All Questions
Tagged with signal-processing fourier-transform
105
questions
1
vote
1
answer
53
views
Wavelength and frequency associated with a wave pulse
What are the definitions of wave length and frequency of a wave pulse?
- 468
0
votes
1
answer
127
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What would happen when two wave functions intersect in a Fourier series representation of periodic signals? [closed]
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(ωt) y=sin(ωt), which are periodic. ...
- 109
0
votes
2
answers
4k
views
How do I convert the Amplitude from Power/Amplitude spectral density?
I've started working on PSD for seismic signals. In theory, PSD signal can be expressed in 2 ways. One in $(PSD=g^2/Hz)$ and other in $PSD=((meter/second^2)^2/Hz)$ and also ASD=(√PSD). Here $g$ is the ...
- 11
19
votes
6
answers
3k
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Can we quantify the pitch of a sound that is a mixture of many frequencies?
How is the pitch of a sound defined quantitatively when it is a mixture of many frequencies? For example, the sound emitted by a plucked guitar string, or say, the pitch of somebody's (normal) voice. ...
- 11.8k
1
vote
1
answer
65
views
Is this a good use of the convolution?
I would like to replicate the real response of an instrument to some signal. Here's what I have in mind: I generate some ideal signal. I then add Gaussian noise to it to produce a realistic signal s(t)...
- 150
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0
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28
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An idea to retrive phase of different frequency from noisy experimental data
There is a lot of idea in this website to retrive phase of certain frequency from a noisy oscillation. For example this one: use band pass filter to filter out certain frequency and then use hilbert ...
- 357
0
votes
0
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34
views
Why the General Lomb-Scargle results are doubled?
I got a problem when computing the GLS on MATLAB for my master deegree thesis.
I need to do a comparison between the PSD and amplitude spectrum of a signal computed with three different metods, the ...
- 1
0
votes
2
answers
284
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Understanding the Fourier transform of a signal already with amplitude and phase information
I'm from an image processing background and am working my way into optics. I'm working on phase retrieval problems, trying to understand the Gerchberg-Saxton algorithm. I found this video which is ...
- 101
1
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2
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411
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How can we show that a lens is a low pass filter?
I understand from the derivation in Goodman Chapter 6 that a lens Fourier transforms light from the front focal plane onto the back focal plane, ignoring aperture effects. I've also read that a lens ...
- 1,356
0
votes
0
answers
79
views
Physical interpretation of FFT frequencies
I need to calculate the PSD of a discrete signal and want to compare it to other processes. By Nyquist theorem, I only can account half of the frequencies.
Assume I have a signal of length $N=100$, ...
0
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1
answer
53
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Is there any known result about the "average period" of a complicated oscillating function?
Say we have some frequency spectrum, $f(\omega)$, where
$$
f(t) = \frac{1}{2\pi} \int_{-\infty}^\infty d\omega \; f(\omega)e^{-i\omega t},
$$
and we know that $f(t)$ is some sort of ...
- 188
9
votes
2
answers
5k
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What is meant by 2D fourier transform of an image?
I have some questions about this interesting concept I came across about 2D Fourier transform, please...
Firstly, the Fourier transform of a 1D signal (such as a sound recording) is as follows:
The ...
user315366
2
votes
1
answer
172
views
Fourier transform of an exponentially decaying waveform
Consider an atom oscillating at a certain frequency. The amplitude of the oscillation decreases over time such that the waveform can be modeled by an exponential function, but the frequency remains ...
- 23
1
vote
1
answer
43
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What is the relation between the frequency vector and the Nyquist frequency?
When trying to comprehend the concept of Nyquist frequency in FFT, I came across the following definition for half of the frequency range:
$$f = -f_{n}/2:df:f_{n}/2-1;$$
where $f$ represents the ...
- 753
5
votes
2
answers
964
views
What, mathematically, is the power spectrum of a signal?
Given a signal $f(t)$ defined on $t\in(-\infty,\infty),$ what is the precise definition of the power spectrum of $f$, i.e., what is the mathematical operation that takes $f$ to the output of an ideal ...
- 3,407