All Questions
Tagged with signal-processing fourier-transform
105
questions
20
votes
6
answers
19k
views
Why are cosine and sine functions used when representing a signal or a wave? [closed]
Actually, in the mathematics sine and cosine functions are defined based on right angled triangles. But how will the representation of a wave or signal say based on these trigonometric functions (we ...
- 339
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
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
14
votes
2
answers
2k
views
Convolutions in Physics
At a high-level Wikipedia states: "A convolution between two functions produces a third expressing how the shape of one is modified by the other."
But there are clearly many ways of combining ...
- 397
14
votes
4
answers
2k
views
Reconstruction of "wavefunction" phases from $|\psi(x)|$ and $|\tilde \psi(p)|$
Consider a "wavefunction" $\psi(x)$, which has a Fourier transform $\tilde \psi(p)$
Suppose that we know, for each $x$, $|\psi(x)|^2$, and that we know, for each $p$, $|\tilde \psi(p)|^2$.
Have we ...
- 17.7k
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
10
votes
4
answers
21k
views
Continuous Fourier transform vs. Discrete Fourier transform
Continuous Fourier transform vs. Discrete Fourier transform. Can anyone tell me what the difference is physics-wise? I know the mathematical way to do both, but when do you use the other instead of ...
- 2,537
9
votes
4
answers
3k
views
Sound of a limited wave after removing main frequency?
From my old studies in signals I can remember that "a signal limited in frequency domain is unlimited in time domain" and viceversa (a signal limited in time domain is unlimited in frequency domain).
...
- 737
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
9
votes
2
answers
4k
views
How to distinguish female and male voices via Fourier analysis?
What makes one, without looking, be able to identify the gender of the talker as male or female?
I mean if we Fourier analysed the voice of males and females, how the 2 spectrums are different which ...
- 17.1k
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
7
votes
3
answers
5k
views
Why is the bispectrum not commonly used in experimental physics?
Power spectra, coherence spectra, and linear transfer functions are ubiquitous tools of experimental physics. However, our instruments often retain small nonlinear effects which can contaminate ...
- 9,541
6
votes
3
answers
2k
views
Can Laplace's equation be solved using Fourier transform instead of Fourier series?
Sorry for the long text, but I am unable to make my question more compact.
Any periodic function can be Fourier expanded. Usually, they say in mathematical physics books, if the function is not ...
- 17.1k
5
votes
3
answers
11k
views
Magnitude of the Fourier Transform of White Noise
Say you have two white noise signals with different variation amplitudes A1 and A2 as shown in this beautiful Excel graph:
Ignoring the DC offset as it's been represented here, how do you relate the ...
- 341
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