Question

Assume an analog signal , x ₐ (t) , with paramether below

Xₐ (t) = [0.5 sin(2πFₘt) + 1] cos (2πF(t)
Fₘ = 5 kHz
F = 25 khz
sample the analog signal at a rate Fₛ = 100,000 samples / sec and
show the equation for the resulting discrete-time signal , x(n)

Answer 1

To sample the given analog signal at 100,000 samples/sec, the resulting discrete-time signal x(n) is obtained by substituting t with n/Fᵓ in the analog signal equation.

Step-by-step explanation:

To sample the given analog signal xᵃ (t) at a sampling rate of Fᵓ = 100,000 samples/sec, you apply the sampling theorem to obtain the discrete-time signal x(n). The analog signal is:

xᵃ (t) = [0.5 sin(2π Fᵃt) + 1] cos (2π F(t))

With Fᵃ = 5 kHz and F = 25 kHz.

Using the given sampling frequency Fᵓ to sample xᵃ (t), the resulting discrete-time signal x(n) is described by the equation:

x(n) = [0.5 sin(2π Fᵃn / Fᵓ) + 1] cos (2π Fn / Fᵓ)

This is achieved by replacing t with n/Fᵓ in xᵃ (t) where n represents the sample number.