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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Vestigial Filter problem?

I have been stuck on this question for a while now. It has to do with vestigial sideband. I wasn't sure if I should be dividing $H(\omega)$ graph values by 2 because only the positive side of the ...
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293 views

Signal Processing using Fourier Transform

So I'm trying to understand how MRI machines work. I understand all the concepts of it, the parts, what they do, how the machine works, etc. The part I'm having trouble with is the fourier transform ...
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Fourier transform of cosine to the power of 3

How can I find the Fourier transform of $$ f(x) = ( \cos(x) )^3$$ I know that for $ g(x) = \cos(x) $ $$\mathcal F \Big\{ g(x) \Big\} = \mathcal F \Big\{ \cos(x) \Big\} = \pi \Big [ \delta(w-\pi / 2)...
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Impulse Response / Frequency response Question [closed]

I have a major question. Please take a look. I have this differential equation (DE): $$ \frac{d^2y(t)}{dt} +\frac{dy(t)}{dt} +4y(t)= \frac{dx(t)}{dt} +2x(t) $$ And I have to find impulse response (...
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FFT spectre graph measurements y-axis

I am very new to this things. Sorry for probably stupid question. I don't understand what units and meaning have the values on Y-axis of Fourier Transform graph? On X-axis it is Frequency (Hz). Pretty ...
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Need an Identity for CTFT Polynomial Raised to an Exponent

I need to the find the inverse continuous time Fourier transform for unitary angular frequency of the following signal: $e^{a\omega^2 - b\omega + c}$ where $a$ and $b$ and $c$ are real numbers and I ...
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Choice of Gaussian kernel parameters when lowpass filtering before image resampling?

I need to decimate a signal by a factor of q. More specifically my signal is a 3D "image": $\ I(x_i,y_j,z_k)$, which I need to downsample by a factor of two in the z direction. I want to do lowpass ...
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Use fourier transform to calculate image pixelation coef in python

I want to calculate a coef of image pixelation to remove bad pictures from a bunch of files. Some pictures results from bad compression and we can see a lot of pixelation on them like img a here: ...
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Calculating the system output using frequency response

Given an input signal $$x(n)=\cos(6\pi n +\frac{\pi}{6})$$ and system $$y(n)=0.5x(n)-0.1x(n-1)$$. In this case, the coefficients of the difference equation are $a_0=1$, $b_0=0.5$, and $b_1=$. The ...
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length of window and overlap rate in STFT

I want to use STFT to analyze my signal and am wondering what are differences between two solutions: Use short windows (for ex. 256 samples window) Use longer windows (to get higher resolution in ...
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Interpreting the inverse fourier transform from a graph

I'm given a graph of the fourier transform of some function $x(t)$. The graph is labelled $F(X(\frac{\omega}{\pi}))$ on the y-axis and $\frac{\omega}{\pi}$ on the x-axis. The graph is plotted only ...
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What's wrong with this code for tomographic reconstruction by the Fourier method?

I've been playing around with tomographic reconstruction algorithms recently. I already have nice working implementations of FBP, ART, a SIRT/SART-like iterative scheme and even using straight linear ...
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FFT, How to decide if there is a signal among noise?

I have sets of data of different deep sky objects. My job is to check for any periodicity. I use IDL to run an FFT and wavelet methods to check for a signal. To test my code I ran the IDL built in ...
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What features describe audio signals? (Besides frequency and amplitude)

I recorded sounds with a microphone and I try to distinguish them in my Java program. The frequency works quite good, but if I look at the fourier transforms it seems like there should be more ...
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Why idft(dft(a) * dft(b)) not equal to convolve(a, b)?

I'm a little confused... I always thought the DFT of a convolution was equal to a product of DFTs, but when I tried this in Python: ...
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Techniques to deriving DTFTs

Are there general techniques to derive DTFTs? Given a bandlimited function $x(t)$, how do I find $$X(\omega)=\sum_{n=-\infty}^\infty x[n]e^{-i\omega n}$$ Generally, it is easier to derive the ...
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Variance of periodogram estimate of the power spectrum

I have been reading chapter 13.4. ("Power Spectrum Estimation Using the FFT") of the Numerical Recipies Book. Some things related to the expectation value of the "periodogram estimate of the power ...
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How can I use the fourier transform of a sequence of x-ray scan images to segment it?

