(a) H() = F{h(t)} is an ideal low-pass filter with H(u) = AT for max <...

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(a) H(µ) = F{h(t)} is an ideal low-pass filter with H(u) = AT for max < µl < µmax and H(u) = 0 otherwise. A band-limited function f(t) can be perfectly recovered from its samples f(t) through: f(t) = h(t) * f(t), where denotes convolution. Show how this leads to: +∞ f(t) = Σ f(nΔΤ) sinc 8=1x t-nAT ΔΤ " with definition sincx = sin(x)/(x). So, f(t) is an infinite sum of sinc functions weighted by the sample values. (b) What ensures that f(t) is equal to the sample values fk for all k? (a) H(µ) = F{h(t)} is an ideal low-pass filter with H(u) = AT for max < µl < µmax and H(u) = 0 otherwise. A band-limited function f(t) can be perfectly recovered from its samples f(t) through: f(t) = h(t) * f(t), where denotes convolution. Show how this leads to: +∞ f(t) = Σ f(nΔΤ) sinc 8=1x t-nAT ΔΤ " with definition sincx = sin(x)/(x). So, f(t) is an infinite sum of sinc functions weighted by the sample values. (b) What ensures that f(t) is equal to the sample values fk for all k? (a) H(µ) = F{h(t)} is an ideal low-pass filter with H(u) = AT for max < µl < µmax and H(u) = 0 otherwise. A band-limited function f(t) can be perfectly recovered from its samples f(t) through: f(t) = h(t) * f(t), where denotes convolution. Show how this leads to: +∞ f(t) = Σ f(nΔΤ) sinc 8=1x t-nAT ΔΤ " with definition sincx = sin(x)/(x). So, f(t) is an infinite sum of sinc functions weighted by the sample values. (b) What ensures that f(t) is equal to the sample values fk for all k?

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