Questions tagged [periodic]

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692 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 ...
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1answer
61 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 ...
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2answers
2k 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)|^...
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1answer
91 views

DFT and periodicity

My problem is related to the periodicity of DFT. Having the following expression $$ Y_{k}=\sum_{n=0}^{2N-1}e^{-j\frac{2\pi mk}{2N}} $$ I can easly find that the upper function is $2N$ periodic. So ...
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2answers
84 views

Very simple question about signal periodicity

$$x[n] = u[n]+u[-n]$$ Is it periodic or not? My answer is $$u[n] = {1 , n\geqslant0}$$ $$u[-n] = {1 , n\leqslant0}$$ which means that the signal $x[n]$ is always equal to $1$ from $-\...
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1answer
677 views

Periodicity of peaks within a signal

I have a signal, in which i want to detect the period of the peaks, that exist within this signal: for example : After each 5mm or (5 seconds depending on the sampling rate and speed of my motor) i ...
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1answer
276 views

Signal's Fundamental Frequency is different from Plotted Signal

I've been attempting to plot the following function using MATLAB: $$ x(k)=\sum_{n=11}^{50} \sqrt{n} \sin (2n\pi k) +\sum_{n=1}^{40}\sqrt[3]{n} \sin (3n\pi k) $$ Note that $k$ is a continuous variable....
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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 ...
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0answers
175 views

Periodic noise attenuation

I have continuous data with very high amplitude periodic noise. Data is sampled at 500 Hz. The period of the noise does change with time but within a short interval (~ a minute) it is constant. Top ...
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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 ...
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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 ...
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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
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1answer
5k 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}|...
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1answer
145 views

Why DFT exact for periodic signals?

I have in my course notes: $$ \sum_{k=0}^{N-1}y(k)e^{-j\omega_nk}\approx\sum_{k=-\infty}^{\infty}y(k)e^{-j\omega_nk} $$ Where the $\approx$ for some reason becomes $=$ when $y(k)$ is periodic. Could ...
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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 ...
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1answer
1k views

How to Calculate the Period of the Discrete Time Sequence from Taking Its DFT

This is my discrete time periodic signal, the time resolution of the samples is 0.2ms. And it's periodic after each 11 samples. So the fundamental period of the signal is 2ms or the fundamental ...
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0answers
920 views

Finding if a signal is periodic

Hello I just started learning Signals and Systems and I have a question regarding periodic signals. For instance: $x(t) = \cos(3.2t) + \sin(1.6t) + e ^{j2.8t}$ is periodic because of the HCF of the ...
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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 ...
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1answer
116 views

Exact formula for alias of Discrete Fourier transform for periodic sigals

Suppose that $f(t): \mathbb{R} \to \mathbb{C}$ is a $T$-periodic signal, with highest frequency $f_h$. Now suppose that our sampling rate frequency is lower than $f_h$, and is not any multiples of $1/...
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2answers
858 views

Discrete Fourier series for a sum of deltas

so Im given a discrete sum $$x[n] = \sum\limits_{r=\infty}^{+\infty}\delta[n-rN]$$ how do I calculate its discrete Fourier series coefficients? Thank you. edit: this is what i've come to up to now:
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2answers
2k 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 ...
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5answers
6k views

Does $ Ev(\cos(4\pi t)u(t)) $ signal has period?

According to Oppenheim's signal and systems solution book and other solutions like this $$ Ev(\cos(4\pi t)u(t)) = 1/2 \times ( \cos(4\pi t)u(t) + \cos(4\pi t)u(-t)) = 1/2(\cos(4\pi t)) $$ $$ \...
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0answers
7k views

How to check whether a continuous signal is periodic or not?

How to check if a continuous signal is Periodic or not? My notes says $\cos(\frac{3}{2}\pi t)$ is periodic because $T=4/3$. And $\cos(\frac{3}{2}t)$ is not periodic as $T=4\pi/3$.
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2answers
720 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 ...
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1answer
904 views

Deriving time-scaling property for Fourier Series

thanks for taking the time to help with this problem! I have to prove the time-scaling property: $$ x_{(m)}[n] = \begin{cases} x[n/m], & n=0,\pm m, \pm 2m,...\\ 0, & otherwise \end{cases} $$ ...
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1answer
496 views

Given two waves, 441 Hz and 700 Hz, how many samples long is each wave's period if the sample-rate is 48 kHz?

The title says it all. I have two waves, Master and Slave. Master is at 441 Hz and Slave at 700 Hz. The sample-rate is 48 kHz. I want to know how to calculate the period of each wave in terms of ...
3
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1answer
251 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 ...
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0answers
1k views

Autocorrelation and FFT : avoid zero-padding

Some posts evocate the computation of convolution or cross-correlation using FFT and zero-padding the temporal signal. I want to compute the autocorrelation of a 3D array using FFTW (2 dimensions are ...
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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 ...
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1answer
585 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_\...
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2answers
8k views

Determine whether a signal is periodic or not and get fundamental period

Here is my signal Cos(n/2)*cos(pi*n/4) cos(n/2) has period 4pi and cos(pi*n/4) has period 8 Now, the question is will the signal be periodic for fundamental ...
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1answer
691 views

how to sample sine wave to 4 points dft output

sinusoid x(t)=1+sin(2*pi *500) sampling rate :1000 samples/s Can I have 4 points DFT output with the above data.
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1answer
338 views

Phase reference of a periodic signal

Assume an arbitrary (discrete) signal that is periodic and known over a whole period. I need a way to select a characteristic point along the signal such that I can always retrieve it even when the ...
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1answer
4k views

use prony method for damped exponentials

let us consider represented of damping exponential model by prony method,there is source code ...
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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 ...
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1answer
876 views

ARMA models for non stationary signals

let us suppose that we have non stationary signal,whose value is given by ...
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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 ...
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0answers
64 views

peak-to-peak test between two signal

Suppose that we have different signals (Pulses). I would like to study which signal has deterministic peak-to-peak distant (lag). For example A=[1 0 0 1 0 0 0 1 0 0 1] and B=[1 0 0 1 0 0 1 0 0 1] and ...
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2answers
256 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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