question 4. For each of the f0 frequencies in Problem 3(c),construct a sinusoidal signal that is turned on at t = 0 andsampled at 100,000/ 2? Hz over the interval ?0.5 ? t ? 0.5 . Again,using Matlab’s convolution command, determine the amplitude andphase (relative to the input) of the response of the filter.Ignoring edges of output that are subject to numerical artifacts.Compare and contrast your answers to those obtained in Problem3(c).
previous question #3
3. Suppose the transfer function of a low-pass filter withfrequency specified in cyclic frequency f is given by H ( f ) =100/ (100 +i2? f ):
a. Manually find and sketch the amplitude and phase spectra (onregular, non-log scale) of the transfer function.
b. If the input to the filter is x(t) = Acos (2? f0t), derivethe general expression of the output. (Hint: use Fourierconvolution theorem.)
c. Find the specific expressions for the outputs for f0 = 10/ 2?, 100/ 2? , 1,000/ 2? , and 10,000/ 2? Hz. (You may use acalculator or Matlab for the computation.)
