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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Find response of discrete time LTI system given input and impulse response
For this question the guide says to use $Y(e^{j\omega}) = H(e^{j\omega}) X(e^{j\omega})$.
I have been able to find the discrete time Fourier transform of the impulse function as $$H(e^{j\omega}) = \...
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How to obtain the exact value of wavelength from a 2D FFT amplitude vs wavenumber plot like it is obtainable from 1D FFT amplitude vs wavenumber plot?
I have a two dimensional multi modal spatial signal generated from a MATLAB code using sinusoidal functions of different wave numbers, amplitudes and phases. What I want to know is that if I have the ...
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Sampling with an alternating phase offset
Suppose, I sample a signal $z=\mathrm{e}^{\mathrm{i}\omega t}$ alternatingly in $I=\mathrm{Re}(z(t))$ and $Q=\mathrm{Re}(\mathrm{e}^{\mathrm{i}\alpha}z(t))$. Thus my data array contains
$$\texttt{data ...
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How to get a non-equally spaced FFT back into the time domain
I have a signal that I STFT and then filter using an ERB spaced filterbank. At some point after this I want to get the signal back into the time domain, how can I go about this? Using a standard iSTFT ...
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FFT of a stretched vector
Lets say I have a small size vector x=[a b c d]. Now I stretch this vector 3 times and I got x3=[a a a b b b c c c d d d]. What would be the relation between fft(x) and fft(x3)?
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Digital Signal Quantized Processor Complexity
In “traditional” digital signal processing, the complexity is computed as a number of multiplication the operation requires, e.g. the computation of the N-point DFT via the decimation-in-frequency FFT ...
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Short Time Fourier Transform has different frequencies than Fourier Transform?
The reason we do the STFT is so that we can analyse for short segments of time how much of the components in the frequencies of the FT are present. However, it may be possible that completely ...
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sampling system and signal [closed]
The signal $x (t)$ with a Fourier transform is given $X (jw)$ The signal enters the system shown in the figure:
These are the data I received:
The question are these:
Find a condition on $T_1$ for ...
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Fourier Transform: $\omega$ vs $f$ as frequency variable
I try to understand how the Fourier transform changes when I try to compute $X(\omega)$ or $X(f)$. Can someone work me through the maths please for two examples, $x(t) = \exp(j\omega_0 t)$ and $x(t) = ...
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Replicate MATLAB's `conv2()` in Frequency Domain
When conv2d is on valid mode, the image needs no padding, because the result is the same size as the image.
When conv2d is on ...
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FFT of square wave - what does output represent?
I am really new to FFT and signal processing. I am doing an analysis of square waves with FFT and I am trying to understand why the FFT output on the frequency domain has a downward slope for square ...
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Does $\cos(bt)\cdot u(t)$ have a Fourier Transform?
If it does,
$$\int_{-\infty}^{\infty} \cos(bt)\,u(t)e^{-j\omega t} dt = \int_{0}^{\infty} \cos(bt)\,e^{-j\omega t} dt = \int_{0}^{\infty} \frac{e^{jbt} + e^{-jbt}}{2}\,e^{-j\omega t} dt$$
Then how do ...
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Confused with using Fourier Transform Properties
I'm seeking the Fourier transform of $t \cdot (u(t+1)-u(t-1))$
Given the fact that (The first minus here should be a plus)
Using properties.
My initial approach was:
but I wasn't sure how I should ...
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Inverse Fourier transform of complex exponential with frequency dependent shift
In the case of a constant delay $\tau$, we have the following equality:
$$\begin{align}\mathcal{F^{-1}}\left\{e^{-j\omega \tau}\right\}=\delta(t-\tau)\end{align}$$
If the delay is frequency dependent $...
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transform signal
Hello everyone I need help solving a Fourier transform for the given signal, I know it will be a frequency convolution for the first function it will be a window function and for the second function I ...
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Confused about the Fourier Transform of $e^{at}u(t)$
This is the problem at hand:
I'm unaware of why we didn't have to say anything about $\omega$ like that it should be also greater than $0$, I know it's variable...but it's multiplied by $t$ ...
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How to relate the cyclic spectrum to correlation between different frequencies of the fourier transform? [closed]
https://en.wikipedia.org/wiki/Cyclostationary_process defines
and then asserts
That assertion is used to justify cyclic periodograms which estimate the cyclic spectrum by taking the correlation ...
