Questions tagged [periodic]

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6
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1answer
3k views

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

In my signals and systems course, we have learned that the discrete-time Fourier transform is $2\pi$ periodic, but the continuous-time Fourier transform is not periodic in general. For reference, we ...
2
votes
2answers
14k views

How do I find the fundamental period of the given signal?

I am having a problem in finding the fundamental period of the signal $x(t)$ given below: \begin{align} x(t) &= 2\cos\left(\frac 45 \pi t\right)\sin^2\left(\frac{16}{3} t\right)\\ &= 2\cos\...
4
votes
3answers
1k views

formula derivation for periodic signal power

Studying DSP on my own. Taking an introductory class. Was given a formula for signal power $$ P = \lim_{M\to\infty} {\frac{1}{2M+1} \sum_{n=-M}^M} \lvert x[n] \rvert^2 $$ I do understand why the ...
0
votes
2answers
6k views

Why is cos(n/6) aperiodic?

This is a very common example in most Signal Processing books I have come across. x(n) = cos($\frac{n}{6}$) is a non-periodic discrete signal because it doesn't satisfy the periodicity condition for ...
4
votes
1answer
3k views

Is the periodogram squared-magnitude DFT or squared-average DFT?

How is the periodogram defined? I have been searching the internet a lot, and I find two different definitions: periodogram is the squared magnitude of the DFT periodogram is the squared average of ...
9
votes
2answers
3k views

Fourier transform artifacts

My starting point in what follows is a radially symmetric random field. Taking the Fourier transform of this (and plotting it in logarithm to highlight the patterns), I obtain the following image in ...
3
votes
2answers
202 views

periodicity coefficient

I wonder if an efficient method exist to compute how much a signal is periodic, it should be ~1.0 when the signal is totally periodic (like a sinusoïdal signal) and ~0.0 when totally random, like a ...
2
votes
1answer
220 views

Testing discrete data for periodicity

I have some data which looks roughly periodic - is there a nice way to measure this? This is an example I'm working on and I'd like a metric that I will be able to just threshold to give a decision ...
0
votes
1answer
3k views

How to find the period of a noisy signal using MATLAB's $\tt xcorr$?

Here is my code: function [ T ] = FindPeriodicity2(x,Fs) ac=xcorr(x,x); [~,locs]=findpeaks(ac); T=mean(diff(locs)/Fs); end and when I pass the signal ...
0
votes
1answer
112 views

Autocorrelation - Understanding reduced correlation at periodic time shifts using np.correlate (versus statistical autocorrelation)?

I'm going through the Think DSP by Allen B. Downey, and I'm struggling to understand a specific aspect of np.correlate and how it differs from statistic autocorrelation. The question is at the bottom, ...
8
votes
3answers
777 views

Is $x(t) = \cos t + \sin\left(\frac{1}{2}t\right)$ a periodic signal?

Is $x(t) = \cos t + \sin\left(\frac{1}{2}t\right)$ a periodic signal? The answer provided by the book is different from my answer. Book says its not a periodic signal. Can you guys tell me why is it ...
2
votes
4answers
328 views

Very basic question about how we define frequency in signal processing

When talking about general periodic continuous-time signals for which $$x(t + T_0) = x(t)$$ where $T_0$ is the fundamental period we define the fundamental frequency $\omega_0$ as $\omega_0 = 2\pi/T_0$...
2
votes
2answers
223 views

Fourier transform with periodicity at the harmonic frequency

Let's suppose I have a signal $F(t)$ that is periodic, with two periodicities $P1$ and $P2$, with $P1>P2$ Suppose that I know the values of the two periodicities. Using the Fast Fourier transform ...
-1
votes
2answers
1k views

Spectral leakage - understanding the integer number of cycles while windowing

I am reading tutorials about windowing and have read following sentence: For an integer number of cycles, all smoothing windows yield the same peak amplitude reading and have excellent amplitude ...