Problem 7.2 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) is passed through an LPF HLPF(ƒ) = (f) to obtain the signal x,(t). Sketch the spectrum Ŷ, (ƒ) 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 = 1 12° (e) What is the maximum value of T for which x(t) = x(t) (up to scale)?

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Problem 7.2 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) is passed through an LPF HLPF(ƒ) = (f) to obtain the
signal x,(t). Sketch the spectrum Ŷ, (ƒ) 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
=
1
12°
(e) What is the maximum value of T for which x(t) = x(t) (up to scale)?
Transcribed Image Text:Problem 7.2 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) is passed through an LPF HLPF(ƒ) = (f) to obtain the signal x,(t). Sketch the spectrum Ŷ, (ƒ) 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 = 1 12° (e) What is the maximum value of T for which x(t) = x(t) (up to scale)?
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