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Suppose we have the following discrete time signal: x[n] = 2(0.8)¹u[n - 1] Let X10 [k] represent the 10-point DFT of x[n] over the range n=0,1,2,...,9 and define x 10 [n] as the inverse DFT of X10 [k]. (a) Find X10 [0] (b) Find 10 [5], 10[10], 10[15], 10[20], 10 [25] Now suppose we have the following discrete time signal: w[n] = (2(0.8)-u[n-1] 0 ≤ n < 10 0 otherwise Let W20[k] represent the 20-point DFT of w[n] and define W20 [n] as the inverse DFT of W20 [k]. (c) Find W20 [0]

Suppose we have the following discrete time signal: x[n] = 2(0.8)¹u[n - 1] Let X10 [k] represent the 10-point DFT of x[n] over the range n=0,1,2,...,9 and define x 10 [n] as the inverse DFT of X10 [k]. (a) Find X10 [0] (b) Find 10 [5], 10[10], 10[15], 10[20], 10 [25] Now suppose we have the following discrete time signal: w[n] = (2(0.8)-u[n-1] 0 ≤ n < 10 0 otherwise Let W20[k] represent the 20-point DFT of w[n] and define W20 [n] as the inverse DFT of W20 [k]. (c) Find W20 [0]

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Suppose we have the following discrete time signal: x[n] = 2(0.8)¹-¹u[n − 1] Let X₁0[k] represent the 10-point DFT of x [n] over the range n=0,1,2,...,9 and define x₁0 [n] as the inverse DFT of X10[k]. (a) Find X₁0 [0] (b) Find X10 [5], X10 [10], X10 [15], X10 [20], X10 [25] Now suppose we have the following discrete time signal: w[n] = {2(0. [2(0.8)n-¹u[n 1] 0≤n<10 0 otherwise Let W₂0[k] represent the 20-point DFT of w[n] and define W20 [n] as the inverse DFT of W₂0[k]. (c) Find W₂0 [0] (d) Find W₂0 [5], W20 [10], W₂0 [15], W20 [20], W20 [25]
Transcribed Image Text:Suppose we have the following discrete time signal: x[n] = 2(0.8)¹-¹u[n − 1] Let X₁0[k] represent the 10-point DFT of x [n] over the range n=0,1,2,...,9 and define x₁0 [n] as the inverse DFT of X10[k]. (a) Find X₁0 [0] (b) Find X10 [5], X10 [10], X10 [15], X10 [20], X10 [25] Now suppose we have the following discrete time signal: w[n] = {2(0. [2(0.8)n-¹u[n 1] 0≤n<10 0 otherwise Let W₂0[k] represent the 20-point DFT of w[n] and define W20 [n] as the inverse DFT of W₂0[k]. (c) Find W₂0 [0] (d) Find W₂0 [5], W20 [10], W₂0 [15], W20 [20], W20 [25]
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