Questions tagged [fourier-transform]

The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.

Filter by
Sorted by
Tagged with
0
votes
2answers
371 views

Derivation of Nyquist Frequency and Sampling Theorem [closed]

I have been looking through different sites and questions over the internet about Sampling theory, but couldn’t find the clear definition of how nyquist frequency condition is derived? It would be ...
0
votes
0answers
49 views

Fourier Transform of finite time series

I have some signal 𝑠(𝑡) which is real data i.e. finite. The time runs from −𝑇 to +𝑇. The signal amplitude is large at 𝑡=0 and small (→0) at the ±𝑇 limits. I can do a finite (discrete) Fourier ...
0
votes
1answer
39 views

What is the form of the spectral derivative in the all-positive-frequency notation in DFT?

The Discrete Fourier Transform (DFT) of a function $u:[0,2\pi] \to \mathbb R$ sampled over $N$ equidistant points $\theta_j = 2\pi j/N,\, j = 0, \dots, N-1,$ is defined by $$ \tilde U_k = \frac1N \...
0
votes
0answers
42 views

Solving equation with convolution

I have the measured signal $y(t)$ that can be modeled in the frequency domain as $Y(f)$: $$Y(f) = X(f)\cdot A(f) - [X(f)\cdot B(f)] \ast C(f)$$ where $\ast$ is the convolution. I know $A(f)$, $B(f)$,...
0
votes
1answer
43 views

Inverse Fourier Transform Dirac impulse with scaled argument

Currently, I am dealing with the sampling problems and I don't understand how to calculate inverse Fourier transform of a scaling impulse function $\textrm{IFT}\{\delta(\Omega T)\} = ?$, $T$ is ...
-1
votes
1answer
60 views

Sampling of frequency response

Let's consider any physical quantity depending on the frequency. For example, the impedance of a certain electrical component: $Z(f)$. Now, imagine to measure it in a continuous interval of ...
0
votes
1answer
197 views

How to perform spectral inversion in the frequency domain to convert a low-pass filter into a high-pass filter?

To convert a linear-phase FIR low-pass filter into a high-pass filter with the same cut-off frequency, we can invert the sign of the low-pass filter's impulse response $h(n)$ and then add one to the ...
0
votes
2answers
74 views

Fourier transform of a periodic/aperiodic signal

Generally speaking, I know that periodic signals (continuous-time domain signals) with period 2pi/wo have a spectrum with equidistance Delta-impulses of distance w0. My question is that, if we have ...
1
vote
1answer
38 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 ...
0
votes
0answers
28 views

FFT freqency bin center in R

I'm trying to do a spectral analysis in R. I learned it in Python from Allen Downey's ThinkDSP book. What is the R equivalent of the Python numpy function, numpy.fft.fftfreq? If you provide a window ...
0
votes
0answers
29 views

Two Consecutive Inverse Fourier Transforms [duplicate]

What happens to a function F(w) if you take two consecutive inverse Fourier transform of it?
0
votes
1answer
48 views

How does one interpret an element of the “transfer matrix” used to calculate frequency domain granger causality (via VAR models)?

I am attempting to gain a better mathematical understanding for how autoregressive models can be used to infer frequency-domain granger causality. All freq. domain measures of causality that utilize ...
0
votes
0answers
60 views

Frequency Domain Signal to Noise Ratio

I am doing some research on low-cost air pollution sensors. I'm measuring the "ground truth" with a single low-noise sensor, and I'm trying to use it to calibrate a low-cost sensor that has high noise....
0
votes
1answer
64 views

If the cosine function is periodic, why does it have a Fourier Transform? [duplicate]

As far as I understand Fourier Transforms are for non-periodic signals and Fourier Series for periodic signals. So why is it we can take the Fourier Transform of a cosine when it is a periodic ...
0
votes
1answer
48 views

How do I make sense of the cosine wave having Fourier Transform coefficients which have infinite magnitude?

To illustrate my question better, consider the Fourier Transform of an aperiodic (as a periodic cosine wave has a Fourier Transform not Fourier Series) cosine wave $$f(x) = \begin{cases} \cos(2\pi ...
0
votes
1answer
153 views

How does minimum-latency partitioned convolution reverb work when you receive input samples in chunks, rather than one at a time?

