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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149 views

Fourier transform of a damped cosine wave with a linear frequency chirp

I want to take the Fourier transform of the following transient signal, $$f(t) = e^{-t/\tau} \cos((\omega_0 + m t)t)$$, where $m$ is some gradient parameter in units of $\rm{Hz}/s$. I thought this ...
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245 views

Evaluate Fourier coefficients at arbitrary point using Python

Lets say I have a sinusoidal function $s$ that looks like ...
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0answers
53 views

Convolution of signals sampled on a logarithmic grid

Is there a practical accelerated algorithm or a theoretical discrete (Fourier) transform based method to convolve discrete-time signals sampled on a logarithmic grid? What I mean is representing a ...
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1answer
116 views

Use samples of Fourier transform as DFT?

Consider the LTI system given by: $H(z) = 1 - \frac{1}{2}z^{-1}+\frac{3}{4}z^{-2}$ Let $x[n] = (\frac{1}{2})^nu[n]$ be the input to the system. We want to find the output for $n = 0,1,...,N_a$, using ...
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1answer
845 views

What's the difference between using DFT, IDFT or DCT to calculate cepstrum of a power spectrum?

I've seen different equations that calculate cepstrum from power spectrum, but the equations are not consistent. Some people use Fourier transform, some use the inverse Fourier transform, and some use ...
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4k views

What's spectral “tilt”?

I am looking at article Speech-in-noise intelligibility improvement based on spectral shaping and dynamic range compression. In paragraph 2.2 the article mentions "tilt" of the spectral envelope. The ...
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66 views

Can you use Fourier transformations (or other) to read multiple superimposed barcodes?

If you printed bar codes on tracing paper/acetate etc. and then positioned several in front of one another, could you extract the individual codes from the aggregate overlaid image? I feel intuitively ...
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0answers
251 views

Aliasing in the Short time Fourier Transform of a pulse

When attempting to take the Short Time Fourier Transform of a pulse, at the end of the pulse I'm running into problems. The signal looks like this at the end (it is a simple $sin^2$ pulse envelope, ...
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133 views

Understanding Walsh coefficients

I am working with Walsh coefficients. I know the intuitive understanding is almost that that they are the degree of connectivity, but it is there a better way of thinking about it? What is the ...
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389 views

Discrete Fourier transform in a multidimensional space

I want to measure the frequencies at which a point oscillates in a multidimensional space, let's take the example of a point on a 2d-surface. For now, I naïvely split the signal in two, along the ...
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109 views

Global Transforms besides the DFT?

This is a simple question. Fourier analysis gives us the DFT, which is known as a global transform of a signal. In contrast, the Discrete Wavelet Transform (DWT) has a plethora of wavelets, all of ...
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2answers
1k views

Problems Using FFT to Compute Impedance in a Model Neuron

I'm a neuroscientist currently investigating the resonance properties of a single neuron model that a colleague and I have constructed. The language we code in is Julia, which I hope is similar enough ...
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49 views

Two versions of Constant Q Transform (CQT) doesn't match each other?

To my knowledge, there's two major CQT papers, the one by Brown in 1991, and the one by Schorkhuber in 2010. The 2010 paper claims to be a more computationally efficient implementation of the 1992 ...
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1answer
65 views

Non-Linear, Non-Stationary spectral analysis methods! When and where?

I have been reading about non-linear non-stationary signal analysis methods and it seems to do this type of analysis the go-to method is the Empirical Mode Decomposition (EMD), then Hilbert Transform (...
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1answer
59 views

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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26 views

What is a correct way to find or “guess” a kernel which transforms an image into another image using Fourier Transformations?

Assuming I have two images, apple and orange; also assuming a filter kernel that transforms an apple image into an orange image possibly exists, how would some series of Fourier Transformations (and ...
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76 views

How to calculate the Fourier Transform of a solvable chaos waveform?

