Signal Sampling and Quantization - Digital Signal Processing: Fundamentals and Applications - page 51

2.10. From Problem 2.9, determine the percentage of aliasing level at the frequency of 500 Hz,

assuming that the sampling rate is 4,000 Hz.

2.11. Given a Butterworth type second-order anti-aliasing lowpass filter ( Figure 2.36 ), determine
the values of circuit elements if we want the filter to have a cutoff frequency of 800 Hz.

2.12. From Problem 2.11, determine the percentage of aliasing level at the frequency of 400 Hz,

assuming that the sampling rate is 4,000 Hz.

2.13. Given a DSP system in which a sampling rate of 8,000 Hz is used and the anti-aliasing
filter is a second-order Butterworth lowpass filter with a cutoff frequency of 3.2 kHz,
determine
a. the percentage of aliasing level at the cutoff frequency;
b. the percentage of aliasing level at the frequency of 1,000 Hz.
2.14. Given a DSP system in which a sampling rate of 8,000 Hz is used and the anti-aliasing filter
is a Butterworth lowpass filter with a cutoff frequency 3.2 kHz, determine the order of the
Butterworth lowpass filter required to make the percentage of aliasing level at the cutoff
frequency less than 10%.

2.15. Given a DSP system in which a sampling rate of 8,000 Hz is used and the anti-aliasing filter
is a second-order Butterworth lowpass filter with a cutoff frequency of 3.1 kHz, determine
a.

the percentage of aliasing level at the cutoff frequency;

b. the percentage of aliasing level at a frequency of 900 Hz.

2.16. Given a DSP system in which a sampling rate of 8,000 Hz is used and the anti-aliasing filter
is a Butterworth lowpass filter with a cutoff frequency 3.1 kHz, determine the order of the
Butterworth lowpass filter required to make the percentage of aliasing level at the cutoff
frequency less than 10%.

C 2

V in

R 1 R 2

V o

+

−

C 2

Choose

14142
(2

.

RR C f c ) ==

C 1

1 2

π

2

1

C =

1

2

RRC (2 π f c )

122

FIGURE 2.36

Filter circuit in Problem 2.11.