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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Is there any optimised algorithm to calculate 2D fourier transform

I m trying to implement my own code for finding the 2D fourier transform of an image in MATLAB using the formula for it, but it take toooo much time to come up with the answer, is there a defined fast ...
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DFT of time reversed signal

I was looking into proof and find something strange: The last part we obtain from DFT definition. $$X[k] = \sum^{N-1}_{n=0}x[n]W^{kn}_N, \quad\text{Where}\quad W^{kn}_N = e^{-j\frac{2\pi}{N}nk}$$ ...
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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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How does a Hermitian FFT work in Numpy?

Say, I create a Hermitian complex signal using, import numpy as np t = np.arange(-4, 4) z = np.exp(1j * t) Here z should be a ...
287 views

Mathematical relationship between highpass and lowpass filtering

Let $g, h_{HP}, h_{LP}: \mathbb{R} \rightarrow \mathbb{R}$ and $G, H_{HP}, H_{LP}$ denote their continuous Fourier transforms under the Fourier operator $\mathcal{F}$. Let $*$ denote the continuous ...
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Windowed Fourier Transform

I need some help with applying the properties of Fourier Transform. We define the windowed Fourier Transform of $f \in L^2(R)$ as $$Sf(\mu,\xi)=\int_\mathbb{R}f(t)g(t-\mu)e^{-i\xi t}dt$$ Prove ...
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FFT of resultant of signals

If one has two signals (say, two acceleromters mounted perpendicularly) and a piece-wise resultant acceleration signal is determined, it appears that frequency content information cannot be determined ...
238 views

Finite moving average filter

I am trying to solve this problem but I need a lot of help. Below are my answers for the separate parts, please check and tell me where I am wrong because I am weak on the fundamental concepts of this....
326 views

Relation between samplingrate and frequency

I am working on Fourier Transformation, and applying this for recognizing an audioclip. I have a 9 second long audio clip of a guitar strumming an A-Minor. The audioclip has a sampling rate of 44100 ...
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How to calculate multiplication of two discrete series

Short version: How to multiply two discrete sequences? Long version: Convolution of two discrete sequences is weighted sum. For instance, convolution of two sequences: ...
103 views

Plotting a sampled signals DTFT using its CTFT

So I know the connection between the DTFT and the CTFT is the following: Where the left-hand side is the discrete time fourier transform. I need to choose a sampling rate which won't cause any ...
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Confused on the difference between the frequency spectrum of an entire song, and the frequency spectrum of a point in time

I am very much a beginner in this field - but find it really interesting. However I am a little confused on a certain area of knowledge. If I have understood correctly: At any point in an audiosignal,...
264 views

Why do wavelets integrate to 0 and how do they match a signal?

I have been reading about the Wavelet transform recently and its relationship to the Fourier transform. From what I understand the wavelet transform represents signal data with many short-lived ...
499 views

Combining spectrograms with different windows to getting arbitrary time and frequency resolution

Spectrograms convert an amplitude-time signal into a frequency-time signal using Short Time Fourier Transform (STFT). The window size L used in STFT is a design choice. As L increases, you get higher ...
2k views

How to do simple extrapolation with Fourier transformation?

I have 1024 sample points, and I would like to do really simple extrapolation using Fourier transformation. First I apply Fast fourier transformation on the data. My first intuition was that I just ...
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Difference in Interpretation: $ω$ (rads/s) vs. $ω$ (rads) and $X(ω)$ vs. $X(e^{jω})$

The fourier transform of a continuous time signal $x(t)$ is $X(ω)$ where the unit of $ω$ is radians/second. And for a discrete signal $x(n)$, the DTFT is $X(e^{jω})$ where the unit of $ω$ is radians. ...
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Parseval's Theorem for discrete series

I need to use Parseval's Theorem to find \begin{equation} S\:=\:\sum _{n=-\infty }^{\infty }\:\left[\left(\frac{\sin\left(\frac{\pi }{4}n\right)}{2\pi n}\right)\left(\frac{\sin\left(\frac{\pi \:}{6}n\...
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How can a changing signal be Fourier transformed?

Fourier transformation is used to split a periodic signal into frequencies, and calculate the phase and shift for each frequency. But what if we would like to record an audio, which is changing, for ...
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Fourier Transformed a signal $f(t) = \cos(2\pi*4t)*5\cos(2\pi*0.4t)$ but did not get expected results. What went wrong?

I created a signal with two sinusoidal components by specifying $$f(t) = \cos(2\pi*4t)*5\cos(2\pi*0.4t)$$ I expected with I used MatLab's fft function on this that signal that I would see a peak ...
213 views

Inverse Fourier Transform of the real part of fourier transform, and inverse transform of the imaginary part of fourier transform [closed]

How can I calculate the inverse fourier transform of the real part of the fourier transformation?
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Inverse DTFT of left-sided sequence

I am pretty new to inverse Fourier transforms and I would like to ask a question. Does anyone know how to bring back to the "sequence domain" this relation below? In other words, get the inverse DTFT ...
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Meaning and unit of frequency in Laplace (Fourier) transform

Imagine transfer function obtained by Laplace transform, for example: $G(s) = \dfrac{1}{s+1}$ Now, I would like to do some frequency analysis, so I replace the $s$ with $\omega i$ (let's consider ...
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What happens when we reconstruct a signal after its Fourier transform is done and some frequencies are altered? [closed]

Since we loose time information when we take a Fourier transform, what happens if we alter a few frequencies from the transform and then reconstruct the signal, do we get the altered frequency at the ...
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Why do signal have mirror signal after pure frequency shift?

In my Matlab code I have a simple simulation of FPGA with the ability to simulate doppler shift, and after I and Q components plugged into IQmod with some carrier freq. In my Matlab code when I ...
115 views

Question related to Deconvolution and Fourier Transform

Currently I am completely new to Signal Processing and I am about to kick off a project related to the system identification. The general idea is given a pair of sent and received signals, I have to ...
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Normalised magnitudes in sliding dft

I am new to signal processing. I am trying to use the output of a sliding DFT to analyse frequency peaks. Take for instance this implementation: https://github.com/bronsonp/SlidingDFT/blob/master/...
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Differences between FFT from acceleration, velocity and displacement data of a dynamic system

I am new to vibration mechanics and signal processing. Recently, I’ve performed an experimental test with an accelerometer mounted on a plate (shaker). The plate vibrates with exact frequencies 10 and ...
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Why phase information is usually ignored after Fourier transform?

Why phase information is usually ignored after Fourier transform? I have read in a tutorial [ref: FFT Tutorial] that interpretation of phase is usually challenging, so scientists do not show it or ...
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Phase error correction for Fourier transform basis vectors

I was wondering what is the best way to account for phase noise in a set of basis vectors? Example: I have a measured signal, say $f'(x)$ that should be related to a desired spectrum $f(\nu)$ through ...
I have radio telescope observations that have resulted in two real-valued signals (corresponding to the right- and left-handed circular polarizations). The signals are sampled at rate $2B$, and ...