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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6 votes
2 answers
561 views

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 ...
3 votes
1 answer
65 views

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 ...
0 votes
1 answer
47 views

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_\...
6 votes
2 answers
773 views

Color Artifacts in Fourier Transformed Image

I am working with images and Fourier transforms. I am trying to understand what might be causing some artifacts in my output image. I am starting with a 512x512, RGB image of Lenna. I FFT the image,...
1 vote
1 answer
56 views

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 = ...
8 votes
3 answers
5k views

Why calculate negative frequencies of DFT?

This answer says that when calculating the DFT on a real valued signal, the (roughly) second half of the bins are the complex conjugates of the first half of the bins. Firstly I was curious if that is ...
4 votes
0 answers
68 views

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 $\cos$ ...
0 votes
1 answer
34 views

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, ...
-2 votes
2 answers
93 views

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 $t < 0$, ...
18 votes
8 answers
17k views

Why Does the DFT Assume the Transformed Signal Is Periodic?

In many signal processing books, it is claimed that the DFT assumes the transformed signal to be periodic (and that this is the reason why spectral leakage for example may occur). Now, if you look at ...
1 vote
0 answers
48 views

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 ...
1 vote
1 answer
92 views

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 ...
-1 votes
1 answer
173 views

DFT of Sinusoid Peaks

I am studying DFT of sinusoids, and my professor gave me this signal. Sinusoid Frequency: 100Hz Number of Samples: 512 Sampling Rate: 8 kHz Plotting the spectral plot I have the following: I was ...
4 votes
2 answers
506 views

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 ...
-1 votes
0 answers
34 views

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 ...
7 votes
2 answers
558 views

Circular Convolution Matrix of $ {H}^{H} {H} $

We all know that Discrete Fourier Transform (DFT) corresponds to circular (not linear) convolution. That is to say, if $x(n),h(n)$ and $y(n)$ is the original signal, the filter and output signal in ...
9 votes
5 answers
2k views

DFT-like transform using triangle waves instead of sin waves

We know that DFT (discrete Fourier transform) breaks down a signal into multiple frequencies of sine waves. Does there exist a transform that does the same thing, but for triangle waves? For my ...
-1 votes
1 answer
144 views

Calculating phase of DFT sinewave?

I have been attempting to make a basic, slow, DFT in Matlab and have noticed peculiar behavior that I don't understand. I have been trying to plot the phase of a 100Hz sinewave captured at 250kHz ...
3 votes
1 answer
5k views

Power spectrum estimate from FFT

I'm plotting the FFT power-spectrum of a signal in MATLAB. I uploaded the 8000 samples time-series signal in a text file here: http://wikisend.com/download/896484/signal.txt I'm using the following ...
1 vote
1 answer
167 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 $$0.9 (z^2 -1.14z + 0.941)$$ and $$z^2 - 1.0232z + 0.757$$ Does anyone explain how he got those numbers?
-1 votes
1 answer
78 views

Fast fourirer transform - Even and odd numbered elements

I'm trying to understand some optimizations on DFT. So in this step, there is a note like the following: The next step involves the mathematical observation that the even-numbered elements can be ...
2 votes
1 answer
372 views

Flipping of x axis values when the Fourier Transform is compared to the FFT

EDITED 3-Jun-20 I have a lorentzian lineshape $$ f(z) = \frac{1+iz}{R(1+z^2)} \qquad (1)$$ where $$ z=\frac{-2\pi(f - F0)}{R} \qquad (2)$$ and $ R $ is the decay rate, $ f $ is the frequency, $ F0 $ ...
0 votes
0 answers
30 views

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 ...
1 vote
3 answers
652 views

Interpolation from discrete time fourier transform in python

I have a function that I sample from over one period. I want to use the Fourier Transform to learn the function and then predict unsampled values. Please see the code below: ...
0 votes
2 answers
30 views

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 ...
2 votes
1 answer
60 views

Averaging of a phase flipping signal

Suppose I want to average a signal $s(t)$ which consists of several spectral components without any DC offset. I sample $M$ points in the time domain. I am interested in the power spectrum which I get ...
10 votes
3 answers
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 ...
0 votes
1 answer
152 views

Inverse FFT - Synch the Phase

Is there any way to synchronize phase of output of inverse DFT in each buffer? When I send the output of inverse DFT to the ...
0 votes
1 answer
84 views

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: ...
0 votes
1 answer
90 views

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 ...
1 vote
2 answers
250 views

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 ...
0 votes
0 answers
108 views

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: ...
0 votes
1 answer
42 views

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 ...
0 votes
2 answers
84 views

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 ...
4 votes
4 answers
2k 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)...
1 vote
1 answer
42 views

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) = ...
1 vote
1 answer
54 views

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'...
2 votes
1 answer
105 views

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 ...
2 votes
1 answer
92 views

Symmetries of analyticity / zero self-correlation

I seek to understand symmetry properties of analytic sequences, without referring to frequency domain: what criteria must a complex sequence $x[n]$ satisfy to be analytic? Framed alternatively, such a ...
2 votes
0 answers
151 views

What is the variance of DFT of Fourier coefficient of difference of a vector of white noise?

Consider $\big\{x[0], x[1], \ldots, x[N-1]\big\}$. Suppose, \begin{cases} x[n] \sim \mathcal N\left(0, \sigma^2\right)\\ \big\langle x[n], x[n-1]\big\rangle = \frac12 & \forall \ n\\ \big\langle x[...
0 votes
0 answers
25 views

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 ...
-1 votes
1 answer
152 views

Using Inverse DFT to reconstruct a sampled sine wave is not perfect?

Start with a 2 Hz signal. The signal is sampled at a 4.167 Hz sample rate. The intent is to reconstruct a sampled signal (top right side) to be identical to the original signal (top left side). ...
0 votes
1 answer
129 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, ...
1 vote
1 answer
213 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 ...
-1 votes
1 answer
141 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 ...
0 votes
1 answer
46 views

DFT explanation for a given signal providing samples per second and total samples

I'm new to the topic of DFT and I need to understand the following question in detail because I'm a bit confused and I need to solve the requirements needed using any programming language so taking ...
8 votes
4 answers
5k views

What is Frequency Resolution?

Im trying to tackle the following problem while still not having a firm idea on what "frequency resolution" means : Suppose we sample a continuous time signal with sampling period Ts = 1/2000, and ...
0 votes
1 answer
27 views

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 ...
-1 votes
2 answers
1k 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.
0 votes
0 answers
13 views

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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