Questions tagged [fourier-transform]

The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.

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Reconstruct $x(t)$ from $y(t)$ and $z(t)$

Let $x(t)$ be band-limited signal with $X(j\omega) = 0$ for $|\omega|\gt \omega_M$. We use $$s(t) = \sum_{k =-\infty}^{+\infty}(-1)^k\delta(t - \frac{kT}{2})$$ for sampling. So we have $z(t) = x(t)s(t)...
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24 views

RMS of signal vs average amplitude

I am trying to estimate the average amplitude of some signal with frequency 6 Hz, sampled at ~300 Hz. See figures for a part of the signal and its dft calculated using matlab. I estimate the average ...
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21 views

Does it make sense to apply convolution in the frequency dimension of a fourier transformed signal?

What I have is more likely a theoretical question. Since I am not from a signal processing background it is hard for me to grasp the issue in using convolution in the frequency dimension of a Fourier ...
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38 views

What is the gradient of fft?

I have a time-series of length N generated by the following equation: ...
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36 views

Zero-padding or Interpolation in 3D FFT

I'm trying to perform a FFT of a 3D regular grid and then compute the bin average (in spherical shell bins) of the Fourier transformed grid. The problem is that the resulted vector is very noisy as I'...
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20 views

Calculating Transfer function numerator and denominator from the rationalfit model

I have a frequency response data called 'AC_data' which is a vector of complex numbers (real and imaginary part) at different frequency points. I have calculated a rationalfit model for the AC_data ...
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16 views

finding FL and FH from continuous time signal

I have a continuous signal $x_{a}$ which is defined as $X_{a}(F)=0$ for $|F|>B$. Now if I multiplied the continuous signal $x_{a}$ by $cos6\pi Bt$. Then the fourier transform of the signal can be ...
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21 views

How to identify the frequencies of periodic peak signals in a noisy time series?

Suppose to have two time series with peak signals at different frequencies, like these two: ...
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27 views

$2\pi$ Periodicity is not working for me for Fourier of Discrete Time Signal

please help me find the error in the following counter example. Consider we take sinus with period of $2\pi$. We sample it many time, and more than 3. We make convolution with rectangle of height 1 ...
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45 views

STFT of ISTFT in the Griffin Lim Algorithm

The Griffin-Lim algorithm for phase recovery (based on the magnitude of an STFT) involves a step that is: STFT(Inverse STFT(...)). This seems to be the key iteration in the algorithm. This Quora ...
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34 views

How will magnitude and phase spectrum of an imaginary function would look like? Like if $x(t)=j \text{rect(t)}$. Is phase spectrum even or odd?

I am confused between when a phase spectrum is odd and when it is an even function of $\omega$(angular frequency, Fourier transform variable).
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Finding the frequency response $H(\omega)$ of a shifted sinc function

Given $$h[n]=\frac{\sin\left(\frac{\pi}{3}n-\frac{\pi}{3}\right)}{\pi n-\pi}\text,$$ use the table to find the frequency response $H(\omega)$. I don't have any clue that how to deal with the ...
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Rule of thumb / Best practice for Audio (voice) data normalization for use in Classification

TRIVIAL QUESTION: I am currently working with some audio data of speech utterances. I am attempting to perform classification on the data based on the phonemes. This means that I manually label the ...
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27 views

How to apply FT to real-life signal that labeled in seconds, not radians

In training examples we always do a transformation on signals which have t-scale in labeled in radians. I understand that Pi is just a number, but I still have some troubles to understanding how to ...
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49 views

Time domain to frequency domain conversion of audio signals to extract 1/3 octave frequencies

I am writing first time in this forum and I am not expert in programming and FFT. We have developed an android app (Noise Tracker) for noise measurement using smartphones. It displays noise levels in ...
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30 views

Resources to understand DSP visually in 2020

I know you have been asked several times but the questions are old, and I would like to know if there are new intuitive web pages of applets or interactive DSP animations (Filters, FFT, Wavelets)
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25 views

Partial column approximation error

Can someone help me understanf how to plot the next partial column in MATLAB: while N=2001 |M|<700 ak =
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15 views

Scalable gaussian window

I would like to determine fractional fourier transform of scalable gaussian window function Can I get help on implementing g(t,u) in MATLAB?
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Why is my Fourier descriptor not rotation invariant?

