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Questions tagged [periodic]

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Fourier series - finding its period from frequency representations

I’ve been given the following signal: $$X^F(\omega) = \sum_{n=-\infty}^{\infty} 2\pi a[n] \delta(\omega - \omega_0 n)$$ and I was asked to: find it’s period given $|X^F(\omega)| \ne 0$ only at $|\...
Piratemetaldrinkingcrew's user avatar
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1 answer
70 views

What function can be used to describe periodicity of the signal

im working on a program in matlab for calculation of sampled signal spectrum, and I have a sinusoidal signal with frequency f=100 Hz, sampling frequency fs=250 Hz, every sample is repeated 4 times (fr=...
Wiktuur's user avatar
0 votes
2 answers
50 views

The utility electric power signal is periodic or not?

The utility electric power signal is periodic or not? Our nationalgrid frequency is 50 hz and in some other places in world, it is 60 hz If I observe this signal on oscilloscope, will I get an exact ...
DSP_CS's user avatar
  • 1,870
2 votes
2 answers
68 views

Recovering a quasi-periodic signal subject to amplitude modulation and additive noise

Consider an unknown, quasi-periodic signal $x(t)$ with approximate slowly varying unknown period $T_x(t)$. A noisy, amplitude modulated version of this signal is observed: $$r(t) = a(t) x(t) + n(t)$$ ...
rhz's user avatar
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0 answers
35 views

Tracking period of quasi-periodic transient type signal in strong non-stationary interference

Consider a desired (pink) signal as well as its observation in heavy, non-stationary interference (green, this is the desired signal plus interference). As seen in the plot, the interference can also ...
rhz's user avatar
  • 457
0 votes
0 answers
40 views

Separating 'heart sound' from 'lung sound'

I have audio files recorded from electronic stethoscope and in those files I want to filter out heart sounds and retain just the breathing sounds. How can I do this using just the signal processing ...
hamza nawaz's user avatar
0 votes
1 answer
222 views

Magnitude and phase spectrum of a periodic signal

Let the following T-periodic signal : I found that $$ x(t) = \frac{A \cdot t}{T} \qquad 0 \le t < T $$ and its Fourier series is : $$ x(t) = \frac{A}{2} - \frac{A}{\pi} \sum_{n=1}^\infty \frac{\...
MOHAMED SALHI's user avatar
0 votes
1 answer
85 views

producing sine signal with few samples

I need to produce a signal of $\sin(2\pi\cdot 60\cdot10^6 t)$, where $t$ in sec, with sample rate of $2^{28}$ Hz. Since the signal has period of $\frac{1}{60\cdot 10^6}$ sec can I somehow sample only ...
Yar Sha's user avatar
  • 25
1 vote
3 answers
113 views

How to separate Transient and Steady-State Expression from Periodic Summation Response?

Background My question comes from here, it's a response of 1st order LPF RC circuit from an arbitrary periodic input. How to determine the transient response of a circuit to causal periodic inputs? ...
Unknown123's user avatar
2 votes
1 answer
228 views

Can time aliasing cause peaks?

For the following I use the terms “time domain signal” and “frequency domain signal” as a Fourier Transform pair. The question is for generalized cases of continuous-time signals that once sampled in ...
Dan Boschen's user avatar
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0 answers
18 views

Is there any method to incorporate boundary periodic conditions into the kernel summation over unstructured data points?

Supposing that there are $N$ particles distributed inside a periodic cubic box of volume $V=L^3$, I want to divide the cube into a regular mesh and calculate the following summation at each grid point ...
Wang Yun's user avatar
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0 votes
2 answers
68 views

How can i get a growing sinusoid in matlab?(by incorporating real part into exp command besides imaginary part which is already there)

I am trying to display a growing sinusoid in MATLAB and i know that imaginary part corresponds to oscillations but i am confused how can i incorporate real part in ...
DSP_CS's user avatar
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5 votes
1 answer
104 views

Finding periodicity in discrete events II - missions to Mars

Per the Space Exploration SE question Are launch windows to Mars avoided if they result in landings during dust storm season? the synodic period of the relationship between the motion of Earth and ...
uhoh's user avatar
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0 votes
2 answers
622 views

Is the unit step function periodic?

I am confused regarding the unit step signal. Is it considered to be periodic signal or non-periodic signal? In MATLAB we use command heaviside to implement it ...
DSP_CS's user avatar
  • 1,870
0 votes
1 answer
133 views

How to detect the end of a period of a repeating pattern in some time series signal

I have an incoming stream of time-series data which looks like in the below figure :- I want to detect the end of each cycle in real-time (marked with red arrows) using C language. What would be the ...
Nitin Singh's user avatar
2 votes
1 answer
323 views

is this signal is perodic?

