ft 2cos3t sin27t sin5t What is the highest angular freque

f(t) = 2cos(3t) - sin(2.7t) - sin(5t). What is the highest angular frequency present in this signal? What is the highest numerical frequency present in this signal? What is the Nyquist rate for this signal? Did you use the angular or the numerical frequency? If you sample this signal with sampling period T, which values of T may you choose to be in accordance with the Nyquist rate? Choose and fix one such T. After sampling (with the T chosen above) you pass the sampled signal through a low-pass filter. Which threshold M_0 can be used in the low-pass filter?

Solution

Sin (5t) is highest frequency component

A) highest angular frequency is w_o = 5 rad/sec and highest numerical frequency is f_o = 5/(2pi) Hz

B) Nyquist rate is w_s= 2w_o = 2 x 5 = 10 rad/sec. For this case it is better to use angular frequency. If signal is expressed in pi terms then use numerical frequency.

C) The preferred value of fs is greater than 2f_oimplies Ts > equals 1/(2f_o). Example value of T_s is 1/(2x 5/2pi) = pi/5 sec

D) The threshold valve M_o or cutoff frequency for low pass filter is w_c = w_o rad/sec