I am trying to implement a simple contour based Fourier descriptor to classify some MNIST images. Nothing fancy. As expected, if I discard the first coefficient, I achieve translation invariance. ...
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25 views

What is the relationship between a signal's Marginal Hilbert Spectrum and Fourier Spectrum?

I am looking at the differences between Marginal Hilbert spectra and Fourier spectra and I was wondering what the mathematical relationship is between them and under what conditions they become ...
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1answer
63 views

Calculating the magnitude spectrum and phase spectrum

From a window function $x(t)=u(t+2)-u(t-2)$, we can get the Fourier Transform $X(j\omega)=\frac{2\sin(2\omega)}{\omega}$. Then, I want to calculate its magnitude spectrum and phase spectrum. The ...
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1answer
37 views

Determine reflections from received signal

I have a reference signal $r(t)$ and the correlation between that reference signal and the received signal : $C_{XR}(\tau)$. The signal I receive contains reflections on walls. I have to build a ...
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62 views

Why is it assumed that $x[n]$ is limited from $0$ to $N-1$ while evaluating DFT?

I am a total beginner in this topic of DFT. I get that the series must be finite for DFT calculation. But everywhere we are assuming that this series must be limited from $0$ to $N-1$. How to evaluate ...
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23 views

How to find phase of two fixed Gaussian of periodical signal (analytically)?

For a periodical signal define on $\phi \in [0, \pi * 2)$, there was supposed to be two peaks, may following Gaussian, but may also be Cauchy or other distribution with one peak, plus Poisson noise. ...
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31 views

Are higher frequency components of constant amplitude of a square wave dependent only on the rise time and independent of square wave frequency?

This question based on the observation that ringing on square wave due to multiple reflections on a transmission line doesn't change with the change in frequency of square wave. From this observation ...
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Create 2-d Dirichlet kernel for use in image processing

I am working on frequency domain CNNs for image classification task, in which I initialize complex kernels of size (k*k). For performing point-wise multiplication between the kernel and the Fourier ...
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1answer
110 views

How to make low pass filter using frequency sampling method?

https://www.allaboutcircuits.com/technical-articles/design-of-fir-filters-using-frequency-sampling-method/ So there is two main equation: I wish to filter out frequency $\le 10000Hz$, for example. So ...
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56 views

Torque signal fft

I have the following torque signal picked up with a 10.240Hz sampling rate from a testbench. I am studying its fft which I create on Octave with the following code: ...
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13 views

average value of modulated signal with Fourier Analysis

I am using an instrument that uses a modulated heating program. The instrument returns an average heat flow signal calculated from the modulated heat flow. I would like to understand how this average ...
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15 views

Why does spectral accuracy of laplacian decrease with sampling size?

We know that for any real-valued function $f(x,y,z)$ whose Fourier transform is $\mathcal F[f]$, its laplacian can be computed from a spectral interpolant as follows. $$ \Delta f(x,y,z) \simeq \sum_{...
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34 views

How to create a synthetic time series where power spectral density estimation is achieves better results than a direct Fourier transform?