What is the time period of $$ x(t) = 7 e^{\jmath(5t + \pi/2)} + 10^{\jmath(7t + \pi/5)}$$ ? X(t) is the combination of two functions. one is the natural logarithm base, $e$, and the other is 10. if ...
Nitish's user avatar
  • 179
0 votes
1 answer
47 views

If I have this discrete time sinusoid composed of a sine and a cosine, how do I find its period?

$$ x \left[ n \right] = 3 \sin \left( 4 \pi n \right) + 2 \cos \left(0.36 \pi n \right), ~~~ 0 \leq n \leq 100 $$ The fact that my signal is composed of both sine and cosine makes it tricky for me.
bob's user avatar
  • 1
1 vote
0 answers
297 views

What would be the fundamental period of this discrete-time signal?

Question: $x[n]= 3\cos(0.3\pi n + 0.1) - \sin(0.11\pi n -\frac{\pi}{3})$ Find the fundamental period for this discrete signal. My attempt: Write the two functions as: $$\underbrace {3\cos\left(\frac{3}...
user avatar
0 votes
2 answers
990 views

Fourier transform of periodic functions

The Fourier transform is derived from the Fourier series by considering a non-periodic signal, thinking of it as a infinitely long periodic signal, putting it into the Fourier series and making this ...
ozgun can's user avatar
2 votes
2 answers
654 views

How do I determine if the fundamental period $T_{x}$ exists and if so what it is?

I recently came across this $$ x(t) = \cos(6t) + \sin(8t) + e^{j2t} $$ signal that I want to find the fundamental period $T_{0}$ and fundamental frequency $\omega_{0} = 2\pi f_{0} = \frac{2\pi}{T_{0}}$...
NoName123's user avatar
  • 125
6 votes
3 answers
1k views

Period and wavelength of a noise signal?

How do I determine the wavelength of a noise signal like the one below? I find it easy to understand for sine waves, but it gets tricky for me when the signal is more complex like a noise signal. If I ...
Magnus's user avatar
  • 61
0 votes
0 answers
30 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
DSP_CS's user avatar
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1 vote
2 answers
528 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 ...
gumust's user avatar
  • 21
0 votes
0 answers
68 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, ...
DSP_CS's user avatar
  • 1,870
0 votes
1 answer
115 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 ...
B.Adlane's user avatar
2 votes
2 answers
527 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); <...
Hirohana Hiro's user avatar
0 votes
1 answer
272 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 & \...
ian's user avatar
  • 1
2 votes
1 answer
343 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 ...
Mathpdegeek497's user avatar
1 vote
1 answer
715 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 $x_2[n]$, ...
Orpheus's user avatar
  • 211
0 votes
1 answer
1k 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 ...
Orpheus's user avatar
  • 211
0 votes
1 answer
46 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, ...
user58547's user avatar
3 votes
2 answers
1k 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 ...
benjaminchanming's user avatar
1 vote
1 answer
787 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 ...
John Siddarth's user avatar
0 votes
1 answer
310 views

Angular frequency of discrete signal

Can someone explain me how to obtain the angular frequency here?
Itzy Death's user avatar
0 votes
1 answer
67 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 ...
Essam's user avatar
  • 267
0 votes
2 answers
646 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\...
mark leeds's user avatar
  • 1,117
-1 votes
1 answer
47 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&...
DSP_CS's user avatar
  • 1,870
2 votes
2 answers
836 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=\...
OverLordGoldDragon's user avatar
10 votes
2 answers
1k 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 $2$...
tfpf's user avatar
  • 203
0 votes
1 answer
235 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 ...
connor449's user avatar
  • 115
0 votes
0 answers
32 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 ...
Daniel Melo Avila's user avatar
0 votes
0 answers
256 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 ...
c111's user avatar
  • 1
1 vote
0 answers
67 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 ...
Cm7F7Bb's user avatar
  • 111
0 votes
1 answer
38 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
99 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 ...
sumer fattoum's user avatar
0 votes
1 answer
154 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 $2N+1$?
sumer fattoum's user avatar
2 votes
5 answers
3k 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] = \...
S.H.W's user avatar
  • 726
2 votes
2 answers
2k 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 ...
Rakshith Krish's user avatar
1 vote
2 answers
2k 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)=...
S.H.W's user avatar
  • 726
2 votes
1 answer
243 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 = ...
S.H.W's user avatar
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