resolution I zero pad the signal before ...
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0answers
38 views

Where to apply zero-padding for convolution dealiasing and appropriate scale

After hours of browsing the DSP posts and resources online, I still struggle to understand why my code diverges when I activate zero-padding dealiasing. When I deactivate it, everything 'works well', ...
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1answer
538 views

inverse discrete fourier transform with plain python

I am trying to calculate inverse discrete fourier transform for an array of signals. I am using the following formula: $$ x[n] = \tfrac1N \sum\limits_{k=0}^{N-1} X[k] \, e^{j 2 \pi k n/N} $$ And my ...
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0answers
17 views

DFT of a function and array convolution

I saw some questions (and answers) on this subject, but they were all about a specific example and I'm not sure I understood. I'm trying to understand the meaning of computing the DFT of an array ...
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1answer
260 views

Analytical Expression for Convolution of Two 2D DFTs

I am trying to do an image analysis problem on some images, and I want to calculate some things in the frequency domain which are giving me problems. Say I have an (discrete) image $I(x,y)$ of size $...
3
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2answers
2k views

Fast Hartley Transform Implementation in MATLAB

I want to implement Fast Hartley Transform (Specifically Discrete Hartley Transform) in a script file in MATLAB. Does anyone know have a reference implementation of this in MATLAB or another language ...
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1answer
74 views

Finding n Amplitudes by DFT, what is correct normalization

Please forgive me if this has already been asked. Let us assume an example with $x(t) = \sum_{i=1}^N A_i \sin(2\pi f_i t) $ under a given sampling frequency $f_s$, frequencies $\omega_i$ and ...
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2answers
894 views

Sinc Interpolation Using DFT (FFT)

Lets say I want to double the number of points in an array f. I had the idea to do this: F=fft(f);N=length(f); FF=[F(1:N/2) zeros(1,N) F(N/2+1:N)]; f=ifft(FF); ...
2
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1answer
54 views

Amplitude estimation of sinusoid in known spiky spectral noise

What is the "best" way to estimate amplitude of a known-frequency sinusoid in the presence of known spiky spectral noise (i.e. noise comprising a few spectral peaks at known frequencies)? By "best", ...
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0answers
58 views

Convolution of a non-symmetrical window function by a cosine signal in the frequency domain

A have a time signal: The associated DFT spectrum of this signal: The time signal can be considered as a non-symmetrical rectangular window function multiplied by a cosine signal with a frequency $...
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2answers
54 views

DFT frequency resolution exercise [closed]

I have a discrete signal that goes as follows: $$x[n]=[-1,4,-1,0]$$ I have already done the DFT for the signal, with the following result: $$X[0] = 2, X[1]=-4i,X[2]=-6,X[3]=4i$$ But for some reason, I ...
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1answer
50 views

solution on the time domain becomes “periodic” after the inverse fourier transform

I was trying to solve european option pricing problem using Conv method (introduced by Lord in 2008 https://pdfs.semanticscholar.org/0632/460bd50b2151f74ac40028df4cc60e73a884.pdf). The final step of ...