Questions tagged [periodic]
The periodic tag has no usage guidance.
1
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1answer
77 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
29 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
45 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
1answer
28 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
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1answer
21 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
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3answers
43 views
Ideal sampling of audio signals-Periodic spectrum [duplicate]
When applying ideal sampling on audio singals, why is the spectrum periodic ?
0
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1answer
43 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
685 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
1answer
33 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
72 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
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1answer
22 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
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1answer
78 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
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0answers
28 views
Multisin-, carrier- frequency signal
i have some doubt in theory if the multicarrier signals. I hope someone can help me.
how i have understood, the multicarrier signal is a periodic signal.
ao...i can describe the signal with an ...
0
votes
0answers
64 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
34 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
54 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
473 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
140 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
173 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
1k 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
46 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
298 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 ...
1
vote
1answer
266 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
$$
DFT\{x[n-...
1
vote
2answers
112 views
Fourier Series of Aperiodic convolution of periodic functions
we were given the following classic exercise:
Given two periodic signals $x(t), y(t)$ with fundamental period $T$
with Fourier series coefficients $c_m^x, c_m^y$ respectively, find the
Fourier ...
3
votes
3answers
168 views
formula derivation for periodic signal power
Studying DSP on my own. Taking an introductory class. Was given a formula for signal power
$$ P = \lim_{M\to\infty} {\frac{1}{2M+1} \sum_{n=-M}^M} \lvert x[n] \rvert^2 $$
I do understand why the ...
2
votes
1answer
56 views
Periodic signal checking when using $\Sigma$
Is the following signal periodic?
$$ \sum_{κ=-\infty}^{\infty}\left[\mathrm{rect}\left(\frac{t+2κ}{10}\right)\right]+\cos\left(\frac{π}{75}t\right) $$
where rect is the rectangular signal
-4
votes
4answers
76 views
Signal periodicity in discrete-time
Let $x[n]$ be a discrete-time signal, and let
$$y_1[n]=x[2n]$$
You have to show that if:
$x[n]$ is periodic, then $y_1[n]$ is periodic. $y_1[n]$ is periodic,
then x[n] is periodic.
So for the ...
0
votes
1answer
148 views
Phantom harmonics when using cosine windows why do they appear and how to avoid them?
Given an L order cosine window, it is possible to show that the width of the main lobe is given by:
$$\omega_w = \frac{2 \pi L}{(2N+1)}$$
Where $L$ is the order of the window, $N$ is the maximum ...
3
votes
3answers
1k views
Periodicity of a constant signal!
This can be a very silly question, but I'm quite confused:
If we take the Fourier transform of any constant signal, we get an impulse at zero, which says that its frequency is zero and, hence, it is ...
0
votes
1answer
59 views
What is special about the frequency $\omega_0=\pi$ that suddenly causes rate of oscillation decrease?
In Alan Oppenheim's book Signals and Systems a comparison is made between the properties of discrete-time and continuous-time complex exponential signals in section 1.3 pg. 26. Specifically it says:
...
0
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1answer
99 views
Confusion about subtle difference between discrete-time and continuous-time
In Alan Oppenheim's book Signals and Systems a comparison is made between the properties of discrete-time and continuous-time complex exponential signals in section 1.3 pg. 26. Specifically it says:
...
3
votes
2answers
99 views
periodicity coefficient
I wonder if an efficient method exist to compute how much a signal is periodic, it should be ~1.0 when the signal is totally periodic (like a sinusoïdal signal) and ~0.0 when totally random, like a ...
4
votes
1answer
219 views
Fourier Series Coefficients
Question:
The fourier series coefficients is given as:
$$c_k= \begin{cases}
1 \qquad & k \ \text{ even} \\
2 \qquad & k \ \text{ odd} \\
\end{cases}$$
the period of the signal is $T=4$, ...
0
votes
1answer
472 views
How to calculate the FFT period
I have a question about finding the FFT duration for 802.11a preamble.
According to the standards, when the bandwith is $20 \textrm{MHz}$ and for $N=64$ we have $\Delta f = 20\textrm{MHz}/64 =312.5 \...
