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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The impact on the frequency of adding zero samples and non zero samples

Can someone give me a brief explanation of what is going on in here? I struggle to understand the full differences between the impact on the frequency of added zero samples and adding samples which ...
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Cosine of amplitude 1 but GNU Radio shows FFT has amplitude > 30,000

I am doing an FFT on a cosine wave which has an amplitude of 1. The FFT is amplitude is not 1 but over 30,000. What am I missing here? It's from the GNU Radio FFT wiki page:
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Calculate displacement from acceleration signal data using Fourier transformation

I recorded acceleration data from an accelerometer attached to a vehicle, and I want to calculate displacement using the Fourier Transformation Integration method. I used software called vibration ...
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Why does MATLAB's dualtree3 function not return the lowpass subband of the imaginary tree?

MATLAB has a function named dualtree3 which computes 3-D dual-tree complex wavelet transform. This function only retains the last low-pass coefficients/subband of ...
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Adding zeroes in between the samples of a discrete frequency domain leads to both zero padding and scaling

I won’t show ALL the calculations, but I’ll describe the problem fairly enough to understand. We’ve been taught that upsampling on one domain leads to padding zeroes or added time period which is zero ...
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Why we add imaginary part in inverse fourier transform since the time domain signal has only real value?

The equation of inverse Fourier transform is the following: $$ f(t) = \frac{1}{2\pi} \int_{-\infty}^{\infty} F(\omega) e^{i\omega t} d\omega $$ $$ f(t) = \frac{1}{2\pi} \int_{-\infty}^{\infty} F(\...
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1answer
50 views

Fourier transform of time division

I know that Fourier transform of $t^n f(t)= i^n \frac{d}{d\omega^n} F(\omega)$. But does this work when $n<0$? Is there any direct relation to compute the Fourier transform of $\frac{f(t)}{t}$?
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Fourier Transform of an Exponential Sine Sweep

The Exponential Sine Sweep (ESS), according to Farina [1], can be described by the following formula: $$x(t)=\sin\left(\frac{2\pi f_1 T}{R}\left(e^{\frac{t R}{T}} -1\right) \right)$$ where, $t$ - ...
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Discrete Fourier Transform on images using OpenCV

I applied DFT on an edge image (attached both). I expected the output image to not have very low frequencies (~0).[Refer this link for more info] But the output I got consisted of low and high ...
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What is the effect of wiping the right half of Fourier Transform bins?

I'm trying to change the pitch of a signal using a Fourier Transform (FFT) followed by an Inverse Fourier Transform (IFFT). I've found many examples, some of which zero out the right half of the real ...
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Prove a property using shift theorem and duality

I'm reading Lectures on the Fourier Transform and Its Applications and I'm going to prove shift theorem for the inverse Fourier transform using duality. According to the mentioned source, the duality ...
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Can you use Bartlett method in reverse? [closed]

I'm wanting to do an inverse Fourier transform. Can I use the Welch method to generate this inverse, by replacing the FT used within with an IFT?
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How to do Frequency Scaling on an Audio File

Please excuse me if my terminology is wrong. I'm from a music production background and have no experience in signal processing. I was wondering if it was possible to stretch out the overtones (...
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Does it make sense to express a given FT from 0 to 1 as a convolution?

I'm learning about Fourier transform, and was asked whether the following FT can be expressed as a convolution: $$X[k] = \sum\limits_{n=0}^{N=1} x[n]e^{-i\frac{2\pi}{N}kn}$$ There are two things I don'...
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How would I spectrally rotate/invert an audio signal (Matlab or Python)?

So I have a 4.5 minute wav audio clip. I want to spectrally rotate the frequencies such that the spatio-temporal characteristics of natural speech are retained, while having the new audio be ...
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Amplitude after Fourier transform

How to obtain the correct amplitude after the numerical Fourier transform of a signal? Example: consider an exponential decaying wave $y(x)=e^{-x}\sin(100\pi x)$ with Fourier transform $y_f(x_f)$ ...
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Inverse discrete time Fourier transform with differentiation

Consider a signal x[n] and its DTFT $X(e^{jω})$ . Assume $X(e^{jω})$ is differentiable. Compute the inverse DTFT of $j\frac{dX(e^{jω})}{d\omega}$ You should write your answer in terms of $x[n]$ and ...
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Is resizing of frequency spectrum a valid method of resampling?

