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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How to Find "pitch" from Fourier Series

The end goal of my project is to create an autotune program, But the problem I'm trying to solve right now concerns finding the pitch of someone singing a note. I have written some code that performs ...
1 vote
2 answers
187 views

Why use sinc function to downsample an image in fourier domain?

I'm very confused about downsampling in image processing and the use of sinc function to do it. I read this post [1]: 2D Fourier downsampling some time ago that talked about my own doubt, that is to ...
2 votes
1 answer
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Need help with DTFT problem

Prepping for exam and this is one of the practice problems: I just want some clarification on some of the steps my professor took. This is the answer in the answer sheet Only thing I dont understand ...
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1 answer
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Fourier transform why can I convert one of the axes into an imaginary number?

Contextualizing This question is inspired by the following video: https://www.youtube.com/watch?v=-qgreAUpPwM&t=60s&ab_channel=3Blue1Brown I own a sign, a drawing of a square with 200 points ...
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2 answers
34 views

What are some approaches / algorithms for reducing size of numerical data of large size with redundancies?

I'm dealing with bunch of .asc(ascii) files that are the output of continous monitoring of various electronic equipments for certification purposes. We monitor various parameters of the equipments ...
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2 answers
237 views

Time domain to frequency domain conversion of audio signals to extract 1/3 octave frequencies

We have developed an android app (Noise Tracker) for noise measurement using smartphones. It displays noise levels in Leq sound pressure levels. I want to implement A & C weighting. As per my ...
2 votes
0 answers
24 views

Removing once per revolution variation from data

I’m looking for help to find a robust technique to remove a once per revolution variation in some vehicle test data. The data is collected by driving a vehicle around a circular path at increasing ...
2 votes
1 answer
45 views

Rayleigh Bandwidth Calculation-Radar

I am trying to generate a simple Gaussian pulse that has a 1 ns pulse width. However, when I generate the pulse, I realized that I did not meet the condition that calculates Rayleigh Bandwidth (1/...
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2 answers
58 views

Fourier transform of periodic functions

The Fourier transform is derived from the Fourier series by considering a non-periodic signal, thinking of it as a infinitely long periodic signal, putting it into the Fourier series and making this ...
1 vote
1 answer
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How to find the inverse Fourier transform of $u(\omega) e^{-j \frac{\pi}{2}} + u(-\omega) e^{j \frac{\pi}{2}}$?

I have been trying to find the following inverse Fourier transform but without success: $$ H(\omega) = \begin{cases} e^{-j \frac{\pi}{2}} & \omega \gt 0 \\ e^{j \frac{\pi}{2}} & \omega \lt 0 \...
3 votes
3 answers
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Maximum Magnitude Deviation between DFT and DTFT

Let $x[n]$ be a finite-length discrete-time signal with length $N$. The continuous DTFT $X(\omega)$ is then $$ X(\omega) = \sum_{n = 0}^{N-1} x[n] e^{-j \omega n}. $$ The length-$N$ DFT of $x[n]$ is $...
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3 answers
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What is the frequency response of binning 2x2 pixels of an image into 1 pixel in software?

What is the frequency response of binning 2x2 pixels into 1 pixel in software? Can the binning introduce aliasing? Since the Fourier of the 2D boxcar function is a 2D sinc I would intuitively think ...
2 votes
1 answer
119 views

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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1 answer
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Is an interval for a function and its Fourier transform based on the time constants?

The Fourier transform of an exponential function is a Lorentzian. For the sum of multiple exponential functions with time constants $k$, is it only meaningful to define the function and its Fourier ...
2 votes
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Answered-Question About Radar Pulse Modulation

I am trying to simulate a radar-transmitted signal with a 4.5 Hz clock frequency and 1.8 GHz carrier frequency. I generated the carrier signal and a rectangle shape pulse signal, then multiplied in ...
0 votes
3 answers
904 views

Why does FFT not have an effect on my smoothed signal?

I'm playing with FFT at the moment and I try to get periods from noisy signals by recreating this example. While experimenting, I've noticed that after smoothing a quite noisy signal, the result of <...
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28 views

Amplitude ratio is larger than 0.5 on a RC-filter if RC = 1.7684e-03

I have two signals ...
11 votes
5 answers
439 views

What is the frequency representation of nonuniform sampling?

