Questions tagged [periodic]
The periodic tag has no usage guidance.
135
questions
0
votes
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 ...
0
votes
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 ...
0
votes
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
$$e^{j(\omega_0 + 2\pi)n} = e^{j2\...
-1
votes
1answer
30 views
confusions regarding periodicity?
I have a sequence $x[n]=\sin(\pi n+2)+\cos(2n/3 +1) $
I want to find its period and I have also attached my working
I have two confusions
Is there any effect of the constant term on period? constant&...
1
vote
1answer
67 views
What is “filter periodization”?
A library defines periodize_filter_fourier, which is an equi-spaced averaging formulated by
$$
v_f[k] = \sum_{i=0}^{\text{n_periods}-1} h_f[i\cdot N + k],
$$
where $v_f$ is periodization of $h_f$, $N=\...
9
votes
2answers
537 views
Fourier series of cycloid
What is the Fourier series representation of a cycloid?
The parametric representation of the curve is as follows.
$$
t=\dfrac{\theta-\sin\theta}{\pi}\\
x=\dfrac{1-\cos\theta}{\pi}
$$
The period is $2$...
0
votes
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 ...
0
votes
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 ...
0
votes
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 ...
1
vote
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 ...
0
votes
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 ...
0
votes
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 ...
0
votes
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$?
2
votes
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] =
\...
2
votes
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 ...
0
votes
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 ...
1
vote
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 $$R_x(\tau)=...
2
votes
1answer
68 views
Fundamental period of $x[kn]$
Let $x[n]$ be a periodic with fundamental period $N$ and $y[n] = x[kn]$ where $k \in \mathbb{N}$ and $k\ge2$. Is $y[n]$ periodic? What's the fundamental period of $y[n]$?
Here is my answer:
If $N = ...
1
vote
5answers
483 views
Change in frequency on differentiation
Is there any possible periodic signal can exist(even mathematically) whose period gets change after differentiation?
1
vote
1answer
330 views
Duality in the discrete-time Fourier series
Suppose $g[n]$ is periodic with fundamental period $N$ and $f[k]$ being its Fourier coefficients i.e. $$ f[k] = \frac{1}{N}\sum_{n=<N>}g[n]e^{-j\frac{2\pi}{N}nk}$$ In more convenient notation $$...
0
votes
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 $w_c = 40rad/s$. ...
1
vote
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 ...
0
votes
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 ...
0
votes
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
votes
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.
...
0
votes
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 ...
0
votes
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 ...
1
vote
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 ...
0
votes
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, ...
0
votes
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, $$x(n)=\begin{cases}
x_p(n),\;\;\;\;0\leq n \leq N-1\\
...
1
vote
2answers
133 views
How sampling aperiodic signal will result in periodic repetitions of the same
I am reading "Digital Signal Processing" - Proakis and often read that sampling guarantees periodicity (not exact as read)
But I wonder how sampling aperiodic signal will result in periodic ...
1
vote
2answers
52 views
Period of a continuous signal
So I have
$$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$$ ...
4
votes
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 ...
1
vote
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. ...
0
votes
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 ...
6
votes
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 ...
0
votes
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 ...
0
votes
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$.
0
votes
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)$...
1
vote
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]$$
then,
Prove that: DFT of the same sequence after insertion of $(M-1)$ zeroes between successive ...
2
votes
0answers
164 views
White noise generation in frequency domain (stfft) produces a periodic pattern
I have created a set of spectral processing modules for SynthEdit next to be released, implenting short time fft, so I am now quite experienced with the matter, but recently encounteted an unexpected ...
0
votes
2answers
107 views
Intermittent Harmonics, Is there a physical explanation?
I am doing some frequency analysis of a vibration signal from a spinning rotor,
I am expecting to see peaks corresponding to the rotational frequency of the rotor. So the fundamental frequency ...
1
vote
1answer
1k views
Find the period of a signal with the DTFT plot
I have an exercise and I'm struggling to resolve it. Here it is :
My problem is about the DTFT. I've always been taught that we use DTFT for infinite-lenght signal that are not periodic (if the ...
1
vote
2answers
867 views
Building periodic sequences from finite-support sequences
Given a discrete-time finite-support signal x[n]
$$x[n] = \left\{ {\begin{array}{*{20}{l}}
{{{( - 1)}^n}n}&{{\rm{ }}n = 1,2,3}\\
0&{{\rm{otherwise}}}
\end{array}} \right.$$
And consider also ...
1
vote
2answers
357 views
How is frequency defined for a periodic signal?
For sinsusoids, frequency is $2\pi/T$, but for general periodic signals, how is frequency defined? Is it $1/T$ or $2\pi/T$?
($T$ is the fundamental period of the signal)
1
vote
0answers
49 views
How to find the period of a given signal? [duplicate]
I'm new to Signal Analysis. I have a manually generated Signal from a Gyroscope, which looks like in the picture below and I need to extract the X-Values for each period. Is there some technique to ...
1
vote
1answer
79 views
Why does this not work: Alt. way to compute the period of a discrete periodic signal that is a sum of 2 complex exponentials
I want to compute the fundamental period of the following discrete time signal:
$ x[n]= \exp^{(j\frac{2\pi}{3})n} + \exp^{(j\frac{3\pi}{4})n}$
I know I can do this by taking the fundamental periods ...
0
votes
0answers
41 views
Periodicity of $\cos(2n + \theta)$
I have to calculate periodicity of e^j(2n + π/4)
If cos2n is Aperiodic then what is the periodicity of ...
1
vote
1answer
502 views
What is a periodic signal in image processing?
In the context of image processing (and computer vision), the concept of convolution comes up a lot. Convolution is quite related to the concept of Fourier transform and DFT. In the context of image ...
6
votes
2answers
2k views
Fourier Transform of Alternating Periodic Rectangular Pulse
I'm having trouble determining Fourier transform of signal. I have 2 ideas on how to solve this problem.
Given the signal is periodic I could use formula for Fourier transform of periodic signals:
$$...
