Consider the cosine wavex(t) =10cos(880πt + ϕ)Suppose that we obtain a sequence of numbers...

Consider the cosine wave

x(t) =10cos(880πt + ϕ)

Suppose that we obtain a sequence of numbers by sampling the waveform at equally spaced time instants nTs. In this case, the resulting sequence would have values

for –∞<n<∞. Suppose that Ts = 0.0001 sec.

(a) How many samples will be taken in one period of the cosine wave?

(b) Now consider another waveform y(t) such that

y(t) = 10 cos(ω0t + ϕ)

Find a frequency ω0 > 880π such that y(nTs) = x(nTs) for all integers n.

Hint: Use the fact that cos(θ + 2πn) = cos(θ) if n is an integer.

(c) For the frequency found in (b), what is the total number of samples taken in one period of x(t)?