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12

An example you run typically across in a text book (Papoulis as an example) is the sine with random phase $$ x(t)=\sin(2\pi f + \phi) $$ where $\phi$ is a random variable, distributed uniformly, over $0$ to $2\pi$. Any realization will have $\phi$ take on a particular value, but it’s random, just like a 6 on a dice after a throw. You could not predict it ...


9

Most realistic signals are both random and periodic. For example, you can modulate a harmonic oscillator with a slow enough random signal that moves its frequency around a $\mu_{f}, \sigma_f$. This looks like: $$y= \sin \left( \frac{2 \pi \mathcal{N_s}(\mu_f, \sigma_f) n}{Fs} \right )$$ Where $\mathcal{N_s}(\cdot)$, denotes a normally distributed random ...


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If you are talking about a given signal as "a deterministic realization of a phenomenon", it can be periodic, but not really random. However, some physical systems are prone to produce randomness and periodicity, like rotating machines, gears, cyclic engines, that produce signals similar to: Naturally rotating bodies (stars, planets) also produce random ...


1

Equidistant Dirac impulses in the spectrum imply a periodic time domain signal. As pointed out in a comment, in continuous time, the signal $x(t)=\sin(\omega_0t)$ is always periodic, regardless of the value of $\omega_0$. Your question about the spectrum being periodic is unclear to me. A one-sided spectrum with equidistant Dirac impulses also implies a ...


0

@Niousha. Regarding your first paragraph, in theory a real-valued continuous-time domain sinusoidal signal, of infinite time duration, will have only one positive-frequency impulse in the frequency domain. (I say "in theory" because such a signal does not exist in Nature. Such a signal is strictly an abstract concept, like a perfect circle or one of Euclid's ...


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