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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Evaluate Fourier coefficients at arbitrary point using Python

Lets say I have a sinusoidal function $s$ that looks like ...
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50 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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3k 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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222 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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120 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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366 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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40 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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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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60 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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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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37 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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114 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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127 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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117 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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90 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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111 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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87 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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135 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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79 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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45 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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54 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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43 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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133 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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50 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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46 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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115 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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31 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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23 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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121 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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96 views

When Is a Power of 2 FFT Slower than Smaller Sized Non Power of 2 FFT in MATLAB

Knowing that computing an FFT is faster if the amount of samples is a power of 2 I have always tried to pad the inputs to Matlab's FFT with zeros until the next power of 2 is achieved. Matlab's ...
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58 views

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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72 views

Compute hilbert transform from DCT- FFTW3 REDFT00

My problem is similar to this but not the same. Edit: Here is a description of Neumann boundary conditions for differential equations: Neumann-type boundary conditions means derivatives are ...
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36 views

Fourier transform of attenuated propagating pulse

I am studying the optical properties of a medium by looking at how a Gaussian pulse is deformed as it propagates through the medium. The initial Gaussian pulse signal and Fourier transform are : \...
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738 views

How to calculate the spatial frequency of an image in cycles per image

I have been attempting to calculate the spatial frequency of a colour image. I first converted it to grayscale and used a Fast Fourier transformation (fft2) that codes the quantity of each spatial ...
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49 views

Determining periodic pattern when there is pattern which period is multiple of former

I have periodic signal, say, it has year period, yearly pattern. I want to check if also has quarterly pattern. Event if there is no visible quarterly pattern, Fourier Transform of this signal has ...
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142 views

How to get the phase offset from the instantaneous phase

The phase components of a signal that they are got from the Fourier Transform, are simply, the phase offset of each sinusiod. Which is the $\phi$ in equation $1$. However, in case of Hilbert transform,...
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405 views

Window size and DFT size

I am using pwelch function of Matlab which returns the power spectral density (PSD) estimate. This got me confused about DFFT size and Windows size. Here my code: ...
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86 views

Fastest way to subtract known music tracks from live videogame audio stream

I want to isolate video game "action" sounds from the video game soundtrack. Given all ~20 songs, I'd like to filter them out from any live audio stream during gameplay. What is a fast and robust way ...
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594 views

Relationship between Wavelet transform and Fourier Power Spectral Density

Is there anyway to obtain the Fourier Power Spectral Density from a wavelet transform of a time series? I am particularly interested in this problem because I was wondering if there is any ...
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79 views

Regressing/interpolating between quasi-periodic sinusoids

This is a cross-post (on recommendation) from CV. My problem is very simple. I currently intend on using Kriging (Gaussian process regression) to perform regression between the trajectories marked ...
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88 views

Optical realization of the Radon Transform

I am trying to reproduce this paper concerning the Optical realization of the Radon Transform, especially the simulation (section 3). Shortly, the experiment is just a "Fourier filtering" with a 4F ...
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58 views

amplitude at exact frequency in wide band signal

Could anyone suggest the most computationaly efficient method for finding amplitude of exact frequency having a noisy wide band signal. To be more specific about a task. I have some physical ...
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219 views

Transfer functions from wavelet transform

So I have this problem where I need to measure the phase of a signal and correct for a delay associated with the travel time of the signal while simultaneously determining the transfer function of my ...
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410 views

How to convert a spatial frequency in a 2D-DFT into the units radians per pixel?

Let's say I have a 2D image, and I take the discrete Fourier Transform (via FFT) of that image. In the frequency domain, I get the following image: In this image, let's just assume all the spatial ...
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298 views

Discrete Fourier Transform for text analysis?

I would like to determine the number of text-blocks verifying a roughly similar pattern. I have the intuition that I could do it using some Discrete Fourier Transform (DFT)-like methodology. Example: ...
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1k views

How do we calculate Power Spectrum Density (PSD) which is given in dB/Hz and not just dB?

I found many definitions for this quantity, PSD. In a document on signal analysis by National Instruments say that it is the amount of power in a unit bandwidth. Let's say P(f) is the power of the ...
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518 views

Fourier transforms of random processes

In the Wikipedia article on Brownian noise, the Fourier transform of Brownian noise is determined. How is that Fourier transform defined? It seems it is a non-random quantity there, so it is not ...