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.
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.
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Transfer function is given need part A,and B do not need matlab.
Transcribed Image Text: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.
Transcribed Image Text:H(s) =
b2s2 - 5,kis+ Kilbo
5². a₁k₁ s + a₂1, K2
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