5.19 The sampling signal δ_(T_(s))(t)=∑_(n=-∞)^(∞) δ(t-nT_(s)) will be important in the sampling theory later on. (a) As a periodic signal of fundamental period T_(s), express δ_(T_(s))(t) by its Fourier series. (b) Determine then the Fourier transform Δ(Ω)=F[δ_(T_(s))(t)]. (c) Plot δ_(T_(s))(t) and Δ(Ω) and comment on the periodicity of these two functions.
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Step 1
Step 1: To express δ_(T_(s))(t) by its Fourier series, we can use the formula for the Fourier series coefficients: c_n = (1/T) * ∫[0 to T] δ_(T_(s))(t) * e^(-j2πnft) dt where T is the fundamental period T_(s) and f = 1/T. Show more…
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