# Tag Info

### Period and wavelength of a noise signal?

Let's start with some definitions (wikipedia): A signal is a periodic signal if it completes a pattern within a measurable time frame, called a period, and repeats that pattern over identical ...
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### Periodicity of a constant signal!

As you say, the constant function is periodic. A signal $x(t)$ is said to be periodic with period $p$ or to have a period $p$ if there exists a $p>0$ such that $x(t+p)=x(t)$ for all real numbers $t$...
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### How can a signal be both periodic and random?

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 ...
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### $2\pi$ periodicity of discrete-time Fourier transform

The argument does not work in continuous time. In discrete time the argument is that $$e^{j\omega n}=e^{j(\omega+2\pi)n},\qquad n\in\mathbb{Z}\tag{1}$$ This is true because by definition $n$ is an ...
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### How to calculate the FFT period

You must have understood the notion of digital linear modulation or discrete time vs continuos time (see Chapter 2). Another reference. OFDM can be thought as FDM with sinc pulse whose delay-$T$-...
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### How do I find the fundamental period of the given signal?

If your top equation is really $$x(t) = 2\cos\left(\frac 45 \pi t\right)\sin^2\left(\frac{16}{3} t\right)\tag{1}$$ You gonna have a hard time getting the fundamental period/frequency as the there ...
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### Why is cos(n/6) aperiodic?

The problem with your reasoning is that $\pi \ne \frac{22}{7}$; $\pi$ is an irrational number. There is no period $N$ for which $x[n] = x[n+N] \ \forall \ n \in \mathbb{Z}$. Hence, the sequence is not ...
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### How can a signal be both periodic and random?

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 ...
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### Why Zero Padding in the Center of the DFT Interpolates / Upsamples the Signal (Sinc Interpolation / DFT Interpolation / Periodic Interpolation)

What you are experiencing is technically called interpolation by DFT; i.e., interpolating a time-domain sequence $x[n]$ by properly zero filling the middle portion of it's DFT $X[k]$ (and taking the ...
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### How can i get a growing sinusoid in matlab?(by incorporating real part into exp command besides imaginary part which is already there)

Here is an alternative: you can pass a complex (not just an imaginary) exponent. The real part of the exponent controls the amplitude, the imaginary part the frequency. The resulting signal is also ...
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### Calculating the complex signal's average power

Solve the integral: $$P = \lim_{T \to \infty} \frac{1}{T}\int_{-T/2}^{T/2} |x(t)|^2 dt$$ This is usually unwieldy to solve directly; it can be shown that if a signal is periodic, you only need to ...
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