I'm writing a reverb system where I receive an input block of samples 480 elements long, do some operation on them, and pass the block on to the next effect. I've been reading up on partitioned ...
0
votes
1answer
74 views

DTFT of even and odd samples

Here to find DTFT of $h(2n)$ they have scaled omega, while in RHS to find DTFT $x(2n+1)$ they didn't, why is that?
0
votes
1answer
143 views

Inverse Discrete Time Fourier Transform of $1$

$\textrm{DTFT}(\delta[n]) =1$, but $\textrm{IDTFT(1)} = \frac{\sin(\pi n)}{\pi n}$. Why it is not equal to the unit impulse $\delta[n]$?
0
votes
1answer
146 views

What determines peaks in FFT?

I ran FFT on three audio files and found that the results for some have more peaks than the other. Could anyone give me any conceptual explanation as to what determines these peaks? Below are plots of ...
3
votes
1answer
112 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, pad it with zeros and take the ...
1
vote
1answer
95 views

Why the spectral coherence is unity for all frequencies between single-frequency time series and itself

In the example below, I am plotting the coherence between time series and itself. The time series do has one frequency.The coherence magnitude was one for all frequencies. I wonder why it is not zero ...
0
votes
0answers
51 views

How to find a Matched Filter Transfer Function from large signal sample

Lets say I have a system where I have a small sample of a signal with no noise $\hat{x}(t)$ and a lot of a similar signal with noise $y(t) = \hat{x}(t) + n(t)$, and from $\hat{x}(t)$ I want to create ...
0
votes
1answer
324 views

Signal processing using numpy python

To process a .wav audio file with numpy (using fast Fourier transform algorithm). I want to process an audio signal at a particular interval with a sampling frequency 44100hz and sampling rate of 20ms ...
0
votes
1answer
77 views

Fourier Spectra : Significance of the Negative Amplitude [duplicate]

For example, for an aperiodic gate pulse, the Fourier Transforms for the continuous time case is a sinc function, while the discrete time case gives a sine over sine periodic kind of a function. In ...
0
votes
3answers
34 views

Is there a version of Welch's method that doesn't look for power?

Welch's method splits a time signal, $x(n)$ into $M$ periodograms $P_m$, $P_{x_m,M }(k) = \frac{1}{M}|F_k(x_m)|^2$ and averages them to give the Power Spectral Density (PSD), $S_{x}(k) = \frac{1}{K}...
-2
votes
1answer
86 views

How do I decide which frequencies are signal and which are noise?

I have an arbitrary recorded digial signal, on which I have run a Fourier transform. I'm not sure what conventions are on a case like this, but I have 1024 frequency bins. Second bin is the highest ...
0
votes
2answers
162 views

Fourier Transform: interpretation of continuous spectrum at specific frequencies

B. P. Lathi in his book "Principles of Linear Systems and Signals" mentions in the Fourier Transform: When $x(t)$ is periodic, the spectrum is discrete, and $x(t)$ can be expressed as a sum of ...
0
votes
2answers
253 views

Aliasing when interpolating with DFT?

I'm coming from an understanding of the continuous-time Fourier Transform, and the effects of doing a DFT and the inverse DFT are mysterious to me. I have created a noiseless signal as: ...
0
votes
0answers
22 views

How to search for irregular signals: Fourier, DWT or k-means?

See my notebook here I want to search for irregular time signals in a data set of ~3 500 000 time signals. By eyeballing I have found hundreds of flat and oscillating signals, but just a few that are ...
0
votes
1answer
47 views

What is Imaginary in Fourier transform?

How to plot graph of $e^{-t}$ in frequency domain. What would be the axis? If its Fourier transform is $1 /(1+j\omega)$, then how can we plot imaginary on frequency domain (amplitude vs frequency ...
2
votes
2answers
319 views

Explain Auto-Tune in a simple way

I have to do a presentation about Auto-Tune and its relation to the Fourier transform. What is a good explanation on how does Auto-Tune work?
1
vote
1answer
39 views

Impulse response of a 3x3 PSF - how to find analytical expression for fourier transform of a 3x3 matrix?

