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4. This problem will investigate a linear combination of continuous-time sinusoids. (1/² + 1/ ) ? a. What is the period of x₁ (t) = sin b. What is the period of x₂ (t) = cos( s(t - 7)? 3 πt c._ Is y(t) = x₁(t) + x₂(t) = sin ( + 7) + cos ( (-) periodic? If yes, what is the period of y(t)?

4. This problem will investigate a linear combination of continuous-time sinusoids. (1/² + 1/ ) ? a. What is the period of x₁ (t) = sin b. What is the period of x₂ (t) = cos( s(t - 7)? 3 πt c._ Is y(t) = x₁(t) + x₂(t) = sin ( + 7) + cos ( (-) periodic? If yes, what is the period of y(t)?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 52E
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1. Consider the real-valued two-sided discrete-time signal x[n] = all, where a is a real number satisfying 0 < a < 1, and || denotes the absolute value. b. Find a closed form expression for the energy E of x[n] as a function of a. c. Numerically compute the partial sum energy over n = -10, ..., 10, for a = ². Specifically, compute -10lx[n] 1². How does this partial sum energy compare with your closed form expression from part b.?
Transcribed Image Text:1. Consider the real-valued two-sided discrete-time signal x[n] = all, where a is a real number satisfying 0 < a < 1, and || denotes the absolute value. b. Find a closed form expression for the energy E of x[n] as a function of a. c. Numerically compute the partial sum energy over n = -10, ..., 10, for a = ². Specifically, compute -10lx[n] 1². How does this partial sum energy compare with your closed form expression from part b.?
3. Consider the discrete-time sinusoid x[n] = sin 2 (77). πη a. Plot x[n] for n = 0,..., 48. b. Is this discrete-time sinusoid periodic? If so, what is the period? c. Find and plot another discrete-time sinusoid y[n] = sin(w₁n) with a different frequency (w₁) that yields exactly the same values as x[n]. 4. This problem will investigate a linear combination of continuous-time sinusoids. πt π a. What is the period of x₁ (t) = sin ¹ (1/² + ²) ² b. What is the period of x₂ (t) = cos ( - ) ? 3 лt c. Is y(t)= x₁(t) + x₂(t) = sin + 1-) 2 + cos πt 3 periodic? If yes, what is the period of y(t)?
Transcribed Image Text:3. Consider the discrete-time sinusoid x[n] = sin 2 (77). πη a. Plot x[n] for n = 0,..., 48. b. Is this discrete-time sinusoid periodic? If so, what is the period? c. Find and plot another discrete-time sinusoid y[n] = sin(w₁n) with a different frequency (w₁) that yields exactly the same values as x[n]. 4. This problem will investigate a linear combination of continuous-time sinusoids. πt π a. What is the period of x₁ (t) = sin ¹ (1/² + ²) ² b. What is the period of x₂ (t) = cos ( - ) ? 3 лt c. Is y(t)= x₁(t) + x₂(t) = sin + 1-) 2 + cos πt 3 periodic? If yes, what is the period of y(t)?
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