Sorry if this question seems to trivial, but I am a bit of a novice when it comes to signal and image processing and I need some guidance. I have a 3D stack of about 256 grey scale images, each ...
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Signal Reconstruction after fourier transform

I'm working from an example posted here. I understand the steps to acquire the fourier transform and can clearly see the spikes at normalized frequencies at 15 and 40 Hz from the 0-centered ...
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periodic spectrum?

I'm relatively new to signal processing, so please excuse me if this is a trivial question. Why is the spectrum of a frame of speech samples periodic? What is the meaning of a periodic spectrum? And ...
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Intuition behind the scaling property of Fourier Transforms

The Fourier transform of $f(ax)$ is $\frac{1}{|a|}F(\frac{u}{|a|})$. So the frequencies are scaled horizontally but the magnitudes are also scaled when the graph of $f$ is scaled horizontally. On the ...
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Why Do I Get This Crackling Noise on Zeroing out the High Frequencies?

I recently started playing with the Fourier transform (after spending a few weeks learning about the mathematics behind it). I decided to try hacking together a low-pass filter on the following sound ...
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Can edge detection be done in the frequency domain?

Can we take advantage of the fact that high frequency components in the FFT of an image generally correspond to edges, to implement an edge detection algorithm in the fourier domain? I did try ...
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Extracting frequencies from FFT

I performed 512 point FFT on a signal. I got another set of 512 Numbers. I understand that those numbers represent amplitude of the various sine and cosine waves having different frequencies. If my ...
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Kernel Convolution in Frequency Domain - Cyclic Padding

I don't know whether this is the right place to post this, but I suppose it is. I know that frequency multiplication = circular convolution in time space for discrete signals (vectors). I also know ...
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Inverse Short Time Fourier Transform algorithm described in words

I'm trying to conceptually understand what is happening when the forward and inverse Short Time Fourier Transforms (STFT) are applied to a discrete time-domain signal. I've found the classic paper by ...
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Autocorrelation of power spectrum

Anyone have an idea of how I can implement autocorrelation of power spectrum of one image? I tried using: autocorrel = ifft( | fft(power spectrum) | ^ 2 ); but ...
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987 views

What should the amplitude be when plotting 1-sided Amplitude Spectrum?

I have a continuous signal x(t) such that $x(t)=12cos(6\pi t)+6cos(24\pi t)+3cos(30 \pi t)$ and is asked to sketch a 1-sided Amplitude Spectrum of the signal x(t) if sampled above the minimum ...
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Analysing 2500 frequencies using FFT with an input vector of 2048 samples?

I am currently reading the paper A Highly Robust Audio Fingerprinting System and on page 4 one can read about the technical parameters they use: Sampling rate of 5000 Hz, frames of 2048 samples as ...
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Sense of zeropadding in a time domain

I have the task related to Radon transform which contains a subtask which uses resampling by means of DFT. Let's consider the non-periodical discretized signal (Fig.1) (for example the string of ...
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How do I create a frequency vs time plot?

I'm a chemical engineer, not an EE, so this is a bit difficult. I'm trying to figure out how to take amplitude vs time data and transform it into frequency vs time. My first instinct is to slice my ...
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Correlation filter output range normalization

I'm developing correlation filters based image recognition. I implemented MACE correlation filter in matlab: training code: ...
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Channel Vocoder producing output with “click” sounds

I'm trying to make a channel vocoder that takes two inputs, one a frequency rich carrier (a musical sound) and the other a modulator (vocals). Applying operations involved in the channel vocoder ...
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Conceptually, how does a Fourier transform differ from an autocorrelation?

