Question

24) Consider the system h: \{x_n\} \to \{y_n\} with $y_n - y_{n-1} = x_n - x_{n-3}$. a) Give the impulse response of this system. b) Give one sine-wave input sequence of the form $x_n = a \cdot \sin(b \cdot n + c)$ (with $a \neq 0$, $b \neq 0$) for which $y_n = 0$ for all n. c) Express the system h as a rational function $H(z)$. d) Determine the values $z \in \mathbb{C}$ for which $H(z) = 0$.

          24) Consider the system h: \{x_n\} \to \{y_n\} with $y_n - y_{n-1} = x_n - x_{n-3}$.
a) Give the impulse response of this system.
b) Give one sine-wave input sequence of the form
$x_n = a \cdot \sin(b \cdot n + c)$
(with $a \neq 0$, $b \neq 0$) for which $y_n = 0$ for all n.
c) Express the system h as a rational function $H(z)$.
d) Determine the values $z \in \mathbb{C}$ for which $H(z) = 0$.

24) Consider the system h: {xn} →{yn} with yn - yn-1 = xn - xn-3.
a) Give the impulse response of this system.
b) Give one sine-wave input sequence of the form
xn = a ·sin(b · n + c)
(with a ≠ 0, b ≠ 0) for which yn = 0 for all n.
c) Express the system h as a rational function H(z).
d) Determine the values z ∈ℂ for which H(z) = 0.

Added by Tiffany M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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e-ux -ux=I-ux -uK yyM{uX} -{ux}:y Uyysxs ayrayprsuO(tZ a) a) Give the impulse response of this system. b) Give one sine-wave input sequence of the form xn = a sin (b.n+ c) (with a â‰ 0, b â‰ 0) for which yn = 0 for all n. c) Express the system h as a rational function H(z). d) Determine the values z âˆˆ C for which H(z) = 0.