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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FFT Artifacts and their cause beyond frequency resolution

I am trying to work through an issue with an FFT for audio : I have no spectral leakage while playing back audio, but the moment I change or zero out a value in any of the FFT bins, artifacts are ...
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6 votes
2 answers
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Downsample a signal by a non-integer factor

I have a signal with a sample rate of 8.9286 MHz and I want to downsample it to 500 kHz. Since 8.9286 is not an integer multiple of 0.5 I can't simply decimate. Which downsample techniques are ...
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Can we recover $|X(k)|$, given $|x(n)|$?

Given a complex vector $x[n]$, we can find the magnitudes of the spectrum by computing: $X_m[k] = |X[k]| = |FFT[x]|$ This involves performing a complex FFT and computing the absolute value of the ...
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How to create an ideal sine wave that will be the best fit for given sine wave with noise and distortion

I have a sine waveform that is a result of simulation. This is always single tone with a constant offset, but with distortion and noise and may have some jitter: $$s[k] = A\sin\left(2\pi \frac{f}{f_\...
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Can I reduce the complexity of multiplication with FFT if the input vector is repeating?

I have a Fourier matrix $F$ with size $N \times N$, such that $y = F \times x$, if I have the vector $x$ contains four identical parts, for example $x = [x_1, x_2,x_3,x_4]’$ and $x_1 = x_2 = x_3 = ...
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Fourier transform of a top-hat function in the Faraday Measurement synthesis context

I'm currently trying to calculate the Fourier transform of a top-hat function in the context of Faraday Measurement Synthesis. This is pretty straightforward, however, I cannot understand why I cannot ...
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Axes of Discrete Fourier Transform

Problem Given $X[k] = \sum_{n=0}^{N-1} x[n]e^{-j2\pi kn/N}, k = 0, ..., N-1$ What are the units on the x-axis and y-axis? Note that for the x-axis there are two answers. Attempted solution My first ...
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Can I calculate the DFT of a specific wavelet by its FT formula?

I'm going to use a Morlet wavelet to filter my signal. The first step is to calculate the DFT (or FFT) of the signal and the wavelet kernel respectively. I guess that as the FT of a Morlet wavelet can ...
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-2 votes
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Is it true that the “DFT can only deal with causal signals"?

I don't understand this remark and it's the first I hear it. Isn't this directly at odds with "DFT assumes input is periodic"? The full statement, the signals are nonzero for $t < 0$, ...
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Fourier transform of modulus of sum of sines

$$ x(t) = |\cos(\omega_0 t) + \cos(\omega_1 t)| $$ with $\omega_0, \omega_1 > 0$. Is there a known result for $\mathcal{F}\{x(t)\}$? Derivation not needed but is welcome. Of main interest is the ...
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Fourier transform of modulus of sum of weighted sines

$$ x(t) = |a \cos(\omega_0 t) + b \cos(\omega_1 t)| $$ with $a, b \geq 0$, $\omega_0, \omega_1 > 0$, but $a, b > 0$ or all $a, b$ (negatives included) is also acceptable, or replacing $\cos$ ...
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How to calculate DFT of signal which occurs from 3 to 8?

How can I calculate discrete fourier transform of this signal? I'm confused as in the normal cases signal always start from 0 to N-1 but in this case it starts from 3 to 8 instead. So what would be ...
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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 ...
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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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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 ...
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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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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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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'...
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What Does "Reduced Modulo N" mean in this context?

I am trying to understand a piece of notation used in several papers, the simplest/shortest of which is this paper by Crochiere. The equation in question is Equation 7 on the second page: $x_m(sR) = ...
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Sparse signal FFT

Say I had a time domain signal $x[k]$ wich is sparse: $\log(N)^2$ nonzero samples and the fourier transform has only a very (very!) small number of high frequency components. Are there any techniques ...
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Confusion Understanding the mathematical expression of duality property of dft?

Duality Property for DFT Above dsp.se question provides good understanding about dft duality property but i am having difficulty understanding its mathematical expression because on Google when i try ...
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Expression for DFT of linear 2D ramp

One dimensional solution is in “Expression for discrete fourier transform of linear ramp“ I need two-dimensional for image processing. We have function f(x,y) = $a_1 \cdot x + a_2 \cdot y$, My ...
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Removing sawtooth wave from DFT transform [duplicate]

We have samples $x_n$ and sawtooth wave $s_n$ with period N (especially if N=$2^k$) $s_n = c \cdot n$ for n=0...N-1 where c is constant. What is formula for coefficients of DFT this wave? I want ...
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Inferring shape of information signal from its DFT?

I came across this question recently, and I am very confused by (b)(ii). b(i) gives $x_n$ = [0.5, 0, -0.5, 0]. My approach to (ii) was to recognise that $X_m$ represents the frequency content of the ...
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Is there other basis possible for DFT?