One method of resampling is to perform a Fourier Transform on a signal, resize the resulting frequency spectrum, and then return to the resampled version of the signal with an inverse fourier ...
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I need help in understanding “Nyquist Criterion” definition

I am researching the split-step parabolic equation and its split step solution as in: Ozgun, Ozlem & Apaydin, Gokhan & Kuzuoglu, Mustafa & Sevgi, Levent. (2011). PETOOL: MATLAB-based one-...
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Time scale and Fourier transform

Consider the Fourier transform $F(\omega)$ of the function $f(t)$. The magnitude of $F(\omega)$ depends on $\omega$ and thus also depends on the scale of the $t$-axis. For example, when $f_1(t)$ is a ...
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What could cause fast Fourier transform to give complex conjugate of the intended result?

I have 2 real time series $x(t)$ and $y(t)$, after fft it should become $\tilde{X}(f)$ and $\tilde{Y}(f)$. Then I need to normalize $\tilde{X}(f)$ with $\tilde{Y}(f)$ : $\tilde{X}(f)/\tilde{Y}(f)=\...
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If a square wave is a sum of odd harmonic impulses, why is it continuous in the frequency domain?

A square wave is a sum of sinusoids so surely it should be represented as individual discrete impulses in the frequency domain, where all other frequencies are 0. Why instead are those intermediate ...
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Why do people use STFT as a preprocessing step to using CNN?

Just briefly looking up some research papers on audio data and I have come across some papers that use STFT as a preprocessing step to using CNN. Why is this the case? What are the advantages and ...
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Determine constant $A$ such that $x[n] = x[n] \star x[n]$

Let $x[n] = A\delta[n] - \frac{\sin(\frac{3n}{2})}{\pi n}$. Determine constant $A$ such that for all $n$ $$x[n] = x[n] \star x[n] \tag{1}$$ I think it's not possible since $(1)$ leads to $$X(e^{j\...
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FFT shows systematic deviations from analytical result

I am calculating the numerical Fourier transform of an exponential decay exp(-|t|) and compare it to the analytically calculated result, a Lorentzian. I find that the numerically calculated spectrum ...
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What's the relation between frequency band of $X(j\omega)$ and $\Phi_{xx}(j\omega)$?

in which: $x_{c}(t)$ is a continuous-time signal $X(j\Omega)$ is the Fourier Transform of $x_{c}(t)$ $\Phi_{xx}(j\Omega)$ is the Power Spectrum Density of $x_{c}(t)$ which defined as Fourier ...
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How do I generate a smaller DFT result?

I have a very large input that I'm Fourier-transforming. Currently, I transform the entire signal and then downsample the result. Although the transform of the large input is expensive, my results ...
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How to sample along diagonal in 2D FFT

I aquire typically 2D time traces which I process by a 2D Fourier transform. The aquisition is done line by line. First, I let the signal evolve for t1, then an action is performed that possibly ...
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Highest frequency component in 2D Fourier transform

I was trying to understand the 2d dft(discrete Fourier transform) and discrete spatial Fourier transform (dsft) of images. But while understanding the graph i didn't understand that how come ($\pi,\pi$...
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Change FFT frequency domain values range

So, I`m currently working on program for computing spectrogram in real-time, using signal from a microphone. And now I want to add "scaling" feature, that allows to look at the spectrum more ...
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DFT and perfect reconstruction of a square wave on a digital computer

I know that in theory, when reconstructing a square wave from its Fourier coefficients, unless we have an infinite amount of them, the resulting reconstruction will have Gibbs ringing artifacts due to ...
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frequency domain representation of the doppler shift sequence

This is a bit of a weird question. I have a bunch of IQ data. Its a very big file that i cant upload on here. Im working through a few exercises trying to analyse the data. I have plotted the signal ...
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Will the phase of the reconstructed data using a single MRI k-space point show any curvature?