Recently I am stucking in frequency estimation of a solvable chaos waveform. Its local analytic expression in time domain is $$ z(t)=s_m(u_m-s_m)e^{\beta(t-mT)}\cos(\omega_0 t+\varphi),mT\leq t<(m+...
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88 views

How to derivate in the frequency domain

I have two Time Domain functions, $f_1(t)$ and $f_2(t)$. I have both Fourier Transforms, $F_1(\omega)$ and $F_2(\omega)$. Functions $f_1$ and $f_2$ are not independent and, in fact, $f_1$ is also a ...
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42 views

Vector parameters in uncountably infinite-dimensional spaces

My question was, in an uncountably infinite-dimensional vector spaces, how to represent a vector by a list of parameters, as we do in finite-dimensional spaces? I was assuming that if we can not ...
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132 views

What is the correct way to do Short term Fourier transform and extract the phase information from local sections of a signal?

I took a triangular voltage signal and taking it's time derivative I obtained the current through a pure capacitor. Then I took different portion of voltage and current signals, took their Fourier ...
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137 views

Constructing $X(\omega/2)$ from the FFT of $x[n]$

Let $X(\omega)$ be the Discrete Time Fourier Transform (DTFT) of $x[n]$, I want to construct $X(\omega/2)$. Precisely, I use FFT function to compute the samples of $X(\omega)$ in one period, say $[0,...
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137 views

$\tt ifft()$ function - absolute vs real form

I have multiple files from an experiment in frequency-domain that I would like to use ifft() function to convert to the time domain in R to apply signal processing ...
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93 views

Elementary proof of Fourier domain formula of multidimensional downsampling by $M$

I am trying to prove a well-know formula for the multidimensional downsampling by arbitrary downsampling integer matrix $M$ in $d$-dimensional case. The formula is $$ \hat{y}(\omega)=\frac{1}{\...
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117 views

Signal rescaling

Please help me out with this one. I think I've been given an impossible task. I'm working on a system that transmits an active signal and looks for strong reflections. The transmitter is actually ...
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90 views

Filtering and Differentiating phase-modulated signals

For a project work, I need to demodulate data from a Laser Doppler Vibrometer. The distance information is phase-modulated, therefore the velocity information is frequency-modulated: $$x \propto \...
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141 views

Optimal method to calculate Fractional Fourier for Chirp signals

There are several method exist in the literature to calculate fractional Fourier transform. My interest is in chirp signals and want to find time delay estimation using fractional Fourier transform (...
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0answers
81 views

Why does filtering the same discrete dataset while choosing different sampling rates yield different results?

If I have a two-dimensional discrete dataset (one space, one time), and I create subsets of this dataset by "sampling" (although the original dataset isn't continuous) it at different rates, should I ...
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47 views

Why doesn't the mel-scale use the twelth-root of 2 instead of a biased sample listener?

For the mel frequency spectrum, which is used extensively in audio-processing, the technique uses subjects to identify pitches of uniform distance from one another. Isn't this distance just the 12-th ...
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56 views

Stationary processes and their power

The top answer to this question: Power spectral density vs Energy spectral density states: However if random process is stationary, then it is for sure that it has some finite power over some ...
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111 views

A simpler method or more descriptive answer to the Fourier Transform

I'm trying to do a CT Fourier Transform of these two signals $$x_1(t)=e^{−a(t−1)} \cdot u(t−1)$$ and $$x_2(t)=e^{−a(t−1)} \cdot u(t)$$ Where $a$ is any real number, and $u(t)$ is the unit step ...
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1answer
163 views

Most appropriate spectral analysis method for a recording of a saxophone note?

I'm currently doing an investigation where I am attempting to resonant frequencies of an Alto Saxophone at various different notes. I have taken audio recordings of the notes with a sample rate of $...
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25 views

Find integral of DTFT after sampling (Graph of CTFT given)

So for the first question: If this is sampled at 10kHz, then the amplitude is scaled by 10000. In the DTFT, the frequency 3.5kHz gets mapped to 3.5/10* 2pi=0.7pi. So this point lies outside the range ...
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1answer
47 views

Why zero padding the 2-d DFT interpolates images in spatial domain?