As I understand, the DFT of a signal $x$ is a representation of this signal in the basis $$ \{ e^{j2\pi kn/N} \}_{k = 0, 1, \dots, N-1}$$ Is it possible to form a base of such discrete complex ...
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Best way to get the bin amplitudes of an audio DFT "normalized" 0-1

I'm working on a spectral processing plugin that's predicated on allowing the user to manipulate per-bin values in an STFT algorithm. I normalize the bin amplitudes by diving them by $N$ (number of ...
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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 ...
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Question about radix-2 DIT FFT and sampling theorem

I'm currently reading this article and trying hard to understand it. According to the article, DFT is as follows: $$ X_k=\sum_{n=0}^{N-1}x_ne^{-\frac{2\pi i}{N}nk} \\\text{where k is integer and its ...
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DFT Graph has too many oscillations? [closed]

I'm very new to the DFT, and am working on it for a HS project. I've taken the DFT of my instrument playing (the original waveform looking like this: But after plotting the DFT onto Desmos, I get a ...
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4 votes
3 answers
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Inverse DFT on the first half time domain

Assume to have c[] representing N DFT coefficients. The complex-valued signal of N samples in the time domain is computed by ...
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What means `crop` in FFT calculation?

In soapy power manual: Crop: -o PERCENT, --overlap PERCENT percent of overlap when frequency hopping (incompatible with -k) -k PERCENT, --crop PERCENT percent of crop when frequency hopping (...
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correct fourier transform of time series starting with different start/end times

I have lots of time series where I want to analyse some periodic signal that occurs beside the signal I wanted to measure (and I didn't expect). The idea is that there's always a peak at a certain ...
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What is edge-effect in discrete convolution?

My professor threw in the random term and never explained what it means cus he's been going on strike for 3 weeks straight.
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Understanding spectral leakage in a pink noise dominated signal

I've been reading about power spectral density estimation based on the DFT, about spectral leakage, windowing functions and the Welch method. I've recorded a signal that's supposed to be pretty much ...
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Understanding $\mathsf{FFT}$ of $x(t):=\cos(2\pi f_{0}t)$

I have been buzzed about this issue for more than an hour. I have been tasked to execute a simple DTFT task using MATLAB for the signal $x(t):=\cos(2\pi f_{0}t)$. Assuming we are sampling at a rate of ...
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What metrics should I use to describe the difference between two magnitude responses in octave band

Suppose that I have two frequency responses $H_1(k)$ and $H_2(k)$, I want to describe the difference or MSE between them in each octave band. The background is that I have a target frequency response $...
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5 votes
1 answer
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Sinc Based Multi Dimension Signal Resampling on the Fourier Spectrum (DFT)

As a generalization of the following questions: The Proper Way to Do Sinc Downsampling (DFT Downsampling) for Uniformly Sampled Discrete Signals with Finite Number of Samples. The Proper Way to Do ...
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Intuition of odd and even complex conjugate symmetry definition of DFT/DTFT so that $X(e^{j w})=X_{e}\left(e^{j w }\right)+X_{o}\left(e^{j w}\right)$

I have been reading through my courses DSP slides and came across something which was not really taught in detail. You can look up here for reference, it is stated almost identical. Given the ...
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4 votes
1 answer
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Applying 2D Sinc Interpolation for Downsampling in the Fourier Domain (DFT / FFT)

Related to The Proper Way to Do Sinc Downsampling (DFT Downsampling) for Uniformly Sampled Discrete Signals with Finite Number of Samples, how can one apply Sinc downsampling in the DFT / FFT domain ...
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Relation between DFT filter bank and sliding DFT

I am reading the book 'spectral audio signal processing'. It says when $n=LN-1$ for any integer $L$, the sliding DFT $$X_n(k)=\sum_{m=0}^{N-1}x(n+m)e^{-j2\pi mk/N}$$ coincides with the DFT filter bank....
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How can I check if a signal its periodic from the graph of FFT?

x is a vector of length 1000 that contains the samples of the signal; n is equal to 16 that its the number of bits of each sample; fa=256 Hz (sampling frequency); <...
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4 votes
1 answer
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Applying 2D Sinc Interpolation for Upsampling in the Fourier Domain (DFT / FFT)

Related to The Proper Way to Do Sinc Upsampling (DFT Upsampling) for Uniformly Sampled Discrete Signals with Finite Number of Samples, how can one apply Sinc upsampling in the DFT / FFT domain for a ...
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What is the magnitude and phase of the wave represents in the k-space or Fourier space?

#Code from https://stackoverflow.com/questions/70768384/right-method-for-finding-2-d-spatial-spectrum-from-cross-spectral-densities I've an array of seismic sensors (say, N=34). Every sensor collect ...
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How to know if filter is lowpass or highpass?

I was trying to solve the following question: Calculate the DFT of the given filter impulse response $h(n,m)$. Based on the result, determine if the given filter is a high-pass or a low-pass filter. ...
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5 votes
1 answer
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Algorithm that enlarges the image to a resolution of $2N \times 2N$ using DFT operations

I'm trying to solve the following question: Given an image at a resolution of $N \times N$. Describe an algorithm that enlarges the image to a resolution of $2N \times 2N$ using DFT operations. As I ...
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Understanding the result of the fft algorithm

Understanding the result of the fft algorithm. I need help understanding the FFT calculation results. Recently, I have been interested in signal analysis, so I have created and understood fft ...
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Calculating the DFT of the image after using a filter

Studying for my finals in Image Processing course. Trying to solve the following question: Let $h$ be a filter that replaces each pixel value with the average of it's 8 neighbors. Let $f$ be a ...
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Fourier Transform of an 2D image and associated units

I have the following rather simple problem and unfortunately I am not getting forward. Imagine a simple 2D image with pixels and a unique value for each pixel of the image. For example, let the image ...
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