Questions tagged [periodic]

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8
votes
3answers
379 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 ...
7
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2answers
1k 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 ...
6
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3answers
3k views

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 ...
5
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2answers
973 views

Power of a periodic sequence

I am trying to find the way to reduce the standard expression to compute the power of a generic sequence $x(n)$: $$P_{\text{x}}= \lim\limits_{N \to \infty}\frac{1}{2N + 1}\sum\limits_{n=-N}^{N}|x(n)|^...
3
votes
3answers
2k views

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 ...
3
votes
3answers
555 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 ...
3
votes
2answers
131 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 ...
3
votes
1answer
243 views

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 $T=4$, ...
3
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1answer
2k 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 ...
3
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2answers
410 views

Fourier Transform of Alternating Periodic Rectangular Pulse

I'm having trouble determining Fourier transform of signal. I have 2 ideas on how to solve this problem. Given the signal is periodic I could use formula for Fourier transform of periodic signals: $$...
3
votes
1answer
420 views

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 ...
3
votes
2answers
225 views

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 ...
3
votes
1answer
248 views

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 ...
3
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2answers
2k views

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 ...
3
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0answers
363 views

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 ...
2
votes
1answer
187 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 ...
2
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2answers
7k 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\...
2
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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 ...
2
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2answers
208 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 ...
2
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4answers
212 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
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2answers
1k views

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 ...
2
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3answers
88 views

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? ...
2
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1answer
593 views

DFT shift theorem proof

Learning DSP on my own time. Can't figure out the proof for DFT shift theorem which states the following: Given, $x[n]$ to be a periodic with period $N$, $\text{DFT}\{x[n]\} = X[k]$, then $$ DFT\{x[n-...
2
votes
1answer
566 views

Fourier coefficients of product of two periodic signals

question: If $x(t)$ and $y(t)$ are two periodic signals(both with period T) with Fourier coefficients $c_{n}$ and $d_{n}$ respectively then, Fourier coefficient of $z(t)=x(t)\cdot y(t)$ is: (a) $\...
2
votes
1answer
58 views

Rationally related frequencies and the Fourier Series representation

Suppose that we have the signal $$x(t) = e^{j\omega t} + e^{j\frac{3}{2} \omega t},$$ and we want to find a Fourier Series representation for that signal. Is this possible? According to my ...
2
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1answer
69 views

Periodic signal checking when using $\Sigma$

Is the following signal periodic? $$ \sum_{κ=-\infty}^{\infty}\left[\mathrm{rect}\left(\frac{t+2κ}{10}\right)\right]+\cos\left(\frac{π}{75}t\right) $$ where rect is the rectangular signal
2
votes
2answers
2k views

How to filter almost periodic noise?

I have signal that looks like this: As you can see there are some almost periodic pulses at the background with amplitude about 1000. I am saying almost, because, if you zoom in, you may see that ...
2
votes
2answers
693 views

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 ...
2
votes
2answers
130 views

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/...
1
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2answers
41 views

How sampling aperiodic signal will result in periodic repetitions of the same

I am reading "Digital Signal Processing" - Proakis and often read that sampling guarantees periodicity (not exact as read) But I wonder how sampling aperiodic signal will result in periodic ...
1
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2answers
84 views

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)
1
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3answers
80 views

Ideal sampling of audio signals-Periodic spectrum [duplicate]

When applying ideal sampling on audio singals, why is the spectrum periodic ?
1
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1answer
69 views

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 ...
1
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1answer
88 views

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 ...
1
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1answer
3k views

Power of periodic signal

Given a signal $s(t) = e^{j(t+\pi)}$, I conclude that the signal is periodic with period $T=2\pi$, so its power should be $$P = \frac{1}{T}\int_{-T/2}^{T/2}|s(t)|^2dt= \frac{1}{2\pi}\int_{-\pi}^{\pi}|...
1
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2answers
31 views

Period of a continuous signal

So I have $$x_1=2 \cos(.6\sqrt\pi x+\pi/6)$$ and $$x_2= \sin(1.2\sqrt\pi x-\pi/3)$$ and need to find the period of $(x_1+x_2)^2$. Let $$a=.6\sqrt\pi x+\pi/6 ~~~\text{and} ~~~ b=1.2\sqrt\pi x-\pi/3$$ ...
1
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2answers
55 views

Estimate “speed” of repeating signal pattern

I have a digitized signal containing a repeating pattern. One could call it periodic, but the time for one period is not constant. The "speed" with which the period is advanced can change over time. ...
1
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1answer
780 views

How can I improve my fit of cosines to periodic data using Python?

I have a space-separated csv file containing a measurement. First column is the time of measurement, second column is the corresponding measured value, third column ...
1
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2answers
69 views

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 ...
1
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1answer
627 views

Looking for cycles of periods longer than the input signal length

There was a similar question asked here, however I would like to focus on some specifics of this problem. Let me present the Python code sample to illustrate the situation when only a part of the ...
1
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1answer
439 views

finding period with autocorrelation is not correct

I have recorded a signal, which I know is periodic (apart from noise). The period length is unknown. I want to extract the last period from the signal. Before going to a noisy signal, I first tested ...
1
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1answer
60 views

Confused about the period of a discretised time-series

I have managed to confuse myself about the periods of discretised time series. It is all rather embarrassing. This is one period extracted from my continuous signal (radians on y, time on x): To ...
1
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1answer
361 views

minimum frequency in periodic components

Suppose we have the following signal model $y(t) = A_1\sin(\omega_1 t+\phi_1) + A_2\sin(\omega_2 t+\phi_2) + ... + A_p\sin(\omega_p t+\phi_p) + z(t)$ When we are sampling at sampling frequency $f_\...
1
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2answers
246 views

Examples of mixture of 'almost periodic' signals/data in nature or practice

I am working on algorithms to separate mixtures of 'almost periodic' signals. One such example is composite ECG consisting of maternal and fetal signal. Can anyone help with examples of such signals?...
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0answers
67 views

White noise generation in frequency domain (stfft) produces a periodic pattern

I have created a set of spectral processing modules for SynthEdit next to be released, implenting short time fft, so I am now quite experienced with the matter, but recently encounteted an unexpected ...
1
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1answer
185 views

Find the period of a signal with the DTFT plot

I have an exercise and I'm struggling to resolve it. Here it is : My problem is about the DTFT. I've always been taught that we use DTFT for infinite-lenght signal that are not periodic (if the ...
1
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2answers
123 views

Building periodic sequences from finite-support sequences

Given a discrete-time finite-support signal x[n] $$x[n] = \left\{ {\begin{array}{*{20}{l}} {{{( - 1)}^n}n}&{{\rm{ }}n = 1,2,3}\\ 0&{{\rm{otherwise}}} \end{array}} \right.$$ And consider also ...
1
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0answers
43 views

How to find the period of a given signal? [duplicate]

I'm new to Signal Analysis. I have a manually generated Signal from a Gyroscope, which looks like in the picture below and I need to extract the X-Values for each period. Is there some technique to ...
1
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2answers
244 views

Fourier Series of Aperiodic convolution of periodic functions

we were given the following classic exercise: Given two periodic signals $x(t), y(t)$ with fundamental period $T$ with Fourier series coefficients $c_m^x, c_m^y$ respectively, find the Fourier ...
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0answers
64 views

Determining periodic pattern when there is pattern which period is multiple of former

I have periodic signal, say, it has year period, yearly pattern. I want to check if also has quarterly pattern. Event if there is no visible quarterly pattern, Fourier Transform of this signal has ...