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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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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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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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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I would like to raise a mathematical question : Let's say we are been given : $$x(t) = \begin{cases} \cos(\pi t) & |t| \leq 0.5 \\ 0 & \textrm{otherwise} ... 1answer 76 views I'm having problems simplifying this discrete-time fourier tranform I have this problem, and I can't get to the solution.$$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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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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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 ...