All Questions
Tagged with signal-processing fourier-transform
32
questions with no upvoted or accepted answers
4
votes
0
answers
150
views
The frame of truncated momentum basis on a 1D lattice
$\def\ket#1{\left|#1\right\rangle }
\def\bra#1{\left\langle #1\right|}$
(This is part of a research problem)
The Setup:
Consider a single particle on a finite 1D lattice with the Hilbert space ...
- 482
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
2
votes
0
answers
86
views
The validity of some "applications" of the uncertainty principle
Given a $L^2$ function $f$ with $\int_\mathbb{R}xf(x)dx=0$, define its variance to be $\sigma_f^2=\int_{\mathbb R}x^2f(x)dx$. The uncertainty principle states that $\sigma_f\sigma_\hat f\geq 1/4\pi$,...
- 1,335
2
votes
0
answers
137
views
Why is the optimum window length for a discrete fourier transform of a signal less than 100%?
I'm trying to determine the best settings for a discrete Fourier transform on a signal with noise. Now I've stumbled on something that I can't seem to explain, I'm hoping someone can give me some ...
- 21
2
votes
0
answers
232
views
Converting (time domain) Fluctuations to Power Spectral Density (PSD)
I have a Voltage signal, $V$, with fluctuations that go as:
$$
\langle\delta V(\tau)^2\rangle=\ln f_a\tau
$$
Here $f_a$ is an attempt frequency from an Ahrennius Law. According to many papers, "...
- 121
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
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
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
1
vote
0
answers
244
views
Fourier transform of sound wave
I am a high school student doing a project in Fourier transform. I was planning to learn Fourier transform and manually apply the calculations to a section of a song and see what I get. However, I ...
- 11
1
vote
0
answers
43
views
Computing a second harmonic resistance out of a wave-like resistance signal
I want to reproduce the results of a paper, in which they measure the Anharmonic Hall Effect (AHE) resistance $R_{AHE}^{2\omega}$. There are several protocols for measuring it experimentally, but I'm ...
- 181
1
vote
0
answers
63
views
Fourier Coefficients
Suppose i've a two voice samples v1 and v2. Comparatively voice v1 is louder than the v2. If both the voice is spoken by the same person.(Spoken normally as he speaks)
Is it good to state the ...
- 121
1
vote
0
answers
1k
views
Fraunhofer diffraction problem in Python: How to interpret discrete Fourier transform (DFT) spectrum?
I have a periodic phase grating consisting of lenslets along the x-direction, invariant in y. I want to use python to calculate the far-field (Fraunhofer) diffraction pattern that one gets when ...
- 19
1
vote
0
answers
432
views
How to convert a wave from Amplitude time to Amplitude Frequency domain? Regarding Gravitational waves strain data
I have read that on applying FFT on gravitational wave strain we can bring Amplitude time domain to Amplitude-frequency domain. But when I apply this conversion on the data I had I get this curve
I'...
- 263
1
vote
0
answers
115
views
Discrete Fourier transform for periodic signal?
From the Signal and System textbook, by Oppenheim, I learned that the discrete-time Fourier transform can be written as
$$
x[n]=\frac{1}{2\pi}\int_{2\pi}X(e^{j\omega})e^{j\omega n}d\omega
$$
$$
X(e^{...
- 209
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