# Questions tagged [periodic]

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### 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 ...
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### Fourier series of cycloid

What is the Fourier series representation of a cycloid? The parametric representation of the curve is as follows. $$t=\dfrac{\theta-\sin\theta}{\pi}\\ x=\dfrac{1-\cos\theta}{\pi}$$ The period is $2$...
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### 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 ...
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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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### $2\pi$ 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 ...
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### 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 ...
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### 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 ...
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### Why Zero Padding in the Center of the DFT Interpolates / Upsamples the Signal (Sinc Interpolation / DFT Interpolation / Periodic Interpolation)

I'm experimenting with the Inverse Discrete Fourier Transform. Starting from the two-cycles continuous $x(t)$ signal below: I have the discrete signal $x(n) = \{ 1, 0, -1, 0, 1, 0, -1, 0 \}$ leading ...
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### Detecting Pattern from Signal Data by Gaussian Mixture Model?

I'm a machine learning newbie. I have sensor data which is generated by several sensors. The data is a series of 'time's. (it is not labeled, in other words, I cannot know which sensor generates ...
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### Downsampling, shifting, high pass and low pass filter commutativity

strong textI have been reading "The Stationary Wavelet Transform and some Statistical Applications" by Nason and Silverman, and there is a claim in the their paper of which I cannot convince myself. ...
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### Periodicity of a constant signal!

This can be a very silly question, but I'm quite confused: 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 ...
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### What is a “pitch period”?

The term pitch period appears in the book Speech and Language Processing by Daniel Jurafsy: As we just said, a pitch-synchronous algorithm is one in which we do something at each pitch period or ...
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### 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 ...
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### Fourier Series Coefficients

Question: The fourier series coefficients is given as: $$c_k= \begin{cases} 1 \qquad & k \ \text{ even} \\ 2 \qquad & k \ \text{ odd} \\ \end{cases}$$ the period of the signal is $T=4$, ...
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### How to Extract a Period of a Periodic Pulsed Signal?

I rercorded a sequence of zeros and ones which is repeated many times. However, the first and the last repetitions may not be complete because I have to start recording at a random time, so the ...
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### Determination of periodicity in data and finding mean

I have to find whether there is any pattern (I mean periodicity or close to periodicity) and if there is, for one cycle i have to perform numerical integration to determine mean. In the first picture ...
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### Line tracing folowing a path of an almost connected components

say we have a binary image like the one in below i would like to extract each black line, even if it's not almost connected i have marked here in red, example of lines that correspond to those to be ...
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### Making sense of the periodogram

I am trying to use the periodogram to tell when a signal is periodic or not by following the tutorial for the astropy Lomb-scargle periodogram here. http://docs.astropy.org/en/stable/stats/...
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### Usefulness of Matrix Notation for Linear Periodically Time Variant Transformations

I am quit puzzled about a notation I found in Gardner's 1986 book titled Introduction to Random Processes. It is in the chapter on Cyclostationary Processes at section 12.4 which pertains to Linear ...
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### Finding the fundamental frequency of a periodic signal

Suppose we have the signal $$x(t) = e^{j\omega_1 t} + e^{j\omega_2 t} + e^{j\omega_3 t},$$ where all the frequencies are rationally related (that is, the ratio of any pair of frequencies is a rational ...
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### What is the autocorrelation equivalent of the spectrogram called?

I'm very knowledgeable about the differences between the Fourier transform, and the autocorrelation; mainly that one converts the time domain to the frequency domain, and the other finds periodicities ...
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### Periodic signals in Continuous and discrete time

Is there any signal which is periodic in Continuous Time but not in Discrete Time? I have this doubt prevailing in me for a long time. Are all CT periodic signals periodic in DT? If so, how is sin ...
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### 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 ...
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### Periodicity of discrete time signal: $x\left [ n \right ] = \cos (\frac{\pi n^{2}}{8})$

I need to find the periodicity of the following signal: $$x\left [ n \right ] = \cos \left(\frac{\pi n^{2}}{8}\right)$$ Now I understand that the basic procedure to determine the periodicity is ...
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### Why must the angle contain $\pi$ for $\cos$ be periodic?

The $\cos(\frac{n}{6})$ is aperiodic, and $\cos(\frac{n\pi}{6})$ is periodic, why? What role does the $\pi$ play? By the way, $n$ must be integer I have seen this question,Why is cos(n/6) aperiodic? ...
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### Is Oversampling a Signal Same as Discretizing the Signal?

I am confused about the new terminology 'oversampling' I have encountered very recently. To explain it better, I am going to use numerical examples. Now let's assume I am using a BPSK modulator and my ...
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### How is frequency defined for a periodic signal?

For sinsusoids, frequency is $2\pi/T$, but for general periodic signals, how is frequency defined? Is it $1/T$ or $2\pi/T$? ($T$ is the fundamental period of the signal)
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### Ideal sampling of audio signals-Periodic spectrum [duplicate]

When applying ideal sampling on audio singals, why is the spectrum periodic ?
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### Why does this not work: Alt. way to compute the period of a discrete periodic signal that is a sum of 2 complex exponentials

I want to compute the fundamental period of the following discrete time signal: $x[n]= \exp^{(j\frac{2\pi}{3})n} + \exp^{(j\frac{3\pi}{4})n}$ I know I can do this by taking the fundamental periods ...
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### What is a periodic signal in image processing?

In the context of image processing (and computer vision), the concept of convolution comes up a lot. Convolution is quite related to the concept of Fourier transform and DFT. In the context of image ...