get h(t), H(s), and H(jw)

$ \ y(t) = 4x(t-1) $

$ \ h(t) = 4d(t-1) $

$ \ H(s) = \int^{\infty}_{-\infty} h(t)e^{-st}dt $

$ \ H(s) = \int^{\infty}_{-\infty} 4d(t-1)e^{-st}dt $

$ \ H(s) = 4e^{-s} $

$ \ H(jw) = 4e^{-jw} $

get the response of H(s) to signal proposed in previous question

$ y(t) = \sum_{k = -\infty}^{\infty} a_k H(jkw) (sin(4\pi t) + sin(6\pi t)) \! $

$ y(t) = \sum_{k = -\infty}^{\infty} a_k 4e^{-jw} (sin(4\pi t) + sin(6\pi t)) \! $

from before:

$ a_5 = \frac{-1}{4}, a_-5 = \frac{-1}{4},a_1 = \frac{1}{4},a_-1 = \frac{1}{4} $


$ y(t) = \frac{1}{4}4e^{-jw} - \frac{1}{4}4e^{-jw} + \frac{1}{4}4e^{-jw} - \frac{1}{4}4e^{-jw} $

$ \ y(t) = 0 $

Alumni Liaison

BSEE 2004, current Ph.D. student researching signal and image processing.

Landis Huffman