I realize the two are derived using different algorithms, and the units are different, but from a conceptual standpoint of the information they provide how do they differ? I'm thinking here about the ...
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FFT with asymmetric windowing?

Common non-rectangular window functions all seem to be symmetric. Is there ever a case when one would want to use a non-symmetric window function before an FFT? (Say if the data on one side of the ...
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What is the sparse Fourier transform?

MIT has been making a bit of noise lately about a new algorithm that is touted as a faster Fourier transform that works on particular kinds of signals, for instance: "Faster fourier transform named ...
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Books that explain DSP well to those not directly in engineering?

I do work with computer graphics and am dipping my toes into ray tracing. That field involves a good number of the subjects covered in DSP (Fourier transform, time vs frequency space, etc) but I was ...
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How to generalise the Fourier transform?

The Fourier transform takes a signal and splits it into a series of sine and cosine waves. I am told that it's supposed to be possible to split a signal into some other set of functions. My question ...
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How to calculate the gain in a bivariate fft in R?

In Statistica gain is defined as follows: Gain. The gain value is computed by dividing the cross-amplitude value by the spectrum density estimates for one of the two series in the analysis. ...
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Solving a Convolution Problem of a 1D Signal

I'm finding in trouble trying to resolve this exercise. I have to calculate the convolution of this signal: $y(t)=e^{-kt}u(t)*\frac{\sin\left(\frac{{\pi}t}{10}\right)}{({\pi}t)} $ where $u(t)$ is ...
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Real-Time Human Pitch Detection

I'm trying to implement a singing game that will analise raw mic input and tell the player how good is he singing. That needs to be done in real-time. I've come across a lot of threads asking the ...
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248 views

plotting phase of a signal adding delay

I'm trying to plot the phase of this signal $s(f)=A^2T^2sinc^2(Tf)e^{-(j\pi Tf)}$ How can I plot manually this signal?I have to follow some particular rules?I have problems with the delay. Edit ...
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What is the $\mathcal Z$-transform of Bessel function $J_0(\alpha n)$ sequence

What is the $\mathcal Z$-transform of the sequence $J_0(\alpha n)$ for $n \in \mathbb{Z}$? The Fourier transform of zero$^{\rm th}$ order Bessel function $J_0(\alpha x)$ is known to be $\frac{2}{\...
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Implementation of wideband beamformer for planar array

I would like to obtain a good reference (or references) on the implementation of a wideband beamformer for a small planar (rectangular) array comprised of 4 rows by 6 columns, for 24 elements in total....
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Fourier descriptor

Statement : BY 1D Discrete Fourier transform, obtaining its spectrum and using first few components of spectrum to describe $g(r)$ , where $g(r)$ is probably of pixel values $r$. My question : ...
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How does causality (i.e. unit step) affect the DTFT of a sine or cosine wave?

Tables of common Discrete-Time Fourier Transform pairs list the transform of a sine wave: $ \sin(\omega_0\ n) $ and its transform: $ -j\pi\ [d( \omega\ - \omega_0\ ) - d( \omega\ + \omega_0\ )] $ ...
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WAV encoding problem

When processing wav files, I encounter this problem: the what I extract PCM from a 8-bit encoded .wav file, I got a sequence of integers. However, when verifying my implementation with ...
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578 views

How to 'interpret' the Fourier Transform (specifically, of a convolution kernel)

As part of a homework assignment, I had to take the Fourier transform of the kernel I was using to convolve a signal. The kernel was a constant rectangular function, that was 1 within the square $(-1,...
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How to combine a rotation matrix and a stretch matrix into a single matrix for easy Fourier Transform

For full disclosure, this is related to homework. I have to find the Fourier Transform of a function that I've boiled down to the following. I have a function $f(x,y)$ that I can think of as another ...
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How does shift and scaling inside of a function affect its Fourier Transform?

The properties aren't entirely clear to me, sorry for the basic question. I know the Fourier Transform of one function. Say, $\text{rect}(x,y) \Leftrightarrow \frac{\sin \pi u}{\pi u} \frac{\sin \...