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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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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