Questions tagged [periodic]

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How does this periodic signal look like?

I'm very new to DSP, and I'm unsure about finding how a signal $y[n]$ would look like. The following is given: Assume we have a finite support signal $x[n]$ which has the values $1, 2, 3$ for $n = 1, ...
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2answers
107 views

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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1answer
30 views

Is a continuous time aperiodic signal discrete in the time domain?

This is a statement I have read from a textbook: Whenever we have periodic signals continuous or discrete time the frequency domain is discrete and time domain is continuous. Whenever we have ...
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1answer
48 views

Angular frequency of discrete signal

Can someone explain me how to obtain the angular frequency here?
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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
79 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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1answer
55 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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1answer
345 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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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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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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2answers
60 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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398 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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1answer
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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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2answers
548 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
42 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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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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2answers
413 views

Confusion about subtle difference between discrete-time and continuous-time

In Alan Oppenheim's book Signals and Systems a comparison is made between the properties of discrete-time and continuous-time complex exponential signals in section 1.3 pg. 26. Specifically it says: ...
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2answers
202 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 ...
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0answers
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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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88 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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2answers
250 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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1answer
173 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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3answers
300 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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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
38 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
637 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
127 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
42 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
460 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)=...
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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
502 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
390 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
106 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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2answers
14k 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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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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35 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
96 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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1answer
63 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_{...
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2answers
30 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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1answer
112 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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3answers
340 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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3answers
121 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
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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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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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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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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
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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2answers
241 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 ...