HW1 - EEE 304 Homework 1 Due Monday in class 1 Linear system characterization(a Suppose a discrete-time system H is linear but not necessarily

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Unformatted text preview: EEE 304 Homework 1 Due Monday, 1/28/07 in class 1. Linear system characterization (a) Suppose a discrete-time system H {} is linear but not necessarily time-invariant. Show that H { x [ n ] } = summationdisplay k =- h [ n,k ] x [ k ] where h [ n,k ] is the response of H {} to an impulse delayed by k samples. Interpret this result. What happens when H {} is also time-invariant? (b) Derive a similar expression for H { x ( t ) } where H {} is a continuous-time linear system, which is not necessarily time-invariant. 2. Differentiation by integration Recall from class discussion that the sequence of pulses, k ( t ), as displayed in Figure 1, has the property that integraldisplay - x ( ) k ( t- ) d x ( t ) as k .-5 5-5-4-3-2-1 1 2 3 4 5 k (t) t 1/k k Figure 1: k ( t ) for Problem 2 1 (a) Now suppose x ( t ) is differentiable for all t . Identify a sequence of real-valued, bounded signals g k ( t ), such that as k , integraldisplay...
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This homework help was uploaded on 04/05/2008 for the course EEE 304 taught by Professor Thornburg during the Fall '08 term at ASU.

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HW1 - EEE 304 Homework 1 Due Monday in class 1 Linear system characterization(a Suppose a discrete-time system H is linear but not necessarily

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