Question

Find the Nyquist rates (frequencies) for these signals. Justify your answers (sketch the magnitude of the FT or provide an equation).

x(t)=15⋅Π(300t)⋅cos(10000πt)

Answer 1

The Nyquist rate is twice the highest frequency component of a signal. In this case, the Nyquist rate is 20000 π.

Step-by-step explanation:

The Nyquist rate, also known as the Nyquist frequency, is the minimum sampling rate required to accurately reconstruct a signal without distortion. In this case, we have a signal defined by the equation x(t) = 15π(300t)cos(10000πt). To find the Nyquist rates for this signal, we need to consider the highest frequency component of the signal.

The highest frequency component is given by the angular frequency, which is the coefficient in front of the t term in the cosine function. In this case, the angular frequency is 10000π.

The Nyquist rate is then twice the highest frequency component, which is 2(10000π) = 20000π.