All Questions
Tagged with signal-processing fourier-transform
105
questions
0
votes
0
answers
46
views
Fourier Transform of periodic Signals
If $f(x)$ is a periodic signal with a period $A$ then the Fourier transform of the signal $F(k)$ is zero, unless $k A$= $2 \pi n$ where $n$ is an integer. How can there Be a Fourier transform of a ...
- 73
12
votes
8
answers
5k
views
Feynman claimed "The ear is not very sensitive to the relative phases of the harmonics." Is that true?
In The Feynman Lectures on Physics, Dr. Richard Feynman claimed that the ear (I assume he meant the human ear) is not sensitive to the relative phases of harmonics.
However, I was asked to test ...
- 145
2
votes
0
answers
44
views
How to extract the "matter fluctuation amplitude" from the CMB power spectrum?
How do you convert the value listed in Planck 2018 results. VI. Cosmological parameters, $A_s = 2.101\times10^{-9}$ to the value of the matter fluctuation amplitude $\sigma_8=0.8111$? I tried ...
- 21
0
votes
2
answers
84
views
I don't understand intuitively why the instantaneous frequency is obtained by calculating the time derivative of the phase
I don't understand intuitively why the instantaneous frequency is obtained by calculating the time derivative of the phase
- 11
2
votes
1
answer
123
views
Where can I learn Fourier analysis and complex signal processing for quantum mechanics?
I'm requesting resourses to dive deep and get a good grip on complex signals, Fourier analysis and connections to information theory and information encoded by complex signals.
My background: 3rd year ...
0
votes
1
answer
70
views
Doubt on time invariant system
Now I am delaying the output of a system (which takes $x \left( t \right)$ as input and gives $t \cdot x \left( t \right)$ as output) by $T$ then final output is:
Let's denote the output of the ...
- 1
0
votes
1
answer
145
views
What is the physical meaning of the pressure of an acoustic point source being complex?
Context
From various sources of Acoustics (such as "Acoustics -
An Introduction to Its Physical Principles and Applications" by Allan D. Pierce and "Fundamentals of General Linear ...
- 1,785
7
votes
2
answers
1k
views
Why does superposing an infinite number of waves of different wavenumbers eliminate periodicity and may sometimes result in a localised wave?
I am studying how wave packets are defined in quantum mechanics, but I am finding it hard to intuitively understand why superposing an infinite number of waves of different wavenumbers $k$ may ...
- 390
0
votes
1
answer
126
views
The solar spectrum on the time domain
This is the solar spectrum by wavelength:
By formula $c=f\lambda$, we can plot the solar spectrum over the frequency domain:
Then we can conduct inverse Fourier transform to transform the plot into ...
- 9
0
votes
1
answer
71
views
Recovering Decay Constant from Fourier Transformed Exponential Decay in NMR
I'm currently in a NMR lab for an undergraduate physics class, and I am attempting to determine the decay constant $\tau$ (e.g. $T_2$) associated with a free induction decay signal. However, our ...
- 3
1
vote
0
answers
41
views
Spectral representation of a white stationary process
I am trying to better understand the spectral representation of stochastic processes. From the book "Spectral Analysis for physical applications" by Walden and Persival:
The spectral ...
- 111
0
votes
2
answers
47
views
How to convert from a wave-reading?
I have a series of wave-readings which show wave amplitudes pr. time unit for different events. So on the $x $-axis we have seconds, and on the $y$-axis, wave height.
If I want to convert this to a ...
- 143
18
votes
5
answers
4k
views
Fourier vs. Laplace transforms
Electronics books often use Laplace to analyze circuits, while in physics we use Fourier, most of the times... if not always: from complex impedances to electromagnetism, quantum mechanics, Green ...
- 501
1
vote
2
answers
85
views
Signal Processing – Discrete Fourier Transform and Incomplete Fourier Series
I'm working on a paper where I'm collecting sound pressure data from a chord's wave and trying to create a frequency spectrum to find the individual frequencies that make up the chord.
However, I can'...
- 13
1
vote
1
answer
85
views
Evaluate action of $f(\frac{d}{dx})$ using the Fourier/Laplace transform
Initially I asked this question on mathoverflow. I however thought physicists may face this sort of problem more than mathematicians (I am an engineer). Due to that, I decided to ask here as well.
...
- 213
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
views
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
views
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
0
votes
0
answers
28
views
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
answers
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
views
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
vote
2
answers
411
views
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
votes
1
answer
53
views
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
views
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
views
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