Consider a “windowed cosine signal” x[n] = w[n] cos(ω0n). (a) Determine an exp...

Consider a “windowed cosine signal”

x[n] = w[n] cos(ω₀n).

(a) Determine an expression for X(e^jω) in terms of W(e^jω).

(b) Suppose that the sequence w[n] is the finite-length sequence

Determine the DTFT W(e^jω). Hint: Use Tables 2.2 and 2.3 to obtain a “closed form” solution. You should find that W(e^jω) is a real function of ω.

(c) Sketch the DTFTX(e^jω) for the window in (b). For a given ω₀, how should L be chosen so that your sketch shows two distinct peaks?