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== Part B: The response to my question 1. == | == Part B: The response to my question 1. == | ||
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| + | <math> x(t) = cos(2 * π * t) * cos(4 * π * t) </math> | ||
Revision as of 17:26, 25 September 2008
CT LTI sytem
An example system would be:
y(t) = 2*x(t)
Part A: The unit impulse response and system function H(s)
The unit impulse response:
$ x(t) \to \delta(t) * h(t) = 2*\delta(t) $
The system function, H(s) derivation:
$ y(t) = \int_{-\infty}^{\infty} x(\tau) * h(\tau) *d\tau $
$ y(t) = \int_{-\infty}^{\infty} e^{-j*w(t-k)} * 2\delta(\tau) *d\tau $
$ y(t) = e^{j*w*t} \int_{-\infty}^{\infty} e^{-j*w*k} * 2\delta(\tau) * d\tau $
$ H(s) = \int_{-\infty}^{\infty} e^{-j*w*k} * 2\delta(\tau) d\tau $
$ 2*1 = 2 $
H(s) = 2
Part B: The response to my question 1.
$ x(t) = cos(2 * π * t) * cos(4 * π * t) $
