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Consider the signal x(t) = sinc(6t)sinc(4t). (a) Sketch the spectrum Ŷ(ƒ). (b) Consider the impulse train sampled signal ∞ xs(t) = Σ x(nT)&(t — nT) n=-∞ where T = ½. Sketch the spectrum of Ŷs(f). (c) The sampled signal x(t) passed through an LPF Hlpf(f) = I\-] (f) to obtain the signal x,(t). Sketch the spectrum Ŷ, (f) and give an explicit expression for the time domain signal x,(t). Is it the same as the original signal x(t) (up to scale)? (d) Repeat (b) and (c) for T = 12. (e) What is the maximum value of T for which x(t) = x(t) (up to scale)?

Consider the signal x(t) = sinc(6t)sinc(4t). (a) Sketch the spectrum Ŷ(ƒ). (b) Consider the impulse train sampled signal ∞ xs(t) = Σ x(nT)&(t — nT) n=-∞ where T = ½. Sketch the spectrum of Ŷs(f). (c) The sampled signal x(t) passed through an LPF Hlpf(f) = I\-] (f) to obtain the signal x,(t). Sketch the spectrum Ŷ, (f) and give an explicit expression for the time domain signal x,(t). Is it the same as the original signal x(t) (up to scale)? (d) Repeat (b) and (c) for T = 12. (e) What is the maximum value of T for which x(t) = x(t) (up to scale)?

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
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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please  have step by step solution and explain. for part c the answer is not up to scale, but please have the steps for that too

Consider the signal x(t) = sinc(6t)sinc(4t). (a) Sketch the spectrum Ŷ(ƒ). (b) Consider the impulse train sampled signal ∞ xs(t) = Σ x(nT)&(t — nT) n=-∞ where T = ½. Sketch the spectrum of Ŷs(f). (c) The sampled signal x(t) passed through an LPF Hlpf(f) = I\-] (f) to obtain the signal x,(t). Sketch the spectrum Ŷ, (f) and give an explicit expression for the time domain signal x,(t). Is it the same as the original signal x(t) (up to scale)? (d) Repeat (b) and (c) for T = 12. (e) What is the maximum value of T for which x(t) = x(t) (up to scale)?
Transcribed Image Text:Consider the signal x(t) = sinc(6t)sinc(4t). (a) Sketch the spectrum Ŷ(ƒ). (b) Consider the impulse train sampled signal ∞ xs(t) = Σ x(nT)&(t — nT) n=-∞ where T = ½. Sketch the spectrum of Ŷs(f). (c) The sampled signal x(t) passed through an LPF Hlpf(f) = I\-] (f) to obtain the signal x,(t). Sketch the spectrum Ŷ, (f) and give an explicit expression for the time domain signal x,(t). Is it the same as the original signal x(t) (up to scale)? (d) Repeat (b) and (c) for T = 12. (e) What is the maximum value of T for which x(t) = x(t) (up to scale)?
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