Question

Consider the function h(t)=sinc(t/T) cos(πβt/T)/1−(4β²2R² /T²). This function describes a raised cosine filter in the time domain. Suppose that T=1 and β=0.5 and plot h(t) in the time interval −5T≤t≤5T.

Answer 1

The plot shows the behavior of a raised cosine filter with T=1 and β=0.5 over the interval -5T to 5T.

Step-by-step explanation:

The student is asking about plotting a function that represents a raised cosine filter in the time domain. The provided parameters are T=1 and β=0.5.

The interval of interest is from -5T to 5T. When plotting the function h(t)=sinc(t/T) cos(πβt/T)/(1-(4β²t²/T²)), we take into account that a sinc function is a sine function normalized by its argument, and the raised cosine part will determine the function's shape within the given envelope.

The plot generated will oscillate and depict the behavior of a raised cosine filter which is often used in signal processing to limit the band of frequencies passed through a filter.