Digital Signal Processing Reference
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b.
the filter DSP equations for
v
k
ðnÞ
; and
c.
the DSP equations for the squared magnitudes
2
2
jXðkÞj
¼ jy
k
ð
205
Þj
d. Using the data generated in Problem 8.46 (c), write a program using the MATLAB
function filter() and Goertzel algorithm to detect the spectral values of the DTMF tone for
key 5.
8.50. Given an input data sequence
xðnÞ¼
1
:
2
$
sin
ð
2
pð
1
;
000
Þn=
10
;
000
ÞÞ
1
:
5
$
cos
ð
2
pð
4
;
000
Þn=
10
;
000
Þ
assuming a sampling frequency of 10 kHz, implement the designed IIR filter in Problem
8.41 to filter 500 data points of
xðnÞ
with the following specified method, and plot the 500
samples of the input and output data.
a. Direct-form I implementation
b. Direct-form II implementation
8.14.1
MATLAB Projects
8.51. The 60-Hz hum eliminator with harmonics and heart rate detection:
Given the recorded ECG data (ecgbn.dat) that is corrupted by 60-Hz interference with its
harmonics and assuming a sampling rate of 600 Hz, plot the signal's spectrum and determine the
harmonics. With the harmonic frequency information, design a notch filter to ehance the ECG
signal. Then use the designed notch filter to process the given ECG signal and apply the zero-
cross algorithm to determine the heart rate.
8.52. Digital speech and audio equalizer:
Design a seven-band audio equalizer using fourth-order bandpass filters. The center frequencies
are listed below:
Center frequency (Hz)
160
320
640
1,280
2,560
5,120
10,240
Bandwidth (Hz)
80
160
320
640
1,280
2,560
5,120
In this project, use the designed equalizer to process stereo audio (“No9seg.wav”). Plot the
magnitude response for each filter bank. Listen to and evaluate the processed audio with the
following gain settings:
a. each filter bank gain
¼
0 (no equalization)
b. lowpass filtered
c. bandpass filtered
d. highpass filtered
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