Difference between revisions of "HW4.3 Austin Melnyk ECE301Fall2008mboutin" - Rhea

Revision as of 16:26, 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 * \pi * t) * cos(4 * \pi * t) $