A second order all-pass filter (APF) passes all frequency components present in an input signal without affecting their amplitude, however affecting their phase (or equivalently the time delay with respect to the input signal). The APF can be implemented using the system shown in block diagram form because its transfer function H(s) is given by H(s)= s² - As + B s² + As + B A and B are positive scalars Without assigning values to the scalars A and B, with s= jo, show that | H(s = jo) |=1 for all possible values of frequency o. Additionally, derive a formula for the phase of H(s = jo) as a function of frequency without assigning values to the scalars A and B. Obtain the step-response of the APF. That is, assume that the system input x(t) is a unit step u(t) and analytically (use Laplace Transform tables) determine the system output y(t). Use MATLAB to plot the output y(t) as a function of time t. Use an appropriately sized time interval that shows the complete response as it settles into its steady state value.