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Questions tagged [periodic]

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1answer
54 views

Why is $x[n]=\sin(\frac{12\pi n}{5})-\sin(\frac{2\pi n}{5})=0$

I was trying to find the period of $\sin(\frac{12\pi n}{5})-\sin(\frac{2\pi n}{5})$, each of the sinusoids has a period of 5 however their difference has a period of 1. It turned out that they're ...
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0answers
17 views

Unable to interpret hypothesis testing whetehr a signal is periodic or not

The meaning of P value is probability which should be number between 0 (the event never occurs) and 1 (the event occurs always). significance testing for periodicity using Matlab gives a documentation ...
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2answers
57 views

Periodicity of complex exponential in continuous and discrete time (Eq 1.51, Signals and Systems by Oppenheim & Wilsky)

Hi All: This is very basic but I've always wondered about it and now I see it in print in a textbook so I may as well ask. In Signals and Systems on page 26, it says $$e^{j(\omega_0 + 2\pi)n} = e^{j2\...
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1answer
30 views

confusions regarding periodicity?

I have a sequence $x[n]=\sin(\pi n+2)+\cos(2n/3 +1) $ I want to find its period and I have also attached my working I have two confusions Is there any effect of the constant term on period? constant&...
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1answer
67 views

What is “filter periodization”?

A library defines periodize_filter_fourier, which is an equi-spaced averaging formulated by $$ v_f[k] = \sum_{i=0}^{\text{n_periods}-1} h_f[i\cdot N + k], $$ where $v_f$ is periodization of $h_f$, $N=\...
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2answers
537 views

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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1answer
40 views

Good test for periodicity between signals

I have two timeseries signals. They look like this: Each signal started out from the same array, but each received different preprocessing treatments. Ultimately, each signal represents the breathing ...
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0answers
18 views

Is it important to learn to find de period of the sum fo two DT signals?

The fundamental period (N) of the sum of two DT signals could be the LCM of the fundamental periods. However, this is not always the case. I would like to know wether, during engineering design or ...
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0answers
83 views

Calculate periodicity of audio signal

I have to calculate the periodicity of a audio signal like this: You can see by eye, that the volume rises the highest every second "blob". The spectogram (that is visualized ...
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0answers
39 views

Detecting periodic components in discrete-time signals [closed]

I am looking for real data examples where it is of interest to detect the presence of a periodic component of some discrete-time signal when the period of the periodic component is not known. Suppose ...
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1answer
33 views

What is the value of the given periodic signal at any time, how to solve it in MATLAB?

Firstly hello all, I need help about periodic signals. I have a question as below. $x(t)$ is a periodic signal and $0.1t^3[u(t) - u(t - 7)]$ describes its one period. What is the value of $x(t)$ at ...
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1answer
35 views

What should go to infinity in power's formula N or the repetition KN?

I have this question : I should now calculate power of y[n], where the formula well in the power's formula N which constant goes to infinity how could this be ? i see in the question that N=7 which ...
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1answer
48 views

Why in formula of power of periodic signal is $2N+1$?

Where does $1$ come from, like from $-N$ to $N$ is $2N$ so why is $2N+1$?
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5answers
548 views

Finding Fourier series coefficients for discrete time signal

Let $x[n]$ be a periodic sequence with period $N$ and Fourier series representation $$x[n] = \sum _{k=<N>}a_ke^{jk\frac{2\pi}{N}n}$$ Determine the Fourier series coefficients for $$y[n] = \...
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2answers
116 views

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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0answers
40 views

Generating a sawtooth function with a variable frequency

So I'm trying to write a script that produces a sawtooth function using the equation: s = 2 a / π atan ( cot ( π f t ) ) Where: a : amplitude f : frequency t : time It's all working fine when f is ...
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2answers
387 views

Autocorrelation for periodic signals

Autocorrelation for power signals is defined by $$R_x(\tau)=\lim_{T\to\infty}\frac{1}{2T}\int_{-T}^Tx(t)x^*(t-\tau)dt\tag{1}$$ Is it true that for periodic signals $(1)$ can be computed by $$R_x(\tau)=...
2
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1answer
68 views

Fundamental period of $x[kn]$

Let $x[n]$ be a periodic with fundamental period $N$ and $y[n] = x[kn]$ where $k \in \mathbb{N}$ and $k\ge2$. Is $y[n]$ periodic? What's the fundamental period of $y[n]$? Here is my answer: If $N = ...
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5answers
483 views

Change in frequency on differentiation

Is there any possible periodic signal can exist(even mathematically) whose period gets change after differentiation?
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1answer
330 views

Duality in the discrete-time Fourier series

Suppose $g[n]$ is periodic with fundamental period $N$ and $f[k]$ being its Fourier coefficients i.e. $$ f[k] = \frac{1}{N}\sum_{n=<N>}g[n]e^{-j\frac{2\pi}{N}nk}$$ In more convenient notation $$...
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2answers
87 views

Ideal low pass filter output at given sampling frequency

Consider the signal $\cos(30t)$ sampled at $w_s=40 rad/s$ using a unit impulse train. The sampled signal is filtered with an ideal low pass filter with unity gain and cutoff frequency $w_c = 40rad/s$. ...
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0answers
29 views

Existence of finite output of a system [closed]

1.If frequently response of a LTI system exist and finite then can we say that, for a periodic or non periodic input signal, output is also finite? 2.if responses(output) of LTI system for ...
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0answers
34 views

$2\pi$ Periodicity is not working for me for Fourier of Discrete Time Signal

please help me find the error in the following counter example. Consider we take sinus with period of $2\pi$. We sample it many time, and more than 3. We make convolution with rectangle of height 1 ...
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1answer
62 views

Why is the total power not the same before and after mixing two signals?

I am trying to simulate an IQ mixer by multiplying two periodic signals IF and LO. Edit: My signals are given by $s_{1} = A_{...
4
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1answer
92 views

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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2answers
29 views

How can it be that there is a series of integrals in Fourier Series if it’s a projection on a continuous basis?

If the process of finding Fourier coefficient is finding the projection of a signal on a member from an orthonormal basis, basis which is continuous in frequency. How can it be that Fourier ...
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0answers
34 views

frequencies in frequency spectrum with no correlation together

I have a lack of understanding of the following questions: If I have a signal from a motor that is recorded with an accelerometer. And the rotating speed of the motor is 150Hz(rpm 9000 ), I can see in ...
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3answers
119 views

Confusion regarding calculation of fundamental period?

I am reading signal processing first and in chapter 3 ex3.8 i came across an example of fundamental period as shown in attached photo It apparently shows that signal $$x(t)=\cos^2(4\pi t)$$ has ...
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1answer
103 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, ...
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0answers
26 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
133 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
52 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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2answers
230 views

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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2answers
77 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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0answers
54 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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3answers
4k 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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2answers
152 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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3answers
2k 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
917 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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2answers
370 views

Prove that, in DFT, Upsampling 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
164 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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2answers
107 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
1k 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
867 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
357 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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0answers
49 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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1answer
79 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
41 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 ...
1
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1answer
502 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
2k 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: $$...