# Questions tagged [periodic]

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### 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 ...
345 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 ...
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### Unable to interpret hypothesis testing whetehr a signal is periodic or not

The meaning of P value is probability which should be number between 0 (the event never occurs) and 1 (the event occurs always). significance testing for periodicity using Matlab gives a documentation ...
3k views

### $2\pi$ periodicity of discrete-time Fourier transform

In my signals and systems course, we have learned that the discrete-time Fourier transform is $2\pi$ periodic, but the continuous-time Fourier transform is not periodic in general. For reference, we ...
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### 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 ...
42 views

### Generating a sawtooth function with a variable frequency

So I'm trying to write a script that produces a sawtooth function using the equation: s = 2 a / π atan ( cot ( π f t ) ) Where: a : amplitude f : frequency t : time It's all working fine when f is ...
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### 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 $w_c = 40rad/s$. ...
14k 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\...
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### 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 ...
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### $2\pi$ 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 ...
96 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. ...