Digital Signal Processing Systems, Basic Filtering Types, and Digital Filter Realizations - Digital Signal Processing: Fundamentals and Applications - page 200

6.7.1 Pre-Emphasis of Speech
A speech signal may have frequency components that fall off at high frequencies. In some applications
such as speech coding, to avoid overlooking the high frequencies, the high frequency components
are compensated using pre-emphasis filtering. A simple digital filter used for such compensation is
given as

yðnÞ¼xðnÞaxðn 1 Þ (6.41)

where a is the positive parameter to control the degree of pre-emphasis filtering and usually is chosen
to be less than 1. The filter described in Equation (6.41) is essentially a highpass filter. Applying
z-transform on both sides of Equation (6.41) and solving for the transfer function, we have
HðzÞ¼ 1 az 1

(6.42)

The magnitude and phase responses adopting the pre-emphasis parameter a ¼ 0 : 9 and the sampling
rate f s ¼ 8 ; 000 Hz are plotted in Figure 6.30A using MATLAB.

Figure 6.30B compares the original speech waveform and the pre-emphasized speech using the
filter in Equation (6.42) . Again, we apply the fast Fourier transform (FFT) to estimate the spectrum of

10

0

-10

-20

0 500 1000 1500 2000 2500 3000 3500 4000

Frequency (Hertz)

80

60

40

20

0

0 500 1000 1500 2000 2500 3000 3500 4000

Frequency (Hertz)

FIGURE 6.30A

Frequency responses of the pre-emphasis filter.