# Questions tagged [cyclostationary-random-process]

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### What mathematical tools exist for understanding modulated noise?

Suppose we have a signal $n$ that consists of Gaussian white noise. If we modulate this signal by multiplying it by $\sin 2\omega t$, the resulting signal still has a white power spectrum, but ...
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### How can a signal be both periodic and random?

Do any examples of such signals exist where the signal is both periodic and random? Because as I see it, if a signal is periodic then the randomness kinda goes away because you know what the signal ...
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### Identifying whether or not a cyclostationary signal is noisy or not using the cyclic autocorrelation

I am trying to determine whether or not a given signal has been corrupted by Gaussian noise, either bandlimited (with a filter) or not. The signal in question is a BPSK or PAM signal that is upsampled ...
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### Proving a cyclostationary processes signal

Suppose a random signal $x(t)=\sum\limits_{n=-\infty}^\infty Z_n \delta(t-n\tau)$, where $z_n = Z$ and $Z$ is a random variable with equal probability to be $+-1$, is passing through a low pass ...
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### Autocorrelation of filtered cyclostationary random process

Background: When a wide-sense stationary (WSS) random process $x(t)$ is passed through a linear, time-invariant (LTI) filter with impulse response $h(t)$ to produce $y(t)$, the following relationship ...
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### Power spectral density of a PAM signal

Say I have a PAM signal as $x(t) = \sum_n a_n h(t-nT)$ where $\{a_n\} \in \{\pm 1\}$ are equiprobable random binary bits and $h(t)$ is bandlimited to $[-1/(2T),1/(2T)]$. ($x(t)$ is random process and ...
### Spectral correlation zero modulation frequency $S_x(\alpha, 0)$
I got a simple modulating signal $x(t)=\sin(2\pi\alpha t)\sin(2 \pi \beta t)$ with carrier frequency $\alpha$ and modulation frequency $\beta$. The spectral correlation will obviously have components ...