Infinite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 343

Simulation in the MATLAB environment is based on the following settings. The audio test signal
with frequency components of 100 Hz, 200 Hz, 400 Hz, 1,000 Hz, 2,500 Hz, 6,000 Hz, and 15,000 Hz
is generated from Equation (8.36) :

xðnÞ¼ sin ð 200 pn= 44 ; 100 Þþ sin ð 400 pn= 44 ; 100 þ p= 14 Þ
þ sin ð 800 pn= 44 ; 100 þ p= 7 Þþ sin ð 2 ; 000 pn= 44 ; 100 þ 3 p= 14 Þ
þ sin ð 5 ; 000 pn= 44 ; 100 þ 2 p= 7 Þþ sin ð 12 ; 000 pn= 44 ; 100 þ 5 p= 14 Þ
þ sin ð 30 ; 000 pn= 44 ; 100 þ 3 p= 7 Þ

(8.36)

The gains set for the filter banks are

g 0 ¼ 10 ; g 1 ¼ 10 ; g 2 ¼ 0 ; g 3 ¼ 0 ; g 4 ¼ 0 ; g 5 ¼ 10 ; g 6 ¼ 10
After simulation, we notice that the frequency components at 100 Hz, 200 Hz, 6,000 Hz, and
15,000 Hz will be boosted by 20 $ log 10 10 ¼ 20 dB. The top plot in Figure 8.26 shows the spectrum for
the audio test signal, while the bottom plot depicts the spectrum for the equalized audio test signal. As
shown in the plots, before audio digital equalization, the spectral peaks at all bands are at the same
level; after audio digital equalization, the frequency components at bank 0, bank 1, bank 5, and bank 6
are amplified. Therefore, as we expected, the operation of the digital equalizer boosts the low

Audio spectrum

10 0

10 1 10 2 10 3 10 4 10 5

Equalized audio spectrum

10 0

10 1 10 2 10 3 10 4 10 5

Frequency (Hz)

FIGURE 8.26
Audio spectrum and equalized audio spectrum.