I was applying different image interpolation techniques and I came know to about interpolation in frequency domain. In this technique we first take 2d DFT of an image, padd it with zeros and take the ...
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25 views

how to reconstruct an phase information from the magnitude spectrogram

I need to recreate the phase of a spectogram of magnitude and when inverse fourier, that the sound is understandable and not pure noise Observe these softwares https://photosounder.com/ http://...
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21 views

Removing striped noise from an image

I was just wondering if anyone could explain to me the approach one would take to removing striped noise from the fourier domain of an image. I was reading an article about MRI image from 1 just ...
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1answer
30 views

Is fft2 in MATLAB unitary? Some differences happen

I meet a problem when implementing fft2 in MATLAB. The question is I try to simulate the realistic measurements $Y = |FCXF^H|^2$ - the intensity of Fourier domain of object $X$, where $F$ denotes ...
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22 views

Calculate phase lag between two signals with perturbed frequencies

This type of question has been asked quite a few times on this forum and others now, but I still haven't found a satisfactory answer to my problem. Given an input signal: $$x_1(t)=\cos\big(2\pi ft\...
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1answer
108 views

Applying duality property to fourier transform of unit step function

For Continuous time aperiodic signals, the duality property of Continuous Time Fourier Transform (CTFT) is following $$\mathscr{F}\Big\{x(t)\Big\} = X(f), \qquad\text{then} \quad \mathscr{F}\Big\{X(t)...
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46 views

Finding the input from the impulse response and output

I have $y,h,x$ which are all vectors. From $y[n]=x[n]*h[n]$ which is basically how I got $y[n]$. I also know $h[n]$. I put this through a Fourier transform. Let's assume that the capitalized ...
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206 views

The Fourier Transform of a periodic function and it's series

Let $X(f)$ be the Fourier transform of $x(t)$: $$ X(f) \triangleq \mathscr{F}\Big\{ x(t) \Big\} = \int\limits_{-\infty}^{\infty} x(t)\,e^{-j 2 \pi f t} \ \mathrm{d}t $$ $$ x(t) \triangleq \mathscr{F}...
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2answers
113 views

Checking Parseval's Theorem for Gaussian Signal by Using Scipy

I'm trying to check Parseval's theorm for Gaussian signal. It's well known that fourier transform of $\exp(-t^2)$ is $\sqrt{\pi}\exp(-\pi^2 k^2)$. So I implement it by using quad and simps. I think ...
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100 views

Generate time domain signal from frequency domain filter

I am familiar with using the Fourier transform to take a signal from the time domain to the frequency domain. What I would like to do is the reverse: describe a signal in the frequency domain and then ...
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89 views

Burst Deblurring algorithm - Understanding the results

I've attempt to implement the algorithm from the paper "Burst Deblurring: Removing Camera Shake Through Fourier Burst Accumulation". The main idea is to take several frames of the same scene, each ...
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0answers
131 views

Is it possible to recover the original signal from an LC circuit?

I'm using some photo detectors called Silicon Photo-multipliers (SIPMs) which produce a signal like the following: Now, I take this signal and pass it through an LC circuit to get the following ...
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35 views

Determine 3 most dominant frequencies in a signal, PSD or just the absolute value of a Fourier transform?

I have a noisy ECG signal recorded for 5 minutes. My goal is to determine heart rate every 2 seconds. To find out 3 most dominant heart rates (Beats per minute) in a 2s-signal should I calculate its ...
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1answer
174 views

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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1answer
334 views

Image zooming with Fourier transform

I want to go from this image into this one: So basically I need to scale the white square. The authors of the paper claim that this can be done in four steps: zero-padding in real space (image is ...
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0answers
33 views

Creating realization of 2D Gaussian field in Fourier space

I want to generate a 2D Gaussian field with dimensions $L\times L$ with $N^2$ cells each of size $l = L/N$. I'm doing this by producing a realization of this field in Fourier space by producing ...
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129 views

Graph signal processing

What's the intuition behind a ''Graph fourier transform'' ? I'm not so much interested in mathematical details or technical applications. I'm trying to grasp what a graph fourier transform actually ...
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1answer
206 views

Bandwidth of Information Signal

I have trouble finding the bandwidth of a signal. Say I have an info bearing signal m(t)=sinc(2t/pi). I found the fourier transform of the sinc function and found that the angular frequency was 1/pi. ...