13 votes

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 ...
Jdip's user avatar
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12 votes
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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 $t$...
MBaz's user avatar
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10 votes

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 ...
A_A's user avatar
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9 votes

$2\pi$ 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 ...
Matt L.'s user avatar
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7 votes
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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-$T$-...
AlexTP's user avatar
  • 6,595
7 votes

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 ...
Gilles's user avatar
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6 votes
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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 ...
Jason R's user avatar
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6 votes
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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 ...
Laurent Duval's user avatar
6 votes

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 ...
Fat32's user avatar
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6 votes
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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 ...
Hilmar's user avatar
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5 votes

formula derivation for periodic signal power

I'd like to show you a more formal derivation. Note that the first formula for arbitrary (non-periodic) signals could be rewritten as $$P_x=\lim_{M\rightarrow\infty}\frac{1}{(2M+1)N}\sum_{n=-MN}^{(M+...
Matt L.'s user avatar
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5 votes
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Periodic signals in Continuous and discrete time

A periodic continuous-time signal satisfies $x(t)=x(t+T_0)$ for all $t$. The period $T_0$ doesn't need to be a rational number. A periodic discrete-time signal satisfies $x[n]=x[n+N]$ for all integers ...
Matt L.'s user avatar
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5 votes
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Fourier series of cycloid

The Fourier series of the cycloid can be expressed in terms of the Bessel functions of the first kind: $$J_n(x)=\frac{1}{\pi}\int_0^{\pi}\cos(nt-x\sin t)dt,\qquad n\in\mathbb{Z}\tag{1}$$ Using the ...
Matt L.'s user avatar
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4 votes
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periodicity coefficient

I suggest using Spectral Flatness, aka Wiener Entropy. It is defined as a ratio of geometric and arithmetic mean of the magnitude spectra $X(k)$: $$\Xi=\dfrac{\sqrt[K]{\prod_{k=0}^{K} X(k)}}{\frac{1}{...
jojeck's user avatar
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4 votes
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Fourier Series Coefficients

You should use the synthesis equation of an impulse train with period $T$ (which is easy to derive): $$x(t)=\sum_{k=-\infty}^{\infty}\delta(t-kT)=\sum_{k=-\infty}^{\infty}\frac{1}{T}e^{jk\frac{2\pi}...
msm's user avatar
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4 votes
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DFT and periodicity

As you have correctly observed, $2N/W$ must be an integer, because the window can only have an integer number of samples. Furthermore, regardless of the upper summation limit, $$Y_k=\sum_{m=0}^Ke^{-j\...
Matt L.'s user avatar
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4 votes
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Power of a periodic sequence

The basic trick is to bound the series above and below. Let us do it on one side, for positive indices. For any $N> 0$, you can write $N=kN_0+r_N$, with $0\le r_N< N_0$. Then if $a_n$ (here $...
Laurent Duval's user avatar
4 votes

Periodicity of a constant signal!

When you are in doubt, use the limiting approach as an aid in your deductions: For example, you can consider a constant signal $x_C(t)=1$ as the limit of a periodic sine wave $x_p(t)= \cos(\omega_0 t)...
Fat32's user avatar
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4 votes

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 ...
Robert L.'s user avatar
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4 votes
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How is frequency defined for a periodic signal?

In my world, frequency is inverse to period, i.e., a sinusoid with fundamental period $T$ has a frequency $f = \frac 1T$. Of course, angular frequencies are also common, in which case we have $\omega =...
Florian's user avatar
  • 2,463
4 votes

Change in frequency on differentiation

No, in a conventional sense of a "periodic signal" phrase, but, if you permit me to delve into a math subtlety, differentiation can turn an aperiodic waveform to a periodic one: $$ \frac{\...
V.V.T's user avatar
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4 votes
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Autocorrelation for periodic signals

The OP states that for a (deterministic) power signal $x(t)$, the autocorrelation function is defined as $$R_x(\tau) = \lim_{T\to \infty}\frac{1}{2T}\int_{-T}^T x(t)x^*(t+\tau) \,\mathrm dt\tag{1}$$ ...
Dilip Sarwate's user avatar
4 votes

Fourier series of cycloid

I haven't managed to completely evaluate the integral, but I've made some progress and perhaps someone can pick up where I leave off. The integral you gave is $$ c_n = \int_0^{2\pi}\left(\frac{1-\cos\...
Dan Pollard's user avatar
4 votes
Accepted

Why is $x[n]=\sin(\frac{12\pi n}{5})-\sin(\frac{2\pi n}{5})=0$

HINT: $$\sin\left(\frac{12\pi n}{5}\right)=\sin\left(\frac{2\pi n}{5}+\frac{10\pi n}{5}\right)=\sin\left(\frac{2\pi n}{5}+2\pi n\right)$$ Taking into account that $\sin(x)$ is $2\pi$-periodic should ...
Matt L.'s user avatar
  • 90k
4 votes

What is a "pitch period"?

The pitch period of a perfectly periodic function, $x(t)$, is the smallest positive value $P>0$ such that $$ x(t+P) = x(t) \qquad \forall t \in \mathbb{R} $$ Now, simply because a function is ...
robert bristow-johnson's user avatar
4 votes

does T = 1/F always hold?

To understand sampling and aliasing I think a useful analogy is a strobe light on a bicycle wheel. The rate of rotation of the bicycle wheel in revolutions per second represents the frequency of an ...
Dan Boschen's user avatar
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4 votes
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is this signal is perodic?

A signal $e^{j(\omega t + \varphi)}$ has an angular frequency $\omega$ and period $T=2\pi/\omega$. The signal $x_1(t) = 7e^{j(5t + \pi/2)}$ thus has period $$T_1 = \frac{2\pi}{5}$$ Since $a^n = e^{n \...
Blackhole's user avatar
  • 155
3 votes

Periodicity of a constant signal!

If we take the Fourier transform of any constant signal, we get an impulse at zero, which says that its frequency is zero and, hence, it is non-repeating and its period is infinity. No, this does ...
Laurent Duval's user avatar

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