Questions tagged [periodic]
The periodic tag has no usage guidance.
105
questions
0
votes
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, $$x(n)=\begin{cases}
x_p(n),\;\;\;\;0\leq n \leq N-1\\
...
1
vote
2answers
41 views
How sampling aperiodic signal will result in periodic repetitions of the same
I am reading "Digital Signal Processing" - Proakis and often read that sampling guarantees periodicity (not exact as read)
But I wonder how sampling aperiodic signal will result in periodic ...
1
vote
2answers
31 views
Period of a continuous signal
So I have
$$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$$ ...
1
vote
2answers
55 views
Estimate “speed” of repeating signal pattern
I have a digitized signal containing a repeating pattern. One could call it periodic, but the time for one period is not constant. The "speed" with which the period is advanced can change over time. ...
0
votes
0answers
45 views
Weird resampling artifacts of a periodic signal
I am trying to grab time series data from a database storing data on a propritary format. When i chose a resolution which is not a multiple of the power of two of the sampling resolution i get these ...
6
votes
3answers
3k views
How can a signal be both periodic and random?
Do any examples of such signals exist where the signal is both periodic and random? Because as I see it, if a signal is periodic then the randomness kinda goes away because you know what the signal ...
0
votes
2answers
61 views
Fourier transform of a periodic/aperiodic signal
Generally speaking, I know that periodic signals (continuous-time domain signals) with period 2pi/wo have a spectrum with equidistance Delta-impulses of distance w0.
My question is that, if we have ...
0
votes
3answers
108 views
Is $x[n]=(-1)^{n^2}$ periodic?
Is $x[n]=(-1)^{n^2}$ periodic? The answer said no, but when I draw it on a graph, it seems to be periodic, with fundamental period equal to $2$.
0
votes
2answers
139 views
Proof regarding the periodicity of a continuous-time sinusoid after sampling
Question
A continuous-time sinusoid $x_a(t)$ with fundamental period $T_p = \frac{1}{F_0}$ is sampled at a rate $F_s = \frac 1 T$ to produce a discrete-time sinusoid $x(n) = x_a(nT)$.
Show that $x(n)$...
0
votes
1answer
129 views
Prove that, in DFT ,interpolation in time domain is equal to replication in frequency domain
Given:
$x[n]$ is an $N$-point sequence whose DFT is $X[k]$
$$x[n]\xrightarrow{\mathcal{DFT}} X[k]$$
then,
Prove that: DFT of the same sequence after insertion of $(M-1)$ zeroes between successive ...
1
vote
0answers
67 views
White noise generation in frequency domain (stfft) produces a periodic pattern
I have created a set of spectral processing modules for SynthEdit next to be released, implenting short time fft, so I am now quite experienced with the matter, but recently encounteted an unexpected ...
0
votes
2answers
100 views
Intermittent Harmonics, Is there a physical explanation?
I am doing some frequency analysis of a vibration signal from a spinning rotor,
I am expecting to see peaks corresponding to the rotational frequency of the rotor. So the fundamental frequency ...
1
vote
1answer
184 views
Find the period of a signal with the DTFT plot
I have an exercise and I'm struggling to resolve it. Here it is :
My problem is about the DTFT. I've always been taught that we use DTFT for infinite-lenght signal that are not periodic (if the ...
1
vote
2answers
123 views
Building periodic sequences from finite-support sequences
Given a discrete-time finite-support signal x[n]
$$x[n] = \left\{ {\begin{array}{*{20}{l}}
{{{( - 1)}^n}n}&{{\rm{ }}n = 1,2,3}\\
0&{{\rm{otherwise}}}
\end{array}} \right.$$
And consider also ...
1
vote
2answers
83 views
How is frequency defined for a periodic signal?
For sinsusoids, frequency is $2\pi/T$, but for general periodic signals, how is frequency defined? Is it $1/T$ or $2\pi/T$?
($T$ is the fundamental period of the signal)
1
vote
0answers
43 views
How to find the period of a given signal? [duplicate]
I'm new to Signal Analysis. I have a manually generated Signal from a Gyroscope, which looks like in the picture below and I need to extract the X-Values for each period. Is there some technique to ...
1
vote
1answer
69 views
Why does this not work: Alt. way to compute the period of a discrete periodic signal that is a sum of 2 complex exponentials
I want to compute the fundamental period of the following discrete time signal:
$ x[n]= \exp^{(j\frac{2\pi}{3})n} + \exp^{(j\frac{3\pi}{4})n}$
I know I can do this by taking the fundamental periods ...
0
votes
0answers
48 views
How to find the filter coefficient of matched filter to detect the pulse of a signal?
