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←++ 0 f[k] 1 1234 Plot the output signal y[k]. 678 This signal has three nonzero values. All other values of f[k] are zero. (a) Write f[k] as a sum of three discrete-time impulses: ƒ[k] = ??? - 8[k-???] + ??? · 6[k—???] +??? - 8[k—???] (b) Find the energy of f[k]. (c) Suppose we pass f[k] as the input to the accumulator shown below: f[k] D₁ (delay 1 sample) y[k] k

←++ 0 f[k] 1 1234 Plot the output signal y[k]. 678 This signal has three nonzero values. All other values of f[k] are zero. (a) Write f[k] as a sum of three discrete-time impulses: ƒ[k] = ??? - 8[k-???] + ??? · 6[k—???] +??? - 8[k—???] (b) Find the energy of f[k]. (c) Suppose we pass f[k] as the input to the accumulator shown below: f[k] D₁ (delay 1 sample) y[k] k

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Consider the discrete-time signal plotted below: f[k] 1 1234 1 678 -2 This signal has three nonzero values. All other values of f[k] are zero. (a) Write f[k] as a sum of three discrete-time impulses: ƒ[k] = ??? - d[k—???] + ??? · 6[k—???] +??? - d[k—???] D₁ (delay 1 sample) (b) Find the energy of f[k]. (c) Suppose we pass f[k] as the input to the accumulator shown below: f[k]- Plot the output signal y[k]. (d) Write y[k] as a sum of three discrete-time unit steps: y[k] y[k] = ??? - u[k—???] + ??? · u[k—???] +??? • u[k—???] k (e) Recall from our lecture notes that the accumulator system has the impulse response h[k]u[k]. Compare your answers to parts (a) and (d), noting how the system responds to each impulse that comes in. You do not need to hand anything in for this part.
Transcribed Image Text:Consider the discrete-time signal plotted below: f[k] 1 1234 1 678 -2 This signal has three nonzero values. All other values of f[k] are zero. (a) Write f[k] as a sum of three discrete-time impulses: ƒ[k] = ??? - d[k—???] + ??? · 6[k—???] +??? - d[k—???] D₁ (delay 1 sample) (b) Find the energy of f[k]. (c) Suppose we pass f[k] as the input to the accumulator shown below: f[k]- Plot the output signal y[k]. (d) Write y[k] as a sum of three discrete-time unit steps: y[k] y[k] = ??? - u[k—???] + ??? · u[k—???] +??? • u[k—???] k (e) Recall from our lecture notes that the accumulator system has the impulse response h[k]u[k]. Compare your answers to parts (a) and (d), noting how the system responds to each impulse that comes in. You do not need to hand anything in for this part.
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