Questions tagged [periodic]

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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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1answer
126 views

Prove that, in DFT ,interpolation in time domain is equal to replication in frequency domain

Given: $x[n]$ is an $N$-point sequence whose DFT is $X[k]$ $$x[n]\xrightarrow{\mathcal{DFT}} X[k]$$ then, Prove that: DFT of the same sequence after insertion of $(M-1)$ zeroes between successive ...
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0answers
24 views

What is the correct representation for discrete time sequence?

I am bit confused after reading Frequency-Domain Sampling and Reconstruction of Discrete-Time Signals section from Proakis where, $$x(n)=\begin{cases} x_p(n),\;\;\;\;0\leq n \leq N-1\\ ...
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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 ...
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2answers
5k 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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2answers
224 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 ...
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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 ...
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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 ...
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1answer
157 views

Is sum of period samples in the DSP domain?

Following program outputs sum of samples of signal's period. Values in program are: ...
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2answers
30 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 $$a=.6\sqrt\pi x+\pi/6 ~~~\text{and} ~~~ b=1.2\sqrt\pi x-\pi/3$$ ...
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1answer
246 views

Phantom harmonics when using cosine windows why do they appear and how to avoid them?

Given an L order cosine window, it is possible to show that the width of the main lobe is given by: $$\omega_w = \frac{2 \pi L}{(2N+1)}$$ Where $L$ is the order of the window, $N$ is the maximum ...
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2answers
161 views

Finding periodicity in discrete events

I have a program that detects events in a large amount of measurement data. When it detects an event, it writes a timestamp. I have thousands of event timestamps. What I wish to do is detect if there ...
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2answers
127 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/...
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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. ...
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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 ...
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0answers
45 views

Weird resampling artifacts of a periodic signal

I am trying to grab time series data from a database storing data on a propritary format. When i chose a resolution which is not a multiple of the power of two of the sampling resolution i get these ...
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2answers
61 views

Fourier transform of a periodic/aperiodic signal

Generally speaking, I know that periodic signals (continuous-time domain signals) with period 2pi/wo have a spectrum with equidistance Delta-impulses of distance w0. My question is that, if we have ...
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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 ...
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3answers
99 views

Is $x[n]=(-1)^{n^2}$ periodic?

Is $x[n]=(-1)^{n^2}$ periodic? The answer said no, but when I draw it on a graph, it seems to be periodic, with fundamental period equal to $2$.
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2answers
134 views

Proof regarding the periodicity of a continuous-time sinusoid after sampling

Question A continuous-time sinusoid $x_a(t)$ with fundamental period $T_p = \frac{1}{F_0}$ is sampled at a rate $F_s = \frac 1 T$ to produce a discrete-time sinusoid $x(n) = x_a(nT)$. Show that $x(n)$...
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1answer
119 views

Remove multiplied white noise from periodic signal

I need to remove noise that is multiplied to a periodic signal using a maximum of 7 periods having no information about the noise. I have tried to use auto-correlation: ...
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2answers
99 views

Intermittent Harmonics, Is there a physical explanation?

I am doing some frequency analysis of a vibration signal from a spinning rotor, I am expecting to see peaks corresponding to the rotational frequency of the rotor. So the fundamental frequency ...
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1answer
175 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 ...
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2answers
121 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 ...
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2answers
75 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)
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1answer
68 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 ...
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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 ...
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2answers
2k views

Calculating the complex signal's average power

$$x(t) = \cos(\pi i t/20+\pi/4) - 2je^{j \,12\pi i t} + 5\sin(2\pi i t/3+\pi/3) $$ I need to find the signal's average power. How can I do that? The $i$ index (represented in red in the below image) ...
3
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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 ...
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0answers
46 views

How to find the filter coefficient of matched filter to detect the pulse of a signal?

I would to understand how to find the coefficient of a matched filter. Let's consider we have a signal and the signal is buried in the following noise. we want to find the coefficient of a matched ...
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0answers
38 views

Periodicity of $\cos(2n + \theta)$

I have to calculate periodicity of e^j(2n + π/4) If cos2n is Aperiodic then what is the periodicity of ...
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1answer
85 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 ...
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2answers
394 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: $$...
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1answer
140 views

Finding period of a square wave with varying sampling frequency

I have a square wave (0-1.8V) with a varying sampling frequency (from a circuit simulator). It is also not a perfect square wave (the high and low signal could be very close to but not precisely zero ...
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2answers
92 views

Discrete signal testing for periodicity

How would one go about determining if the following discrete time signal x[n] is periodic, and if it is, determine its fundamental period? I understand that the ...
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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? ...
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2answers
4k 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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1answer
52 views

Reason of effect of continuity and discreteness on periodicity of signal?

We know that a sine signal in continuous time is a periodic signal with a period $2\pi$ whereas the same sine signal in discrete time is aperiodic. My question is how changing just a type of signal (...
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1answer
121 views

Does dividing the magnitude spectrum of white noise by sqrt(2) give an RMS magnitude spectrum?

I understand that the RMS Amplitude of a sinusoidal signal is around 0.707 ($\frac1{\sqrt2}$) times the Peak Value, but this is not true for noise. However, an FFT of a noise signal indicates ...
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1answer
762 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 ...
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1answer
158 views

periodicity of constant discrete time signals

are constant discrete time signals periodic? example \begin{equation} e^{i10\pi n} \end{equation} my proffesor says that this signal is aperiodic, in the discrete sense. but it seems wrong, because ...
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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 $T=4$, ...
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1answer
560 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) $\...
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1answer
126 views

Finding the fundamental period by using four elementary operations (+,-,x,/)

The idea is to find the fundamental period of any periodic and bounded signal. This is all that we know about the signal. Nothing else. Only allowed operations are: $+,-,\times , \div$. We can also ...
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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 ?
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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}|...
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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 ...
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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\...
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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 ...
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1answer
143 views

Estimating variance in arbitrary, periodic signal

I have a periodic signal $x[m], m \in [0;M-N+1]$ made of modulated templates $s[n],~ n \in [0;N-1],~ N \ll M = NK$ of finite energy and support (i.e. zero outside of its defined interval, which does ...