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2) Solve the difference equation using z-transform yk+2-3 Yk+1 + 2yk = 0, with y₁ = 0, y₁ = 1. Explain the procedure in your words 3) Find the following in the Fourier series expansion of the following functions: a. ao for f(x) = sin(x) defined over the interval (-1, 1). b. bn for f(x) = 3x defined over the interval (0,2). 4) What do you mean by even and odd function? Give two examples and show by calculation that those are even and odd. 5) If F(s) is the complex Fourier transform of the function f(x), then prove that F{f(x-a)} = e-ias F (s).

2) Solve the difference equation using z-transform yk+2-3 Yk+1 + 2yk = 0, with y₁ = 0, y₁ = 1. Explain the procedure in your words 3) Find the following in the Fourier series expansion of the following functions: a. ao for f(x) = sin(x) defined over the interval (-1, 1). b. bn for f(x) = 3x defined over the interval (0,2). 4) What do you mean by even and odd function? Give two examples and show by calculation that those are even and odd. 5) If F(s) is the complex Fourier transform of the function f(x), then prove that F{f(x-a)} = e-ias F (s).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.4: Values Of The Trigonometric Functions
Problem 23E
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2) Solve the difference equation using z-transform yk+2 - 3 yk+1 + 2 yk = 0, with yo = 0, y, = 1. Explain the procedure in your words 3) Find the following in the Fourier series expansion of the following functions: a. a, for f(x) = sin(x) defined over the interval (-7, T1). b. bn for f(x) = 3x defined over the interval (0,2). 4) What do you mean by even and odd function? Give two examples and show by calculation that those are even and odd. 5) If F(s) is the complex Fourier transform of the function f (x), then prove that F{f(x – a)} = e-ias F(s).
Transcribed Image Text:2) Solve the difference equation using z-transform yk+2 - 3 yk+1 + 2 yk = 0, with yo = 0, y, = 1. Explain the procedure in your words 3) Find the following in the Fourier series expansion of the following functions: a. a, for f(x) = sin(x) defined over the interval (-7, T1). b. bn for f(x) = 3x defined over the interval (0,2). 4) What do you mean by even and odd function? Give two examples and show by calculation that those are even and odd. 5) If F(s) is the complex Fourier transform of the function f (x), then prove that F{f(x – a)} = e-ias F(s).
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