Questions tagged [periodic]
The periodic tag has no usage guidance.
143
questions
0
votes
1answer
34 views
Fourier Series of a piecewise function
I've been given the task to find the Fourier Series Representation. All I'm given is this $$x(t)= \begin{cases}-t & \text { for } 0 \leq t<1 \\ 1 & \text { for } 1 \leq t<2 \\ 0 & \...
2
votes
1answer
57 views
Fourier transform of shifted periodic function
Assuming $x(t)$ is a periodic function of period $T$ and having the Fourier transform $X(\omega)$, it is required to calculate the Fourier transform of the signal $x(t)+x(t-T)$. Since x(t-T) is equal ...
1
vote
1answer
75 views
Prove Convolution Property for DFT using duality
If $x_1[n]$ and $x_2[n]$ are finite length sequences of length $N$
$$\mathcal{DFT}(x_1[n] \circledast x_2[n]) = X_1[k]X_2[k]$$
where $X_1[k]$ and $X_2[k]$ are the DFTs of$x_1[n]$ and $x_2[n]$, ...
0
votes
1answer
72 views
Prove Discrete Time Fourier Series Multiplication property
Note: This is not a homework problem. I'm just stalled at a point because I think I might be interpreting the duality property incorrectly.
If $x_1[n]$ and $x_2[n]$ are periodic with period N, then if ...
8
votes
5answers
834 views
Simple and Effective Method to Estimate the Frequency of a Single Sine Signal in White Noise
Given a sinusoidal signal, how can we efficiently determine its frequency?
0
votes
1answer
42 views
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, ...
3
votes
2answers
316 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 ...
0
votes
1answer
50 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 ...
0
votes
1answer
62 views
Angular frequency of discrete signal
Can someone explain me how to obtain the angular frequency here?
0
votes
1answer
56 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
20 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
89 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
34 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
107 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
593 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
54 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
19 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
98 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
43 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
53 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
49 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
1k 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
$$y[n] =
\...
2
votes
2answers
312 views
Periodic signals in Continuous and discrete time
Is there any signal which is periodic in Continuous Time but not in Discrete Time?
I have this doubt prevailing in me for a long time.
Are all CT periodic signals periodic in DT?
If so, how is sin ...
1
vote
2answers
860 views
Autocorrelation for periodic signals
Autocorrelation for power signals is defined by $$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
78 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
562 views
Change in frequency on differentiation
Is there any possible periodic signal can exist(even mathematically) whose period gets change after differentiation?
2
votes
1answer
595 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
170 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
31 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
37 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
65 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
115 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
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 ...
0
votes
0answers
37 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
192 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)$$ has ...
0
votes
1answer
146 views
Autocorrelation - Understanding reduced correlation at periodic time shifts using np.correlate (versus statistical autocorrelation)?
I'm going through the Think DSP by Allen B. Downey, and I'm struggling to understand a specific aspect of np.correlate and how it differs from statistic autocorrelation. The question is at the bottom, ...
0
votes
0answers
27 views
What is the correct representation for discrete time sequence?
I am bit confused after reading Frequency-Domain Sampling and Reconstruction of Discrete-Time Signals section from Proakis where, $$x(n)=\begin{cases}
x_p(n),\;\;\;\;0\leq n \leq N-1\\
...
1
vote
2answers
179 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
61 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 $$a=.6\sqrt\pi x+\pi/6 ~~~\text{and} ~~~ b=1.2\sqrt\pi x-\pi/3$$ ...
7
votes
2answers
381 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
102 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
67 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
181 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
3k 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
1k 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
536 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
1answer
239 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
112 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 ...
