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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56 views

Minimum statistics noise estimate - how to calculate the underestimation factor?

I have implemented a basic noise estimator using the minimum statistics method. Noise power estimate is obtained as a minimum of the short time power estimate within a window of subband power samples. ...
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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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2answers
904 views

Separation of overlapping frequencies

I have a signal with multiple frequencies, and two of them, one of which is my main frequency, overlap. Are there any techniques that could separate two frequencies that almost overlap? I can ...
3
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0answers
32 views

How to find the difference between maximum and minimum of a time signal, having only Fourier series cofficients

I currently know the Fourier coefficients of a signal $c_n$, from the exponential Fourier series of this form: $$f(t) = \sum^{+\infty}_{n=-\infty} c_ne^{in\omega t}$$ Using these Fourier coefficients, ...
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0answers
60 views

real time - active noise control

I am trying to implement an adaptive filter for system identification and active noise control for realtime signal processing on an FPGA using Labview. For system identification, I implemented the ...
3
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1answer
153 views

Constructing a Gaussian kernel in the frequency domain

I'm currently learning about Fourier transform, but find the differences between spatial domain and frequency domain a bit confusing at times. Let's say I would like to perform convolution of an image ...
3
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1answer
339 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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0answers
906 views

Evaluate Fourier coefficients at arbitrary point using Python

Lets say I have a sinusoidal function $s$ that looks like ...
3
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0answers
79 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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0answers
5k 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 ...
3
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0answers
70 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 ...
3
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0answers
323 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, ...
3
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0answers
177 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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0answers
440 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 ...
3
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0answers
110 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 ...
2
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0answers
26 views

Derivation of Strehl ratio

I am in trouble proving the following fact: The Strehl ratio is the ratio of the volume of the aberrated OTF (optical transfer function) and the ideal OTF, i.e. \begin{align} \mathcal{S}=\frac{\int\...
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0answers
54 views

Discrete Fourier Transform of 2-D Images

I'm a high school student doing an essay on the applications of the Fourier transform on signal processing, but I haven't been able to find much information when applying the discrete fourier ...
2
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0answers
64 views

Multiple 1D gaussian filter

Given $$ \begin{cases} &f_0(x)=1 \\ &f_{n+1}(x)= (\varphi*(f\mathbb{I}_{[a_n,b_n]}))(x)=\int_{-\infty}^{+\infty}\varphi(x-t)f_n(t)\mathbb{I}_{[a_n,b_n]}(t)dt = \int_{a_n}^{b_n}\varphi(x-t)f_n(...
2
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0answers
74 views

calculate or decompose a Fourier transform signal amplitudes with unknown weights on sources

migrated from math-se... I am trying to calculate , or approximate the solution of following Fourier-sine transform problem that can be expressed as a contributions of periodic sources $f_i(x)$ and ...
2
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0answers
196 views

Welch Method FFT Python - Scaling factor?

I've been implementing a Welch method FFT and I am trying to work out the correct scaling factor that should be applied to the output of the function so the PSD is accurate because at the moment it's ...
2
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0answers
119 views

Windowing function for Inverse Fourier Transform

It is a common practice to apply windowing function, such as Hann or Hamming, to a time domain signal before FFT, in order to reduce spectral leakage. Often, we do 1) Windowing, 2) FFT, 3) frequency ...
2
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0answers
96 views

Find a LTI system such that $\mathcal{T}\{\frac{\sin t}{t}\} = \frac{\sin 2t}{t}$

Let $$x(t) = \frac{\sin t}{t} \qquad\text{and}\qquad y(t) = \frac{\sin 2t}{t}$$ Is it possible to find a LTI system such that $\mathcal{T}\{x(t)\} = y(t)$? If not, what's the reason for ...
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0answers
539 views

Is rotation of a Fourier transform the same thing as Fourier transform of a rotation?

I'm working on an image processing problem and wondering if DFT(rotation(image)) == rotation(DFT(image)) (1). My final goal is to apply rotations in the Fourier domain then do an inverse Fourier ...
2
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0answers
64 views

Getting the right frequency (using FFT)

I am implementing the method from this paper: https://dspace.mit.edu/bitstream/handle/1721.1/66243/Picard_Noncontact%20Automated.pdf?sequence=1&isAllowed=y The main idea is cardiac pulse ...
2
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1answer
65 views

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 ...
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0answers
99 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 ...
2
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1answer
510 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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0answers
29 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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0answers
136 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+...
2
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1answer
308 views

Uniqueness of Fourier Series Representation and the Fourier Transform of Periodic Signals

If we are given a signal of the form $$x(t) = \sum_{k = -\infty}^{+\infty} a_k e^{j k \omega_0 t},$$ can we call it a Fourier Series representation of $x(t)$ right away? Suppose we are given the ...
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0answers
259 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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0answers
49 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 ...
2
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0answers
171 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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0answers
1k 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 ...
2
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0answers
241 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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0answers
186 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 ...
2
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0answers
101 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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0answers
165 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 ...
2
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0answers
96 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 \...
2
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0answers
163 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 (...
2
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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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0answers
50 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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0answers
65 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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0answers
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 ...
2
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1answer
215 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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1answer
54 views

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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0answers
25 views

Which conditions must fulfill a time-limited signal (so of unlimited bandwidth) $f(t)$ to have a bounded maximum slew rate?

Which conditions must fulfill a time-limited signal (so of unlimited bandwidth) $f(t)$ to have a bounded maximum slew rate? I want to know about which conditions must fulfill a real-valued time-...
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0answers
75 views

Wrong amplitude in the FFT for 10 seconds measured signal

I measured a signal with the Osziliscope that I generated with a signal generator. The signal is a pure sine wave with a frequency of 1 kHz and a peak amplitude of 2.5 V, I measured the signal for ...
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0answers
41 views

Remove Noise from Discrete Signal with given Noise Model

I am interested in finding the true signal $p \in \mathbb{R}^D$ of an observed discrete signal $t \in \mathbb{Z}_{+}^D$. I know that each observed $t_{i}$ with $1 \leq i \leq D$ is the result of a ...
1
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1answer
35 views

Differentiate betwee sibilant "sssh" voice sounds and instruments like hi-hat?

How would I differentiate betwee sibilant "sssh" voice sounds in a music track and a similar sounding instrument sounds like hi-hat or cymbals?

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