Some courses tell that each point in k-space (spatial-frequency domain) represents a certain stripe pattern in spatial domain. Reference: https://www.sciencedirect.com/science/article/pii/...
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Phase Spectrum in Fourier Transform

Probably a simple question to answer. I have been trying to use the fft function in MATLAB and have been succesful to get the amplitude spectrum of a known signal. But when working out the phase ...
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Can largest-triangle-three-buckets downsampling method used with fourier transformed signal?

I've been reading on the largest-triangle-three-buckets downsampling method for downsampling. Though it was originally published in the thesis "Downsampling Time Series for Visual Representation&...
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How to downsample a fourier transformed signal?

I have a signal of length 100000 timestamps sampled at a frequency of 25kHz. First I apply a high pass filtering at (300Hz) and then do the Fast Fourier Transformation. Then the absolute values are ...
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Reconstruct $x(t)$ from $y(t)$ and $z(t)$

Let $x(t)$ be band-limited signal with $X(j\omega) = 0$ for $|\omega|\gt \omega_M$. We use $$s(t) = \sum_{k =-\infty}^{+\infty}(-1)^k\delta(t - \frac{kT}{2})$$ for sampling. So we have $z(t) = x(t)s(t)...
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Fourier transform of the sampled signal

I want to calculate Fourier transform of the sampled signal in two ways. Let $$s(t) = \sum_{k = -\infty}^{\infty}\delta(t - kT)$$And $z(t) = x(t)s(t)$. So we have $$z(t) = \sum_{k = -\infty}^{\infty}x(...
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Getting the power of a signal from its Fourier transform?

I have a non-periodic signal that contains the sinc function in the time domain and so it is a bit difficult to calculate its power (because of the integral) through: $$ {P_x} = \lim_{T \to \infty} \...
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Frequency Domain Distribution

I have a complex signal in the time domain normally distributed. What will be its distribution in the frequency domain? I assumed since the frequency domain is a linear transformation the distribution ...
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Does Short-time Fourier transform impact quality of signal?

I am playing with spleeter to separate voice from an audio signal. They go to the frequency domain by computing the Short-time Fourier transform to create a spectrogram. As there are some ...
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Meaning of negative frequencies in Baseband non sinusoidal, non periodic signal

I can understand the meaning of negative frequencies in a sine or cosine signal, since by using Euler's identities, you have two complex phasors moving to different directions, which when added, give ...
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Fourier transform of the magnitude of the fourier transformed signal

I've come to realize that the Fourier transform of an already Fourier transformed signal gives the time-reversal signal. $$\mathcal F(\mathcal F(x(t)))=x(−t)$$ ref 1,ref 2 However, my question is, if ...
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Behaviour of integrator at steady state

I wanted to calculate response of integrator of sinusoidal input at steady state via these two methods as mention in image but these two methods give two different answers at steady state, so where ...
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RMS of signal vs average amplitude

I am trying to estimate the average amplitude of some signal with frequency 6 Hz, sampled at ~300 Hz. See figures for a part of the signal and its dft calculated using matlab. I estimate the average ...
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Frequencies of complex exponentials in Discrete Fourier Transform

What I understand is that using DFT, we are representing a given discrete signal using a basis of complex exponentials of different harmonic frequencies. If I am taking 16 point DFT of a signal ...
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MRI K-space to image: why track frequencies in two dimensions?

While trying to better understand how an MRI goes from k-space to an image, I came across this wonderful website that explains how you would represent an image as a collection of rows of pixels where ...
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Names of system functions in frequency domain

I was just trying to refresh my systems theory known from long ago, and I realized that I had forgetten the name of the basic functions. Specifically, what are the names of these functions ...
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Showing error energy goes to zero

Let $$\hat{x}[k] = \frac{1}{2\pi}\int_{-W}^{W}X(e^{j\omega})e^{j\omega k}d\omega,\label{ift}\tag1$$ where $$X(e^{j\omega}) = \sum_{n=-\infty}^{+\infty} x[n]e^{-j\omega n}\label{dft}\tag2$$ Also, $$d[k]...
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Steady state variance of a stochastic differential equation - relation between the frequency and time domains

Consider a stochastic differential equation: $$ dx(t) = a x(t)dt + b y(t)dt \quad (1) $$ where $y(t)$ is a stochastic process satisfying $\langle y(t)y(t')\rangle = \delta(t-t')$. We will assume that ...

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