a. Why do we use Discrete Fourier Transform (DFT) instead of Discrete-Time Fourier Transform (DTFT) in real-world signal processing applications? b. Given the 4-point discrete-time sequence x[0], x[1], x[2] and x[3], write a separate formula for each of its 4-point Discrete Fourier Transform X[0], X[1], X[2] and X[3].(Hint: X[.] is a function of x[0],x[1],x[2], and x[3]) c. Consider the "time-reversed" sequence y(n) = x[3 - n] for n = 0,1,2,3. Write its 4- point Discrete Fourier Transform Y[0], Y[1], Y[2] and Y[3] in terms of X[0], X[1], X[2] and X[3], where they are the Discrete Fourier Transform of x[n].

a. Why do we use Discrete Fourier Transform (DFT) instead of Discrete-Time Fourier Transform (DTFT) in real-world signal processing applications? b. Given the 4-point discrete-time sequence x[0], x[1], x[2] and x[3], write a separate formula for each of its 4-point Discrete Fourier Transform X[0], X[1], X[2] and X[3].(Hint: X[.] is a function of x[0],x[1],x[2], and x[3]) c. Consider the "time-reversed" sequence y(n) = x[3 - n] for n = 0,1,2,3. Write its 4- point Discrete Fourier Transform Y[0], Y[1], Y[2] and Y[3] in terms of X[0], X[1], X[2] and X[3], where they are the Discrete Fourier Transform of x[n].

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 20E

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