Questions tagged [periodic]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0 votes
0 answers
27 views

Is there any rule of thumb for determining periodicity of a signal just by observation of mathematical expression?

Is there any way(rule of thumb) to determine periodicity of a signal just by observation of mathematical expression as rule of thumb mentioned in attachment for determining time invariance of a system
user avatar
  • 1,088
1 vote
2 answers
74 views

How to calculate frequency of a periodic signal?

I know there are similar topics but I can not find any solution in my situation. I have an accelerometer sensor and a basic microcontroller. Accelerometer data is collected in an array via i2C. I want ...
user avatar
  • 21
0 votes
0 answers
49 views

Difference between time period formulas? Continuous time vs discrete time?

For calculating period of continuous time signal,we simply divide 2pi by omega and get period value But in case of discrete time signal, procedure is not straight forward like continuous time, ...
user avatar
  • 1,088
0 votes
1 answer
63 views

does T = 1/F always hold?

i just want to know if i use a sampling frequency of 100-110Hz and get a useful signal frequency of 50Hz (because of Nyquist–Shannon sampling theorem), is the period 1/50Hz or 1/100Hz? I've been told ...
user avatar
2 votes
2 answers
84 views

How can I check if a signal its periodic from the graph of FFT?

x is a vector of length 1000 that contains the samples of the signal; n is equal to 16 that its the number of bits of each sample; fa=256 Hz (sampling frequency); <...
user avatar
0 votes
1 answer
58 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 & \...
user avatar
  • 1
2 votes
1 answer
117 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 ...
user avatar
1 vote
1 answer
194 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 $x_2[n]$, ...
user avatar
  • 191
0 votes
1 answer
193 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 ...
user avatar
  • 191
9 votes
5 answers
1k 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?
user avatar
0 votes
1 answer
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, ...
user avatar
3 votes
2 answers
601 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 ...
user avatar
1 vote
1 answer
116 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 ...
user avatar
0 votes
1 answer
87 views

Angular frequency of discrete signal

Can someone explain me how to obtain the angular frequency here?
user avatar
0 votes
1 answer
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 ...
user avatar
  • 267
0 votes
2 answers
173 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\...
user avatar
  • 1,082
-1 votes
1 answer
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&...
user avatar
  • 613
1 vote
2 answers
215 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=\...
user avatar
9 votes
2 answers
663 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 $2$...
user avatar
  • 193
0 votes
1 answer
59 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 ...
user avatar
  • 115
0 votes
0 answers
22 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 ...
user avatar
0 votes
0 answers
125 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 ...
user avatar
  • 1
1 vote
0 answers
47 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 ...
user avatar
  • 111
0 votes
1 answer
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 ...
user avatar
0 votes
1 answer
55 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 ...
user avatar
0 votes
1 answer
53 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 $2N+1$?
user avatar
2 votes
5 answers
2k 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] = \...
user avatar
  • 701
2 votes
2 answers
569 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 ...
user avatar
1 vote
2 answers
1k 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)=...
user avatar
  • 701
2 votes
1 answer
82 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 = ...
user avatar
  • 701
1 vote
5 answers
649 views

Change in frequency on differentiation

Is there any possible periodic signal can exist(even mathematically) whose period gets change after differentiation?
user avatar
2 votes
1 answer
871 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 $$...
user avatar
  • 701
0 votes
2 answers
265 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 $w_c = 40rad/s$. ...
user avatar
1 vote
0 answers
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 ...
user avatar
0 votes
0 answers
38 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 ...
user avatar
0 votes
1 answer
67 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_{...
user avatar
4 votes
1 answer
135 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. ...
user avatar
  • 183
0 votes
2 answers
31 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 ...
user avatar
0 votes
0 answers
39 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 ...
user avatar
  • 131
1 vote
3 answers
215 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 ...
user avatar
  • 1,088
0 votes
1 answer
192 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, ...
user avatar
0 votes
0 answers
29 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\\ ...
user avatar
  • 571
1 vote
2 answers
249 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 ...
user avatar
  • 571
1 vote
2 answers
76 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 $$a=.6\sqrt\pi x+\pi/6 ~~~\text{and} ~~~ b=1.2\sqrt\pi x-\pi/3$$ ...
user avatar
  • 75
7 votes
2 answers
516 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 ...
user avatar
1 vote
2 answers
121 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. ...
user avatar
0 votes
0 answers
86 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 ...
user avatar
6 votes
3 answers
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 ...
user avatar
  • 71
0 votes
2 answers
212 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 ...
user avatar
  • 467
0 votes
3 answers
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 $2$.
user avatar