1
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0answers
30 views
Determining periodic pattern when there is pattern which period is multiple of former
I have periodic signal, say, it has year period, yearly pattern. I want to check if also has quarterly pattern.
Event if there is no visible quarterly pattern, Fourier Transform of this signal has ...
2
votes
2answers
138 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 ...
0
votes
1answer
140 views
Is sum of period samples in the DSP domain?
Following program outputs sum of samples of signal's period. Values in program are:
...
0
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0answers
65 views
Event detecting on periodic signals
I have a set of traces of 1m point each, the traces are periodic, i need to detect random behavior of the signal, i.e. in all traces i have 16 blocks of 6 peaks, in some blocks of some traces there ...
0
votes
1answer
2k views
How to find the period of a noisy signal using MATLAB's $\tt xcorr$?
Here is my code:
function [ T ] = FindPeriodicity2(x,Fs)
ac=xcorr(x,x);
[~,locs]=findpeaks(ac);
T=mean(diff(locs)/Fs);
end
and when I pass the signal ...
1
vote
1answer
394 views
Looking for cycles of periods longer than the input signal length
There was a similar question asked here, however I would like to focus on some specifics of this problem. Let me present the Python code sample to illustrate the situation when only a part of the ...
3
votes
1answer
277 views
Determination of periodicity in data and finding mean
I have to find whether there is any pattern (I mean periodicity or close to periodicity) and if there is, for one cycle i have to perform numerical integration to determine mean. In the first picture ...
1
vote
1answer
123 views
Periodicity of signals
$$x(t) = \cos(2 \pi t) \cdot u(t)$$
$$y(t) = x(t) + x(-t)$$Is $y(t)$ periodic. If so, what is the $T$?
$$x(t) = \sin(2 \pi t) \cdot u(t)$$
$$y(t)= x(t) + x(-t)$$
Is $y(t)$ periodic?
1
vote
0answers
108 views
The signal $\frac{e^{j10\pi n}}{10}$ is periodic/aperiodic?
How to verify the function
$$
\frac{e^{j10\pi n}}{10}
$$
is a period/aperiodic function ?
My attempt:
$\omega_o=10\pi\implies f_o=\omega_o/2\pi=5$, which is a rational number. So the given function ...
0
votes
0answers
30 views
Rectangular window to insulate two sinusoids
We have two sinusoids with the same amplitude and two different frequencies: $15 \ \mathrm{kHz}$ and $18 \ \mathrm{kHz}$. Sampling frequency is $100 \ \mathrm{kHz}$. What is the minimum length of the ...
3
votes
0answers
266 views
What is the autocorrelation equivalent of the spectrogram called?
I'm very knowledgeable about the differences between the Fourier transform, and the autocorrelation; mainly that one converts the time domain to the frequency domain, and the other finds periodicities ...
1
vote
1answer
230 views
finding period with autocorrelation is not correct
I have recorded a signal, which I know is periodic (apart from noise). The period length is unknown. I want to extract the last period from the signal. Before going to a noisy signal, I first tested ...
1
vote
1answer
59 views
Confused about the period of a discretised time-series
I have managed to confuse myself about the periods of discretised time series. It is all rather embarrassing.
This is one period extracted from my continuous signal (radians on y, time on x):
To ...
6
votes
2answers
383 views
Power of a periodic sequence
I am trying to find the way to reduce the standard expression to compute the power of a generic sequence $x(n)$:
$$P_{\text{x}}= \lim\limits_{N \to \infty}\frac{1}{2N + 1}\sum\limits_{n=-N}^{N}|x(n)|^...
0
votes
1answer
70 views
DFT and periodicity
My problem is related to the periodicity of DFT. Having the following expression
$$
Y_{k}=\sum_{n=0}^{2N-1}e^{-j\frac{2\pi mk}{2N}}
$$
I can easly find that the upper function is $2N$ periodic. So ...
0
votes
2answers
78 views
Very simple question about signal periodicity
$$x[n] = u[n]+u[-n]$$
Is it periodic or not? My answer is
$$u[n] = {1 , n\geqslant0}$$
$$u[-n] = {1 , n\leqslant0}$$
which means that the signal $x[n]$ is always equal to $1$ from $-\...
