# Tagged Questions

Questions on the mathematical aspects of signal processing. Please consider first if your question might be more suitable for http://dsp.stackexchange.com/

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### Sampling a Chebyshev polynomial with the discrete cosine transform

I have a Chebyshev polynomial $f$ of degree $n$ in point-value form \begin{align} f&=:S = \left( \left( x_i, y_i \right) \right)_{i=0}^n, \tag{1} \\ x_i &= \cos\left( \frac{i \pi}{n} \right), ...
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### Approximate a polynomial function using a sum of sine waves

I have a polynomial function which I need to approximate by a sum of sine waves with constant amplitude along a given domain. From what I hear, this might be a good time to make use of Fourier ...
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### Plot recursive signal in Matlab

I need to create and plot this signal in matlab with 2000 points: x(n) = 0.6530 x(n-1) - 0.7001 x(n-2) + v(n) Where $x(-1)=x(-2)=0$ and $v(n) =$ white noise I ...
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### What is the impulse response of the system

Given this input-output system what is the impulse response 𝑑𝑦(𝑡)/dt + 𝑦(𝑡) = 𝑡𝑥(𝑡), 𝑡 ≥ 0, 𝑦(0) = 0 I used an integrating factor to find y(t) y(t) = ${\int t*x(t) *e^tdt\over e^t }$ ...
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### What could be the mathematical equation of the given signal?

We know that Fourier series for periodic signal $y(t)$ is given by $$y(t) = \sum\limits_{m=0}^{+\infty} a_m \cos(w_m t) + \sum\limits_{m=0}^{+\infty}b_m \sin(w_m t). \quad (2)$$ Now,I want to find ...
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### Fourier synthesis of periodic signals

I was reading the Fourier synthesis of periodic signals But I didn't understand the sentence i.e. "Although the calculation of $a_0, a_1, b_1, a_2, b_2$, is a mathematically straightforward ...
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### How can I calculate the frequency when my samples don't span a whole period?

I am taking samples at 30Hz of a signal which is a slowly-varying sinewave. The period of the sinewave is expected to drift slowly, but will always be somewhere between 0.5s and 2s. I would like ...