Infinite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 395

8.17. Design a fourth-order digital lowpass Chebyshev filter with a cutoff frequency of 1.5 kHz and
a 0.5 dB passband ripple at a sampling frequency of 8,000 Hz.
a. Determine the transfer function and difference equation.
b. Use MATLAB to plot the magnitude and phase frequency responses.
8.18. Design a fourth-order digital bandpass Chebyshev filter with a center frequency of 1.5 kHz,
a bandwidth of 200 Hz, and a 0.5 dB passband ripple at a sampling frequency of 8,000 Hz.
a. Determine the transfer function and difference equation.
b. Use MATLAB to plot the magnitude and phase frequency responses.
8.19. Consider the following Laplace transfer function:

10
s þ 10

HðsÞ¼

a. Determine HðzÞ and the difference equation using the impulse-invariant method if the
sampling rate f s ¼ 10 Hz.
b. Use MATLAB to plot the magnitude frequency response jHðf Þj and the phase frequency
response fðf Þ with respect to HðsÞ for the frequency range from 0 to f s = 2 Hz.
c. Use MATLAB to plot the magnitude frequency response Hðe jU Þ

¼jHðe j 2 pfT Þj and the
phase frequency response fðf Þ with respect to HðzÞ for the frequency range from 0 to
f s = 2 Hz.
8.20. Consider the following Laplace transfer function:

1

HðsÞ¼

2

s þ 3 s þ 2

a. Determine HðzÞ and the difference equation using the impulse-invariant method if the
sampling rate f s ¼ 10 Hz.
b. Use MATLAB to plot the magnitude frequency response jHðf Þj and the phase frequency
response fðf Þ with respect to HðsÞ for the frequency range from 0 to f s = 2 Hz.
c. Use MATLAB to plot the magnitude frequency response Hðe jU Þ

¼jHðe j 2 pfT Þj and the
phase frequency response 4ðf Þ with respect to HðzÞ for the frequency range from 0 to
f s = 2 Hz.
8.21. Consider the following Laplace transfer function:

s

HðsÞ¼

s

2

þ 4 s þ 5

a. Determine HðzÞ and the difference equation using the impulse-invariant method if the
sampling rate f s ¼ 10 Hz.