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MATLAB Plot of FT(Cos) Displays Weird Impulse
It is known that:
$$
\mathcal{F}\{\cos(2\pi t)\}=\frac{\delta(f-1)+\delta(f+1)}{2}
$$
However, on MATLAB, I used F=fftshift(fft(x))/N; to obtain the FT of $\cos(2\...
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calculate or decompose a Fourier transform signal amplitudes with unknown weights on sources
migrated from math-se...
I am trying to calculate , or approximate the solution of following Fourier-sine transform problem that can be expressed as a contributions of periodic sources $f_i(x)$ and ...
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Can I find the frequency when I have a signal is an array on python? [duplicate]
I got an signal:
...
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$\int_{-\infty}^{+\infty} |G(f)| \,e^{j2\pi ft}df=|g(t)|$?
Given the absolute value of the Fourier transform of a signal $g(t)$:
$|G(f)|$
If I compute the inverse Fourier transform of $|G(f)|$,
$$\int_{-\infty}^{+\infty} |G(f)|\, e^{j2\pi ft}df$$
do I obtain ...
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Interference fringes movement analysis
I have searched Stackexchange forums for ideas, but could not find anything useful for me. I am registering real-time stability of the He-Ne laser interferometer by analyzing interference fringe ...
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Application of the spherical Radon transform property in tomography
Let function $f$ be even and continuous on the unit sphere $S^n$. Let $R$-be a spherical Radon transform.
There is a known property:
$R(f^n)=f$ whenever $f$=constant.
What would this property mean in ...
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Proof of Bedrosian's theorem
I was looking for a straightforward proof for Bedrosian's theorem which says the Hilbert transform of the baseband signal times the passband signal is the original baseband signal times the Hilbert ...
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Adding noise in frequency domain while solving an SPDE
I’m implementing a numerical solver to a certain kind of a 2D stochastic PDE using Fourier Transforms.
So, this solver is a Galerkin type method, which means that choosing the right basis functions I ...
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1answer
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FFT/PSD/IFFT analysis on single axis piezoelectric accelerometer signals for curb impacts
I'm trying to denoise the signal by performing PSD analysis and followed by IFFT. Ultimately, I want to generate Force and Displacement plots from the denoised acceleration signal.
Noisy Acceleration ...
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1answer
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Where did we get the DC term of the Accumulator from DTFT?
Define $y[n]:=\displaystyle\sum_{m=-\infty}^{n}x[m]$. The DTFT is found as follows:
\begin{align*}
y[n]&=\sum_{m=-\infty}^{n}x[m]\\ \\
&=\sum_{m=-\infty}^{n-1}x[m]+x[n]\\ \\
&=y[n-1]+x[n]\\...
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1answer
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Spatial domain vs. Frequency domain filtering of an image. Which one is better?
The question might seem naive but I'm new to this and a little confused.
So, I recently came to know that gaussian smoothing can be applied to an image both in spatial domain and in frequency domain. ...
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I cannot find reference (paper) of this relation $u(t)t^{α} ↔^{FT} f^{-(α+1)}$
I am struggling a lot in finding the reference (book or, even better, academic paper) that states that:
$u(t)$ $t^{α} ↔^{FT} f^{-(α+1)}$
as I found here An Interesting Fourier Transform - 1/f ...
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Why is there a time-frequency precision tradeoff
I understand the science - I think. Looking at a spectrogram, the lower frequencies are fuzzier due to a lower ratio of: frequency/time.
My main question is: why ...
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How to visualize this statement regarding Conjugate Symmetry
A property of real signals states that if $x(t)$ is real then the Fourier series coefficient (frequency spectrum) is given by :
$$
c_{k}=c_{-k}^{*}
$$
In polar form, this can be expressed as :
$$
|c_{...
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3-point DFT with two multiplications
I'm trying to understand DFT in the context of an integer ring (i.e. the number theoretic transform) and I was wondering how to reduce the number of multiplications by the twiddle factors.
Consider 3-...
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How can I Improve my 2D Fourier Transform Graph?
I'm very new to signal processing. I have been tasked with running Fourier analysis on some velocity waves that I have found in a simulation. My supervisor would like me to plot the angular velocity ...
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Physically, what does the usage of two variables mean for convolution
My intuition of convolution is that it is just a way to depict multiplication of two signals where each signal is made up of various frequencies and phases.
Since it isn't easy to find the value of $\...
