0
votes
1answer
46 views

Fourier transform with periodicity at the harmonic frequency

Let's suppose I have a signal $F(t)$ that is periodic, with two periodicities $P_1$ and $P_2$, with $P_1 > P_2$. Suppose that I know the values of the two periodicities. Using the Fast Fourier ...
0
votes
1answer
74 views

Image K-Space and SNR

I am imaging a sample using CMOS camera. The pixel ratio is 6um x 6um and a total resolution {480, 752}. I understand that each pixel on the camera sensor is 6um x 6um in size (Have I understood this ...
9
votes
3answers
255 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 ...
0
votes
0answers
79 views

Discrete Fourier Transform: Why do we only consider a full cycle?

I am studying Fourier analysis and I am still new to this topic. If I understand that the maximum frequency that can be used in a DFT is given by $N/2$, where $N$ is the number of samples in our ...
1
vote
3answers
1k views

What is the meaning of “frequency of a human voice”?

The term frequency for a periodic wave can be defined as the number of times a repeating pattern occurs in a given time period (eg: no. of crest and trough cycles per second for EM wave). But what ...
1
vote
1answer
213 views

Parseval's Theorem on a Random Signal

NB - I'm re-posting this question in physics because I haven't had any luck getting a response from the maths StackExchange site - it's a rather applied problem so is probably better suited here ...
3
votes
2answers
361 views

>What is the physical interpretation of the Fourier transform $(\mathcal{F}Z)(t)$ an impedance?

If I compose a impedances out of smaller ones in series and parallel configurations, e.g. $$Z(\omega)=i\omega L_2+\tfrac{1}{\tfrac{1}{R_1}\ +\ i\omega C_1+\ \tfrac{1}{i\omega L_2}},$$ then I get a ...
2
votes
3answers
496 views

Fourier series of single tone modulated wave

When a single-tone continuous modulating signal modulates a sinusoidal carrier, isn't the modulated wave periodic? If so, can't we apply fourier series and determine the harmonic frequency components ...
1
vote
3answers
2k 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 ...
3
votes
3answers
178 views

What information is stored on gramaphones/tape recorders/CDs/DVDs

I'm a Software Developer by profession and my physics knowledge is limited what I had learned at high school level. Please excuse me if the question is trivial. Question: From what I know, a sound ...
6
votes
2answers
904 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 ...
5
votes
3answers
1k 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 ...
2
votes
2answers
410 views

Simulating eye diagrams

I'm trying to figure out how to simulate eye diagrams for communications systems using Python. I'm not sure I have the theory down completely, though. From what I could figure out using some old ...
6
votes
3answers
1k 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 ...