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Questions tagged [periodic]

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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
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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 ...
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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 ...
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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 ...
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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 ?
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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
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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
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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
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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 ...
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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: ...
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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 ...
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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
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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
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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
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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
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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
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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
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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
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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 ...
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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
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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-...
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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 \...
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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
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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
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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: ...
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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
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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
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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
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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
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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?
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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 ...
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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 ...
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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
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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
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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
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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
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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 ...
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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 $-\...