I have a filter $\mu[n_1, n_2]$ with taps: $$ (1/8) (1/4) (1/8)$$ $$ (1/4) (1/2) (1/4)$$ $$ (1/8) (1/4) (1/8)$$ How do I find an analytical expression for $\hat\mu(w_1, w_2) $? Since it looks so ...
2
votes
2answers
120 views

STFT on time varying signal with good time and frequency resolution

I am trying to determine the main frequency of a noisy signal that varies in frequency over time. Ideally I want to detect changes in the frequency as rapidly as possible - say 50Hz update rate, but I ...
11
votes
6answers
6k views

Is there any practical application for performing a double Fourier transform? …or an inverse Fourier transform on a time-domain input?

In mathematics you can take the double derivative, or double integral of a function. There are many cases where performing a double derivative models a practical real-world situation, like finding the ...
2
votes
0answers
55 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 ...
0
votes
0answers
29 views

How can I relate my amplitude from a FTT to the actual signal?

Sorry for disturb you guys, I've been playing with this the last days. I am computing signals of a wave produced with a wavemaker. Cause I have several sensors (wave gauges) I am sensing the same wave ...
0
votes
4answers
193 views

Determining LTI system response to a scale change

We know that for an LTI system, if $y(t)$ is the output for $x(t)$ then the response for $x(t-2)$ will be $y(t-2)$ and so on. But my question is what will be the system response for the input $x(-2t)$...
2
votes
2answers
147 views

How to reconstruct a sound from magnitude spectrogram?

I have an audio magnitude spectrogram but I don't have the phase, try to randomize the phases of each container and then make a reverse fourier, but only pure noise is heard How can I reconstruct the ...
1
vote
1answer
52 views

Non Circulant Translation Using Fourier Transform

The translation property of Fourier Transform (FT) for a two dimensional image $f$ is as $$ f(x-x_0, y - y_0) = F(u, v)e^{-j2\pi(ux_0/M+vy_0/N)} $$ Using this equation, the following code (in Matlab) ...
2
votes
2answers
344 views

Sinc interpolation in spatial domain

I have tried to perform sinc interpolation (in 1D) with the following Matlab code: ...
1
vote
0answers
29 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://...
4
votes
4answers
938 views

Is Fourier series a sampled version of Fourier transform?

I recently learned about dtft and how dft/dfs is the sampled version of dtft. I was wondering if Fourier series is also obtainable by sampling Fourier transform? I am a noob in the subject so sorry if ...
0
votes
1answer
57 views

Estimation / Reconstruction of an Image from Its Missing Data 2D DFT

Given the 2D DFT of an image i.e. a NxM matrix of complex numbers, with some missing lines (or even partial lines), considering we have zeros in the missing positions. Any suggestions for an ...
0
votes
0answers
46 views

Is the whole data needed for the fast fourier transform with an ongoing signal?

I sample an signal with around 840k values a second, to check the spectrum around <400kHz. But i can't save the whole data as it is just to much for my microcontroller. I know that for the ...
0
votes
1answer
123 views

Fourier transform in Matlab and hermitian symmetry

According to the conjugate symmetry property of Fourier transform, shouldn't the following command not return 1 (=true): ...
1
vote
0answers
132 views

Implementing rotation in frequency domain and map it back to spatial domain

Please consider the following small example: ...
2
votes
2answers
865 views

What effect does rotation in the spatial domain has on phase in Fourier transforms?

More precisely, let's say I apply a 45 degrees rotation to an image (in the spatial domain) say, in Matlab : Ir=imrotate(myImage,45,'crop'); FT_I=fft2(I); In the ...
2
votes
1answer
58 views

Continuity and its relationship with asymptotic spectral decay

The asymptotic decay of the magnitude of the Fourier transform of a function appears always to be determined by its continuity properties as follows, with examples given in Fig. 1: Continuous ...
2
votes
1answer
133 views

Approximating Lorentzian Fourier transform with FFT

I have a Lorentzian frequency distribution $F(w) = \frac{1+iz}{1+z^2}$ Where $z = \frac{w-\Omega}{R}$ With $\Omega$ being the peak frequency and R the decay constant. I know that analytically ...
14
votes
4answers
5k views

“The Fourier transform cannot measure two phases at the same frequency.” Why not?

I have read that the Fourier transform cannot distinguish components with the same frequency but different phase. For example, in Mathoverflow, or xrayphysics, where I got the title of my question ...

1
3 4
5
6 7
30