Uniform sampling can be thought of as multiplication of a function $x(t)$ with a Dirac comb function: $$\text{III}_T(t) = \sum_{k=-\infty}^{\infty}\delta(t-kT)$$ Multiplication of $x(t)$ with $\text{...
1 vote
1 answer
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How to explain the meaning of the intersection in a Fourier series representation of periodic signals?

I saw a piece of code on github which transforms the planetary movement into the Fourier wave function. These circles are given by the $x$ and $y$ ordinates: $x=\cos (\omega t)$, $y=\sin (\omega t)$, ...
3 votes
1 answer
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Practical applications of wavelets

I know wavelets were all the rage a few years ago, but I missed that boat and am wondering if it is worth putting significant effort into learning about them. My impression is that they were a little ...
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1 answer
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How to inject a 2D plane sine wave to the array of seismic sensors?

I've several sensors positioned at various points in the $X$,$Y$-Cartesian coordinate system, and I've experienced a problem to inject a planar Sine wave to the spatially positioned sensors, the ...
0 votes
3 answers
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Verify FFT results without equation of waveform

I used python to convert the time-domain signal below into a frequency spectrum so that I can analyze the harmonics. To do this I used Python libraries, specifically numpy and called fft to get the ...
5 votes
3 answers
566 views

Period and wavelength of a noise signal?

How do I determine the wavelength of a noise signal like the one below? I find it easy to understand for sine waves, but it gets tricky for me when the signal is more complex like a noise signal. If I ...
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Applying 1D wiener filter radially to 2D image

I am new to image processing. Using python, I have constructed a 1D wiener filter from the power spectrum of a Noisy Image, with Noise as a function of k. They both have the same dimension which is ...
2 votes
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2D Cooley-Tukey FFT in Python

I've been trying to confirm the process for the Cooley-Tukey approach for FFTs. Currently I have a function that generates random input data for a matrix with $n_1$ rows and $n_2$ columns. The result ...
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1 answer
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perform fourier-type integration using DFT misunderstanding

I need to perform the following integral ($i^2 = -1$) (with a fixed value of $m$): $ \int_{\phi=0}^{\phi=2\pi} \psi(\phi) e^{-im \phi} \hspace{0.7mm} d\phi $ for all values of $m$ in $\{-N_{\theta}, -...
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1 answer
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Scaling factor in DFT: pure math or bandwidth issues?

I'm trying to match the amplitudes of a signal before performing DFT and after. So, let's consider a 64-point sine signal with amplitude of $1$: The DFT of such a signal will give us the amplitude (...
2 votes
2 answers
5k views

Relation between the DTFT and the spectrum of a sampled signal

In the $\rm DTFT$ (Discrete Time Fourier Transform) the spectrum is periodic with a period of $2\pi$ . A continuous signal when sampled has a spectrum which is a repeated version of its original ...
12 votes
3 answers
4k views

Slow Down Music Playing While Maintaining Frequency

Playing a piece of music audio at a slower speed would lower its pitch (frequency). Is there a tool and theory to slow down the song playing while keep the frequency the same? I suppose one can do ...
-1 votes
2 answers
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Impulse invariance vs. DT representation of a CT system: Where is the inconsistency?

Suppose you have a continuous-time (CT) system $h_c(t)$, bandlimited to $B$. Your goal is to represent the system as a discrete-time (DT) system $h[n]$, sampled at $f_s \leq 2 B$. Clearly $h[n]$ won't ...
1 vote
1 answer
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Showing Fourier slice theorem and Radon transform relation in MATLAB

I wrote some code to demonstrate the Fourier slice theorem and it's relation to the Radon transform. However the sampled FFT from the 2D FFT and the 1D FFT of the projection at the same angle don't ...
2 votes
2 answers
283 views

One integral inverse CWT

MATLAB's icwt docs state inversion to be done by a single integral: $$ f(t) = 2 \Re e\left\{ \frac{1}{C_{\psi, \delta}} \int_0^\infty \left< f(t), \psi(t) \right> \frac{da}{a} \tag{1} \...
3 votes
3 answers
109 views

Effect of overlapping percentage on STFT output

I know STFT is generally applied to non-stationary signals but I tried to apply it to a stationary signal to get a working knowledge. I created a stationary signal composed of three frequencies as ...
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How do I generate the approximate Fourier Transform of the signal using Principle of Stationary Phase?

