# Questions tagged [periodic]

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### 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. ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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, ...
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I am bit confused after reading Frequency-Domain Sampling and Reconstruction of Discrete-Time Signals section from Proakis where, $$x(n)=\begin{cases} x_p(n),\;\;\;\;0\leq n \leq N-1\\ ... 2answers 137 views ### How sampling aperiodic signal will result in periodic repetitions of the same I am reading "Digital Signal Processing" - Proakis and often read that sampling guarantees periodicity (not exact as read) But I wonder how sampling aperiodic signal will result in periodic ... 2answers 52 views ### Period of a continuous signal So I have$$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$$... 2answers 250 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 ... 2answers 81 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. ... 0answers 57 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 ... 3answers 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 ... 2answers 163 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 ... 3answers 2k 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. 2answers 961 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)... 2answers 398 views ### Prove that, in DFT, Upsampling 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]$$then, Prove that: DFT of the same sequence after insertion of (M-1) zeroes between successive ... 0answers 172 views ### White noise generation in frequency domain (stfft) produces a periodic pattern I have created a set of spectral processing modules for SynthEdit next to be released, implenting short time fft, so I am now quite experienced with the matter, but recently encounteted an unexpected ... 2answers 107 views ### Intermittent Harmonics, Is there a physical explanation? I am doing some frequency analysis of a vibration signal from a spinning rotor, I am expecting to see peaks corresponding to the rotational frequency of the rotor. So the fundamental frequency ... 1answer 1k views ### Find the period of a signal with the DTFT plot I have an exercise and I'm struggling to resolve it. Here it is : My problem is about the DTFT. I've always been taught that we use DTFT for infinite-lenght signal that are not periodic (if the ... 2answers 905 views ### Building periodic sequences from finite-support sequences Given a discrete-time finite-support signal x[n]$$x[n] = \left\{ {\begin{array}{*{20}{l}} {{{( - 1)}^n}n}&{{\rm{ }}n = 1,2,3}\\ 0&{{\rm{otherwise}}} \end{array}} \right. And consider also ...
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)