Power spectrum Definition and 58 Threads

This is more of a data analysis question than a mathematics question so feel free to move it to wherever you think it is most likely to be answered. I have some time series data that looks (just by eye) like it should have several peaks in its power spectrum. However, when I compute the power...

Input: sine wave at 10Hz, amplitude 1. After the transform the plot has a spike at 10Hz with amplitude 0.5. If I vary the amplitude of the sine wave I get: sine amp. - FT spike amp. 1 - 0.5 2 - 2 4 - 8 So it seems A' = A^2/2 Is this because power is proportional to A^2 and it is...

I am looking for a way to calculate the power spectrum of short signals of variable duration (between 200 and 500 ms). Standard methods seem wildly inaccurate. Are there any tricks for short segments? Thanks anyone for a response.

Homework Statement Calculate the power spectrum in dBm of a zero offset, 10MHz square wave with amplitude A from DC to 50MHz. Homework Equations - The Attempt at a Solution I was given this problem but am not sure how to go about solving it. Is the power spectrum the same as the...

Fourier transform --> power spectrum Hey all! I've been learning about the discrete Fourier transform (and FFT too) recently. What I don't understand is why applying it to a signal gives its power spectrum. I am not really good in physics, so to me it just seems like a magical formulae, one...

phi(t)=A_o*e^(2*pi*i*mu_0*t) (label:1) Calculate the power spectra of the following waveforms (using 1): 1) for all t 2) a pulse duration of two tau for |t|<tau, and for phi(t)=0 --- 3)an exponentially decaying sinusoid: phi(t)=A_0*(e^(-t/(2*tau)))*e^(2*pi*i*mu_0*t) for t>0 and...

Would the power spectrum of the CMB tell you whether the cosmological principle is correct? Ack, I was going to try to explain my reasoning, but it doesn't really count as reasoning. :redface: I guess I was wondering what the CMB power spectrum tells you. If it's complicated, nevermind; I'm...

From Kosmoi.com/Science/Cosmology/http://kosmoi.com/Science/Cosmology/Big_Bang/wiki.shtml "A critical further prediction was that the further away one looks, the hotter the universe should appear to be (as looking further away corresponds to looking backwards in time), and at some extremely...