The following excerpt is taken from the textbook "Digital Processing of Synthetic Aperture Radar" by Ian G. Cumming The Principle of Stationary Phase (POSP) can be briefly explained as ...
4 votes
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Fourier transform of modulus of sum of weighted sines

$$ x(t) = |a \cos(\omega_0 t) + b \cos(\omega_1 t)| $$ with $a, b \geq 0$, $\omega_0, \omega_1 > 0$, but $a, b > 0$ or all $a, b$ (negatives included) is also acceptable, or replacing $\cos$ ...
2 votes
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61 views

pocketfft delivers wrong values

does anyone understand how to use the pocketfft by martin reinecke? Link: https://gitlab.mpcdf.mpg.de/mtr/pocketfft Basically it's just this snipped of code: ...
1 vote
1 answer
61 views

Fourier transform of the energy

If I have the time history of the energy, Does it make sense to do the fourier transform of this energy? or if I want to see the energy in frequency the PSD is the only tool? and Why
2 votes
1 answer
390 views

Why does Hilbert filter distorts the shape of the signal?

If all the harmonics composing a the signal are shifted by the same amount, this would be the same as sampling later or earlier in time. I think. Take a simple pulse train as an example. If Fourier ...
6 votes
3 answers
139 views

What are the criteria for a change-of-basis transform to be doable in $O(n \log(n))$?

The Fourier basis is a common choice for transformations, but a lot of times, it's not the best for a specific application. For instance, wavelet bases give us better spatial / temporal locality than ...
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2 answers
783 views

Purpose of Phase Information

I am learning Fourier Transform from many days but till now I am not able to understand what does phase angle image show us or tell us? They say that MAGNITUDE tells "how much" of a certain frequency ...
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2 answers
4k views

Estimate phase using STFT in Matlab?

My signal oscillates back and forth on the interval [-1, 1] at varying frequencies, with some added higher frequency noise components (example data shown below). I want to to estimate the phase of the ...
1 vote
1 answer
415 views

Spacing between gaussian windows for STFT

I'm computing discrete short time Fourier transform. Data is split into overlapping chunks and gaussian window is used for each chunk. However, I'm not sure how much overlap there should be between ...
2 votes
1 answer
401 views

General question about DFT

I am learning Fourier analysis and without any teacher, just trying to read books on my own. I think I have made some decent progress but they are a couple of points which are still very unclear to me ...
3 votes
1 answer
412 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 ...
1 vote
0 answers
146 views

Bring two Fourier transforms to same range to add them

I have Fourier transforms of two images which I wish to add (Basically I have an input Fourier transform which I mask, reconstruct the underlying image using an algorithm, and then try to replace the ...
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1 answer
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Multiply and divide by the same function in convolution

I am calculating the convolution of two functions $F(x), G(x)$ in $\mathbb{R}^{n}$, n-dimensional space. I have another function $h(x)$ that is a Gaussian. What effect does multiplying $F(x)$ by $h(x)$...
3 votes
1 answer
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Finding a periodic signal knowing its period, mean value and power

I've found an interesting exercise which I have been trying to solve for a couple days, without success. Let $x(t) \in \mathbb{R}$ be a periodic signal with fundamental period $T_0 = \tfrac{1}{4}$, ...
1 vote
1 answer
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My fft gives always gives the correct frequency or double the correct frequency

I will do anything to get help. Please help me find a solution. I can safely say that my fft algorithm, implemented with pyfftw, works as intended when a sine wave with a certain frequency is passed. ...
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1 answer
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Why is FFT module for smaller df showing uexpected malfunctioning in Python?

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1 answer
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Frequency domain filtering: must filter coefficients always be conjugate symetric?

While trying to do frequency domain filtering of audio signals using windowed overlap-add methodology, I came across some pre-calculated frequency domain coefficients. I noticed that the coefficients, ...

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