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1answer
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What is imaginary part after IFFT and how to use it?
let's say we have signal in time domain.
After we make FFT on it we will receive that signal in frequency domain.
And as far as I know the real numbers mean magnitudes of each frequency bin, and ...
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Can velocity be calculated in first stage FFT?
I understand that, For an FMCW radar, the velocity of a target is proportional to the phase changes at same time instants across the chirps.
I have a MxN data cube with N chirps(columns) & M ...
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1answer
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Why is the range of frequency for discrete time Fourier transform $-\pi<\omega<\pi$? [duplicate]
In my class we are taught that the range for the frequency is $-\pi<\omega<\pi$ for discrete time Fourier transform, however for continuous time the limit is $-\infty<\omega<\infty$
why is ...
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1answer
71 views
Scaling the input vs scaling the impulse response for an LTI system
Two different cases:
We pass $x(t)$ to an LTI system with impulse response $h(2t)$ and get the output $y(t)$.
We pass $x(2t)$ to an LTI system with impulse response $h(t)$ and get the output $z(t)$.
...
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1answer
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Unilateral Laplace Transform's Differentiation Property
I've read in numerous places that the unilateral laplace transform is extermely useful in solving differential equations with initial conditions based on the differentiation property of the unilateral ...
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Inverse Fourier Transform of piecewise function
Objective : Compute $y(t)$ from $Y(j\omega)=H(j\omega)X(j\omega)$ where :
$$
x(t)=\left(\frac{\sin(2t)}{\pi t}\right)^{2}
$$
and
$$
H(j\omega)=\begin{cases}e^{-j\omega}&\text{if $|\omega|<4$}\\...
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Integration of FTIR Absorbance Spectrum in Python
Hello I have a FTIR (fourier transform infrared) absorbance spectrum of a sample, Integrating the single lines is correlated to the quantity of substance present in the sample.
The spectrum part I'm ...
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Update: Fourier Transform of a shifted and scaled $\operatorname{sinc}$ signal
Let $x_N$ be the function given by
$$x_N(t)=A\frac{\sin(M\pi(t-N))}{\pi(t-N)}$$
The Fourier Transform of $x_N$ is
$$\begin{align}
X_N(j\omega)&=\mathscr{F}\{x_N\}(j\omega)\\\\
&=\int_{-\infty}^...
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Clarification Regarding Changing the Variable
Assume I have that :
$$
X(j\omega)=\begin{cases}e^{-2\omega}&\text{if $|\omega|<2\pi$}\\0&\text{if otherwise}\end{cases}
$$
Say, I want to make this change substitution $X(j(\omega-\Omega))$...
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Pure Imaginary Poles (Why is it problematic?)
Consider the LCCDE :
\begin{equation}
\sum_{k=0}^{N}\alpha_{k}\frac{d^{k}f(t)}{dt^{k}}=\sum_{m=0}^{M}\beta_{m}\frac{d^{k}g(t)}{dt^{k}}
\end{equation}
Taking the Fourier transform on both sides, we get ...
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Welch Method FFT Python - Scaling factor?
I've been implementing a Welch method FFT and I am trying to work out the correct scaling factor that should be applied to the output of the function so the PSD is accurate because at the moment it's ...
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1answer
28 views
Is there an a method to fit a wave created from two wave?
I need to get the frequency and amplitude for a wave that consists of multiple function.
for example, if I have a sine curve (created from two sine waves), How can I extract the parameters for this ...
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Analysing DAC Spectra: Transient Noise Analysis
I am working with a new Digital-to-Analog Converter (DAC) design in simulation and I'm trying to analyse the output. The device takes in an ideal 14-bit digital representation of a sine wave and ...
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Inconsistency Between Analysis and Simulation Results of Fourier Transform of a Sinc Function
First of all, hello.
This question is about a problem that I’ve faced during an attempt to obtain both time and frequency responses of a sinc function in MATLAB. The problem is an inconsistency ...
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382 views
Meaning of a null coefficient at 0 Hz
I am analysing a wave with a timespan $\tau$ and after applying the fft I obtain the following plot of the coefficients
I assume that the peak at $t=1$ followed by smaller coefficients means that the ...
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2answers
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Amplitude spectrum (transfer function) of signal?
I have one question related to finding amplitude spectrum (transfer function) of signal knowing that output signal is time derivative of input signal. I have the answer graph but I don't understand ...
