0
votes
1answer
128 views

Harmonic mean of absolute value squared discrete Fourier transform

Let $X[k] \in \mathbb{C}$ be the discrete Fourier transform of $x[n] \in \mathbb{R}$, where $k,n = 0,1,2,...,N-1$. Parseval's theorem relates the arithmetic mean (AM) of absolute value squared ...
3
votes
2answers
82 views

Estimating time in harmonic signal

I hope someone can help me with the following problem: Assume a periodic signal of the form $$\begin{align} s(t) &= \sum\limits_{p=1}^P \sin(p\Omega_0t)\\ &= \sum\limits_{p=1}^P ...
2
votes
0answers
75 views

Proof of Caratheodory's theorem about the unique determination of a linear combination of sinusoids

Following is a statement of Caratheodory's Theorem about a positivelinear combination of sinusoids :- Any positive linear combination of k sinusoids is uniquely determined by its value at time t ...
2
votes
1answer
685 views

Hilbert transform of white noise

What is the Hilbert transform of a white noise $\xi(t)$? By the Hilbert transform I mean: http://mathworld.wolfram.com/HilbertTransform.html Thank you.
1
vote
1answer
458 views

Is this a square wave signal?

i have a decomposition of a square wave signal: $$ y = \frac{4h}{\pi}(\sin(x) + \frac{1}{3}\sin(3x) + \frac{1}{5}\sin(5x) + ...) $$ I computed the fundamental wave and 2 harmonic waves: $$ U_{r0} = ...