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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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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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DFT on cosine wave where the sample rate is equal to the wave frequncy [closed]

How will the frequency domain will look if I'll apply DFT on 1KHz cosine wave with 1KHz sample rate?
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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
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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/...
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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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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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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
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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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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
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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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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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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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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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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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1answer
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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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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
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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 ...
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1answer
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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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DFT calculations returning different results

My coworker ran a DFT query using a software in C downloaded to his PC. His results was the following chart: I am using a JS tool from corbanbrook/dsp.js My results were very different. any ideas ...
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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 ...
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1answer
118 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 ...
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1answer
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Is it possible to reduce the complexity of radix-2 FFT if the input vector contains identical elements?

my question is about reducing the complexity of radix-2 FFT when the input vector has a specific structure. For an input vector of x with N elements, the complexity is given by O(N log2 N). My input ...
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1answer
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Orthogonal Basis for a 2D Signals (Compressive Sensing)

I have a 2-D signal that is (1536x128) and that is sparse in the Fourier domain (after applying fft2). I want to apply compressive sensing to recover the signal using fewer random elements, but I am ...
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1answer
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Inverse discrete Fourier transform

If anyone can help solving this exercise I'll be grateful. It's urgent. (I've added my answer, but I think it's wrong)
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Derive DFT of $x((n+1)/2)$

If $X(k)$ is the $N$-point DFT of $x(n)$, and $y(n)= x\left(\frac {n+1}{2}\right)$ for odd $n$, and $0$ for even $n$. What is the $2N$ point DFT of $y(n)$ in terms of $X(k)$? So far, I've ...
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The effect of upsampling on DFT coefficients

I am learning DSP by myself and I encountered a problem that bewilders me. If I have a sequence of length N, and I upsample it by a factor of 3. How would the DFT change or related? For example: <...
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What is the form of the spectral derivative in the all-positive-frequency notation in DFT?

The Discrete Fourier Transform (DFT) of a function $u:[0,2\pi] \to \mathbb R$ sampled over $N$ equidistant points $\theta_j = 2\pi j/N,\, j = 0, \dots, N-1,$ is defined by $$ \tilde U_k = \frac1N \...
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2answers
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Dominant Frequency Peak Decreases with Increasing Window Size

I have a signal that looks like this. I analyse it using fast Fourier transforms to identify the frequency with the largest peak, which is always close to zero. (There are no other clear peaks.) If I ...
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Understanding convolution of Chirp z algorithm

I dont´t understand how works the convolution part of the Chirp z. I understand how the DFT is transformed \begin{align*} x(k) = \sum_{n=0}^{N-1} x(n) W_N^{kn} \end{align*} to this expresion: \...
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Find repeating sequences in audio file

I have a long audio file (12+ hours). I know that there are some unknown small (2 minutes each or thereabout, it varies) repeating (not bit by bit: it is recorded with a mic) chunks in it, repeating ...
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1answer
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Frequency estimation of circularly shifted single tone signal

I have a discrete signal $y[n] = <e^{j ~ 2 \pi f ~ n}>_J + ~w[n]$ with $n \in [0, N[$ and $w[n]$ AWGN, $<x[n]>_K$ denotes the signal $x[n]$ circularly shifted by $K$ samples. Let's define $...
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How to compute properties of a song like key, bpm? [closed]

How to compute the key and BPM of a piece of music? Is the Fourier transform necessary? I tried to approach this issue from the music theory angle and I found that I get stuck at trying to understand ...
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Do twiddle factors of the fixed-point DFT have to be scaled to the input signal?

I have sensor data that is digitized by a 12-bit ADC that has analog range -1.65 to 1.65 V. The digital sensor data has thus scaling $3.3\cdot 2^{-12}$. I need to perform fixed-point DFT using ...
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63 views

FFT algorithm for real-time analysis

In a project, I have real-time voice audio being delivered in buffers of around 128 samples at a time. I want to calculate the autocovariance of the signal and use it to control an AR filter. To do ...
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3answers
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Phase of the DFT

I'm new to the numerical processing of sampled measurements so my question is probably trivial. Let's suppose that I have the following sampled signal generated in MATLAB: ...
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1answer
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Prove that, in DFT ,interpolation in time domain is equal to replication in frequency domain

Given: $x[n]$ is an $N$-point sequence whose DFT is $X[k]$ $$x[n]\xrightarrow{\mathcal{DFT}} X[k]$$ then, Prove that: DFT of the same sequence after insertion of $(M-1)$ zeroes between successive ...
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2answers
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Why there is error between My DFT and built in Matlab FFT?

I'm trying to implement DFT/IDFT and FFT/IFFT in Matlab and C. I got wrong values while I implement IDFT/IFFT. So I'm trying to find a mistake. Just for DFT, I used this algorithm to implement it in ...
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1answer
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Why would FFT interpolation using zero-padding undershoot the true frequency of a single tone sinusoid?

Why would FFT interpolation by zero-padding or using the Chirp Z-Transform produce a maximum at a bin that corresponds to a frequency less than the input frequency of a single tone sinusoid? I am ...
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1answer
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Contributions to a DFT frequency bin

So, a frequency bin is centered around an interesting frequency $f_0$. Assume the spectrum is such that there is no spectral leakage from other frequencies to that specific frequency $f_0$. Now. I ...
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Is the value of a frequency bin of a DFT-output the average of the 'real' frequency values within that bin's range?

I am wondering whether the value of a frequency bin with a certain resolution is the average of the fourier transform values of the 'real' frequencies within that bin's range.
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Does the DFT calculate spectral components up to half the sampling frequency, $f_s/2$?

This question is prompted by a statement made in this response (reproduced below): The DFT calculates spectral components up to $f_s/2$, no matter what the input signal is. A book I'm reading ...
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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, ...
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Should PSD be smoothed for SNR computation in frequency domain?

When taking the Power Spectral Density of a short duration signal (say 1 second, sampled at 4096 Hz), should it be smoothed to compute SNR? I want to computed the matched filter SNR, perfectly knowing ...
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How to use a size N complex DFT to compute a size N/2 real DCT? [duplicate]

Can someone (maybe @hotpaw?) Explain How to use a size N complex DFT to compute a size N/2 real DCT? Also, I noticed that the DCT matrix (which can be obtained in Matlab by dctmtx(n)) contains dct ...
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1answer
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How can I “smooth” square wave/pulse data to remove/reduce harmonics?

First, I have reviewed close-match questions, but can't find something that seems to match what I'm looking for. Also, it's been 30 years since college, so forgive me for forgetting stuff.. :) I am ...
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1answer
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Practical question about DFT in Matlab

Please consider this piece of code: ...
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2answers
165 views

DCT vs DFT why do we need/want phase?

Why do we use complex exponentials in the Fourier transform, why do we want the phase part? As opposed to in DCT where there is no phase and only magnitude? Moreover, what does this phase concretely ...
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Clarification on defining FFT bin sizes

When reconstructing the frequency domain for an FFT, what is the most self-consistent way to do this -- i.e. how is it best to define the bin width, $\Delta f$? For example, previously I thought it a ...
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1answer
155 views

MATLAB FFT Amplitude

I am trying to understand FFT, DFT through Matlab and I am fairly inexperienced in all of these. I have a time vector t and a corresponding simple sine wave x = 0.25*sin(t). Now I would like to view ...
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1answer
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Matrix form of 2D-DFT for a vectorized image

I want to apply 2d DFT to a N by N image. However, image is vectorized such that it is NxN by 1. How can i find the matrix form of 2d DFT such that resulting vector from multiplication is the ...