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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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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How to interpret a 1D-DFT of an image with a sinus grating compared to it's 2D-DFT outcome?

For getting a better understanding on how the 2D-DFT works I was playing around with sinus gratings in grayscale. I tried to compute the 1D-FFT first and compare it with the 2D-DFT to get a better ...
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Multiply signal $x[k]$ with $\cos(2\pi\nu_0k)$, then given $X(\nu)$ draw resulting function in frequency domain?

Let $$y[k]=x[k]\cdot \cos(2\pi\nu_0k) .\tag{1}$$ Then, given a signal $x[k]$ with the DTFT $X(\nu)$ according to the following figure what will the frequency domain for $Y(\nu)$ look like for a ...
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Why is the arithmetic mean the same as the DC component of its fourier transform?

When we define $$\overline{\left|x\right|} = \frac1T\int_0^T x(t) dt$$ as the arithmetic mean of a signal we can see that it is the same as its dc component in the fourier transform. Why is this the ...
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Spectral function value of a frequency above the nyqist limit

this was the question on my today's exam on signals and systems: *We have a continuous function $f(t)$. Its value of the spectral function at an angular frequency of $8000\pi\ rad/s$ is $\frac{1}{...
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Mixing with Deformed Local Oscillator Signal

I've decided to build up an AM receiver which is intended to capture sound signals from a nearby broadcasting station that is operating at 954 kHz. I've completed the system design and started to test ...
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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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Why doesn't the magnitude of Fourier Transform change when signal is shifted (i.e when a time shift is introduced)?

I understand that a time shift in the time domain produces a corresponding phase change / phase shift in the frequency domain. But I don't understand why the magnitude is unchanged (I am referring to ...
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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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Unexpected result with custom FFT implementation

To fully understand the Fourier Transform I have been working on a rather standard implementation of the FFT algorithm. I tried generating a 440 Hz sin wave and passing it through the algorithm, ...
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2D Spatial Fourier Tranform on a pressure field

I'm doing some research on Fourier Near-field Acoustic Holography (NAH). The basic theory behind Fouerir NAH is that you take a sound pressure field measurement in a 2d plane p(x,y), 2d spatial ...
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What transformation preserves first term and averages the opposite conjugates?

I can't figure not find any reference on what is this transformation (what $X$ represents in relation to $A$). If $A=[a_1+jb_1, a_2+jb_2, a_3+jb_3, ..., a_n+jb_n]$, $X$ is defined as:$$X=\left[j b_1, \...
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Calculating the Norm of Each Sample of the DFT Transform

Given a discrete signal $ \left\{ x[n] \right\}_{n=0}^{N-1} $ and its Discrete Fourier Transform $ X[k] = DFT \left\{ x[n] \right\}[k] $. I'd like to effectively compute the norm of each sample of ...
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Why does the 2D-DFT of a sinus gradient not show energy along the diagonal straigh lines and only vertical/horizontal from the diagonal point?

I have been experimenting a little bit with simple examples of the 2D DFT to get a better sense for it's interpretation. For this purpose I have been using sinus gratings with the following code: <...
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Ft and DTFT of negative frequency

I have a question that might sound silly but if I have a real and even signal x(t) can I define the FT and DTFT of the negative frequency if I can show: $$X(-\omega) = \int_{-\infty}^{\infty} x(-t)e^{...
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Can you quickly find the inverse Fourier Transform using the duality property?

Cheers, in an exercise of mine I reach the point that I have to find the $F^{-1}\{Λ(ω)\}$ (where $Λ(ω)$ is the triangle function, with $1-|ω|$ for $|ω| \leq 1 $ and 0 elsewhere. Using the duality ...
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Doing the inverse of the fourier on EEG data?

I have EEG data. I have 51 values(complex numbers) that are supposed to represent the frequency. I plot the absolute values. They have negative values and have an imaginary component as well: ...
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Fourier Transform of the signum function, using the integral property

Cheers, I am trying to find the fourier transform of the signum function, which is $$ \operatorname{sgn}(t) \triangleq \begin{cases} 1 \qquad & t>0 \\ 0 \qquad & t=0 \\ -1 \qquad & t<...
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Find fourier transform given the graph of a function

Cheers, I am given the following graph for $x(t)$: and I am asked to find the fourier tranform by using the integral property and knowing that $F(Π(t)) = sinc (\frac{\omega}{2\pi})$ The solution I ...
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1answer
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Zero padding affects the DTFT?

I wanted to understand better how zero padding affects a signal: Which is just N ones. where $ N > 0$ is an Integer $$ X[n] = 1, 1, 1, ... 1 $$ Zero padding it gives: $$ X[n] = 1, 1, 1, ... 1, 0, 0,...
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Error in the computation of PSF?

I am in trouble computing a PSF of an optical system in optical turbulence. Background The optical transfer function (OTF) for an imaging system in optical turbulence can be modeled as the product of ...
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Phantom harmonics when using cosine windows why do they appear and how to avoid them?

