Consider a sinusoid cos(kπn + θ), where k is an odd integer. In this case, the frequency Ω = kπ is on the border between the shaded and unshaded regions of Fig. 4.15b, and the apparent frequency can...

Consider a sinusoid cos(kπn + θ), where k is an odd integer. In this case, the frequency Ω = kπ is on the border between the shaded and unshaded regions of Fig. 4.15b, and the apparent frequency can be assigned from either region.

(a) Show that Eq. (4.17) computes the apparent frequency of this sinusoid as Ωa = −π, which corresponds to the shaded region of Fig. 4.15b. Express the sinusoid in terms of this apparent frequency.

(b) Assuming that Ω = kπ is assigned to the unshaded region, determine the apparent frequency Ωa, and express the sinusoid in terms of this apparent frequency.

(c) Letting Ω = 11π and θ = π/3, evaluate the two apparent sinusoids from parts (a) and (b). Comment on the results.