I would to understand how to find the coefficient of a matched filter.
Let's consider we have a signal and the signal is buried in the following noise. we want to find the coefficient of a matched ...
0
votes
0answers
38 views
Periodicity of $\cos(2n + \theta)$
I have to calculate periodicity of e^j(2n + π/4)
If cos2n is Aperiodic then what is the periodicity of ...
1
vote
1answer
88 views
What is a periodic signal in image processing?
In the context of image processing (and computer vision), the concept of convolution comes up a lot. Convolution is quite related to the concept of Fourier transform and DFT. In the context of image ...
3
votes
2answers
410 views
Fourier Transform of Alternating Periodic Rectangular Pulse
I'm having trouble determining Fourier transform of signal. I have 2 ideas on how to solve this problem.
Given the signal is periodic I could use formula for Fourier transform of periodic signals:
$$...
0
votes
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 ...
0
votes
2answers
162 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 ...
2
votes
2answers
130 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/...
0
votes
1answer
55 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 (...
1
vote
1answer
780 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 ...
0
votes
1answer
162 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
...
0
votes
1answer
125 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 ...
0
votes
2answers
93 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 ...
0
votes
1answer
127 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 ...
1
vote
3answers
80 views
Ideal sampling of audio signals-Periodic spectrum [duplicate]
When applying ideal sampling on audio singals, why is the spectrum periodic ?
2
votes
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? ...
2
votes
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\...
1
vote
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 ...
0
votes
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 ...
0
votes
1answer
23 views
detection of periodicities in n-dimensional signals
Generally speaking, what analyses are necessary and sufficient for the detection of periodicities in an n-dimensional signal amounting to a discretely sampled density distribution over n-dimensional ...
0
votes
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:
...
0
votes
0answers
129 views
State Space conversion of Sinusoidal model
i would like to learn how to convert sinusoidal model into state space form which has following equation
our model consist of sum of periodic components with additive of white noise, given by ...
0
votes
1answer
43 views
Numerical error while implementing a periodic pulse signal
I'm trying to illustrate the principle of constructing a periodic signal using an elementary pattern. This is the code I use (python 2.7 + numpy + scipy.signal) :
...
0
votes
1answer
90 views
Is Oversampling a Signal Same as Discretizing the Signal?
I am confused about the new terminology 'oversampling' I have encountered very recently.
To explain it better, I am going to use numerical examples.
Now let's assume I am using a BPSK modulator and my ...
0
votes
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) ...
2
votes
1answer
566 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) $\...
2
votes
4answers
212 views
Very basic question about how we define frequency in signal processing
When talking about general periodic continuous-time signals for which $$x(t + T_0) = x(t)$$ where $T_0$ is the fundamental period we define the fundamental frequency $\omega_0$ as $\omega_0 = 2\pi/T_0$...
3
votes
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 ...
2
votes
1answer
58 views
Rationally related frequencies and the Fourier Series representation
Suppose that we have the signal $$x(t) = e^{j\omega t} + e^{j\frac{3}{2} \omega t},$$ and we want to find a Fourier Series representation for that signal. Is this possible? According to my ...
-1
votes
1answer
736 views
sum of two periodic signals with different length
So, I have those two signals (x1,x2) and I want to make a new signal (x) which is the sum of them. What bothers me here is the length of each one of the signals. I made this little code over here in ...
2
votes
1answer
592 views
DFT shift theorem proof
Learning DSP on my own time. Can't figure out the proof for DFT shift theorem which states the following:
Given, $x[n]$ to be a periodic with period $N$, $\text{DFT}\{x[n]\} = X[k]$, then
$$
DFT\{x[n-...
1
vote
2answers
244 views
Fourier Series of Aperiodic convolution of periodic functions
we were given the following classic exercise:
Given two periodic signals $x(t), y(t)$ with fundamental period $T$
with Fourier series coefficients $c_m^x, c_m^y$ respectively, find the
Fourier ...
3
votes
3answers
554 views
formula derivation for periodic signal power
Studying DSP on my own. Taking an introductory class. Was given a formula for signal power
$$ P = \lim_{M\to\infty} {\frac{1}{2M+1} \sum_{n=-M}^M} \lvert x[n] \rvert^2 $$
I do understand why the ...
2
votes
1answer
69 views
Periodic signal checking when using $\Sigma$
Is the following signal periodic?
$$ \sum_{κ=-\infty}^{\infty}\left[\mathrm{rect}\left(\frac{t+2κ}{10}\right)\right]+\cos\left(\frac{π}{75}t\right) $$
where rect is the rectangular signal