Given an $L$ order cosine window, it is possible to show that the width of the main lobe is given by: $$\omega_w = \frac{2 \pi L}{(2N+1)}$$ Where $L$ is the order of the window, $N$ is the maximum ...
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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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Output of LTI (in time and frequency $\omega$ domain) : when input goes through LPF

I would like to raise a mathematical question : Let's say we are been given : $$x(t) = \begin{cases} \cos(\pi t) & |t| \leq 0.5 \\ 0 & \textrm{otherwise} ...
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I'm having problems simplifying this discrete-time fourier tranform

I have this problem, and I can't get to the solution. $$X(e^{j\omega}) = \sum_{n=-\infty}^{\infty} {(0.6)^{|n|}[u(n + 10) − u(n − 11)]}e^{-j\omega n}$$ The solution is $$X(e^{j\omega}) = \frac{0.64 − ...
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Questions about MP3 bitrate conversions

I was trying to analyse the lossy compression of MP3 audio files through their Spectrograms and the results were something like this (where the upper is 80Kbps and lower is 128Kbps). It is obvious ...
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iFFT and extracting dw

I have a trivial fourier transform question. I have a correlation function, C(t), with complex components in the time-domain, and dt. I would like it in the frequency domain, C(w), like from ...
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Is there an order to apply time shifting and frequency shifting to signals in DTFT?

For instance in one question applying frequency shifting first and then applying time shifting yields a different answer wrt applying time shifting first. Please elaborate i am clueless. if i use ...
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Detection of Troughs and Notches in a PPG Signal

I'm working a project which tries to determine Blood Pressure from PPG signals.I'm trying to extract the features as shown below... I'm having problem in finding the troughs and dicrotic notch for ...
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inverse fourier transform coefficients

Context I want to implement (real) cepstrum on stock data (for example MSFT stock) and achieve cepstral coefficients of this time series. as noted in "Cepstral-based clustering of financial time ...
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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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aperiodic sum of periodic signals

Asumme that a continous signal is a finite sum of sinusoid. If the signal "begins" at $-\infty$ and "ends" at $\infty$, using Fourier transform, one can find the frequency, the ...
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Relation between two k-spaces phase-frequency and spatial frequencies in

When I see MRI explained, two types of 2D k-space images seem to be described as if they were the same. Axes are the two spatial frequencies. This images is directly fourier-transformed into the ...
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Filter filters out more than needed

I am currently coding a school assignment. I have a 1.5s recording of someone's speech that has 4 rogue cosines mixed in. With sampling rate 16000Hz, I divided the recording into frames of 1024 ...
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Phase Correlation with Mask for Translation-Invariant Log-Polar Registration

At the moment, I have implemented a registration method utilizing the mask in the log-polar domain, which consists of the below steps: Algorithm 1 Transfer Image, Template, and Mask into Log-Polar ...
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A few last (general) questions about my FT programme

Third and (hopefully) last question from me about my FT program to display the magnitude of 18 discrete frequencies in the signal as a bar graph (audio visualizer). Good news first: I've now got 80% ...
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Problem identifying the analytic expression of such determined signal

I came across this problem I am supposed to find the Fourier transform of $g(t)$, but I am not able to find the analytical expression of such signal. The teacher suggests that I should consider ...
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2-d circularly symmetric low-pass filter

For a square pixel grid, the ideal 2-d low-pass filter with a horizontal and a vertical cut-off angular frequency $\omega_c$ in radians has an impulse response (kernel) $h_{\small\square}(x, y)$ that ...
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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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Is interpolation of an audio signal to increase frequency resolution possible?

I apologize if some of what I ask is not entirely correct, I'm new to this field, but extremely interested. I have an Audio signal of sample rate 44.1 kHz that I want to segment into 30 frames, and ...
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Unfortunately, my self-written Fourier transformation is not that good

In my question yesterday I said that I have a self-written Fourier transform and have to get to the data of the sound card. I have the latter now. I've already answered my question from yesterday. (...
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Palmprint Identification - Why do we align the images before we use the Fourier Transform?

I was reading the paper PALMPRINT IDENTIFICATION BY FOURIER TRANSFORM by WENXIN LI, DAVID ZHANG and ZHUOQUN XU about identifying persons based on an image of their palm. The first step in their ...
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Recovering phase of harmonics in an arbitrary pulse train

I want to recover the phase of the harmonic components of a pulse train. There's a lot of cool resources out there that talk about recovering power spectra from signals in several ideal and non-ideal ...
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What's the base and height of triangle obtained by FT{$\operatorname{sinc}^2(7\pi t)$}?

I'm a little confused about the $\operatorname{sinc}^2(7\pi t)$ function. How do you know the base and height of the triangle produced in the frequency domain only looking at the $\operatorname{sinc}^...
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How to calculate the Fourier transform of a mean filter in Matlab?

In Matlab, how can I calculate the discrete-space Fourier transform of a mean which takes the average of 4 adjacent points, with this kernel $$\begin{pmatrix} 0 &1& 0\\ 1 &0&...
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How to use inverse 2D Fourier transform to reconstruct the original image?

I have managed to get the forward Fourier transform of an image to the frequency space like so: But I cannot for the life of me reconstruct the original image from the inverse Fourier transform of ...
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Why don't I see linear chirp for IFFT of gaussian with quadratic phase?

I am trying to set up a program for numerically simulating a pulse in the time domain after it is transmitted through a material that imparts linear, quadratic, and third order phase in the spectral ...
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Why the energy is a good feature extraction for detect disturbances in signal processing?

To detect disturbances in signal processing a common step is to extract signal characteristics to analyze them, among these characteristics it is recommended to use the signal energy. Why energy is ...
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Confusions regarding differences between Fourier transform & Laplace transform?

Although this topic has already been addressed in multiple popular questions of SE but i have few confusions in this regard Number 1) Link of question https://electronics.stackexchange.com/questions/...
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What will the output of a system which has no Fourier transform?

Let's assume a system $h(t)= e^{j2t}$. This system has no region of convergence. What will be the output if I provide any input to this system?

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