I am trying to create a synthetic time series where PSD estimation is necessary and useful to recover the correct spectral information of the time series. But so far I can only create a time series ...
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20 views

Cancelling effect of a system on a signal

I have a signal $A(t)$ and it's been transformed using an unknown system to a signal $A'(t)$. I also have another output signal $B'(t)$ from the same system and I want to retrieve the corresponding ...
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48 views

express pass band filter as sum of low pass filter

I have to find impulsive response of an ideal pass band filter, but I have a problem to express $$ H_{BP} (f) $$ as a sum of $$ H_{LP} (f) $$. I mean that $$ H_{BP} (f) = rect ( \frac{f-f_0}{B} ) + ...
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Interpolating the spectrum at L levels

I am new to signal processing but having some experience in implementing Fast-Multipole-Method (FMM - single level) and now looking forward to understand the interpolation of samples from fine $\...
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68 views

Energy of a sinc signal

My book give me two signals to demonstrate that the temporal translation does not alter the energy and area. It gave me $$ x(t)=\operatorname{sinc}(t) $$ and $$ s(t)=x(t-T)$$ and I found that ...
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25 views

Fourier Transform of an acceleration signal containing engine orders

I am trying to understand how to evaluate this equation in the context of acceleration data which contain engine orders $a^{f_{e}^{crit}}(f)=\sum_{o}^{K}A^{o,f_{e}^{crit}}\mathscr{F}(cos(2\pi \cdot ...
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67 views

How to design FFT for 2000 points?

How should I design FFT with fixed samples - always 2000, sampling frequency is also 2000, memory is external, there is no need to get sorted array. As far I know it may go like factoring 2000 into $2^...
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1answer
66 views

Relationship between real and imaginary part of a real-valued and causal system

I have one question about the real part of a real-valued and causal system with the imaginary part of its Fourier transform given by $$\textrm{Im}\big\{X(e^{j\omega})\big\}=3\sin(2\omega)-2\sin(3\...
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58 views

inverse discrete FFT in python, multiple times?

I was wondering what really happens when taking the inverse discrete FFT on some set of numbers, for 3 times? Because looking at it, it looks like we're getting an output that is identically with the ...
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1answer
84 views

Fourier Transform of the full Morlet wavelet

In 2014 someone asked here the Fourier transform of the Morlet wavelet; link below: Fourier Transform of Morlet wavelet Function? However, it was the approximated Morlet wavelet not written with the ...
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161 views

Getting different spectrum from velocity, and position data using Omega arithmetic

I am solving a very long problem and one part of it requires me solving an ODE and computing FFT of the resultant data. Essentially I have a differential equation$\frac{dz}{dt}$ for velocity, from ...
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26 views

Limitations in Backing Out a Transfer Function

Suppose you have an LTI system for which the (complex) frequency response $H(j\omega)$ has been measured in some frequency window $[\omega_1,\omega_2]$. Now imagine that you want to provide an input $...
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17 views

Formula for PSD across an axis of a 2D output

Consider a 2D stationary input $e(x,y)$ and a 2D real convolution function $h(x,y)$. Let $S=h*e$ be the result of the convolution of $e$ by $h$. If needed, we may assume $e$ is isotropic (spectrum ...
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I want to invert my fourier transform components to waves again

Hi I am using R to analyze some data I basically did fft(data) and got a vector of complex numbers but from that now I want to remove certain harmonics from my actual wave but how do I convert one of ...
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1answer
41 views

Fourier transformed acceleration from Fourier Transform of velocity and position using Omega arithmetic

Let's say the position of an object is given by simple sine function. By elementary calculus, I can calculate the acceleration in the time domain and find its Fourier transform. I can also calculate ...
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81 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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150 views

turn circular convolution into linear convolution by zero padding: A special case

We know that, multiplying a kernel and signal spectrum in Fourier domain will lead to a circular convolution and not a linear convolution, so in order to it become linear convolution we must zero pad ...
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1answer
42 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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17 views

DTFT based Frequency Sampling

H($e^{jw}$)= 1, |w| < $\pi/2$ and 0, $\pi/2$ <= |w| <= $\pi$ I took M equally spaced frequencies from 0 to $2\pi$. If we assume h[n] to be causal, $H(e^{jw})$ should have some phase and it'...
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68 views

Why does an anti-symmetric function has zero amplitude at the center of an even length window

I am performing FFT on a real odd function and the resultant transform has zero amplitude in the last bin. Essentially if Y= rfft(X), then Y[-1] is always zero. I stumbled on this answer which says ...