Question

In PAM, the amplitudes of a pulse train are proportional to the sampled values of the modulating signal. In δ function sampling the Nyquist rate is the minimum sampling rate that allows undistorted reconstruction of the modulating signal (assuming an ideal reconstruction filter).

PROBLEMS
1. Derive an expression for the amplitude spectrum in the f domain of a 5 V amplitude, 50μs wide rectangular pulse. Calculate its value at 30kHz.

Answer 1

The amplitude spectrum of a 5 V amplitude, 50µs wide rectangular pulse is given by the Fourier transform and can be expressed as a sinc function. To find the value at 30kHz, substitute f = 30kHz into the amplitude spectrum formula and evaluate.

Step-by-step explanation:

The student asked for the amplitude spectrum in the f domain of a 5 V amplitude, 50µs wide rectangular pulse and its value at 30kHz. To derive the amplitude spectrum, we can use the Fourier transform of the rectangular pulse, which is given by the sinc function (sin(πfT)/(πfT)).

For a pulse width of T = 50µs, and amplitude A = 5 V, the amplitude spectrum S(f) will be S(f) = AT ∗ sinc(πfT). Substituting the values, we get S(f) = 5 V ∗ 50µs ∗ sinc(πf ∗ 50µs). To find the specific value at 30kHz, we substitute f = 30kHz into the equation and calculate the result using the sinc function.