0195136047.pdf

14.3 INTERFERENCE AND NOISE 657

1

f

− 5 f 0 − 4 f 0 − 3 f 0 − 2 f 0 −f 0 0 f 0 2 f 0 3 f 0 4 f 0 5 f 0

(a)

1 +

f^2

f 02

|Hp(f)| =

1

1

f

− 5 f 0 − 4 f 0 − 3 f 0 − 2 f 0 −f 0 0 f 0 2 f 0 3 f 0 4 f 0 5 f 0

(b)

1 +

f^2

f 02

|Hd(f)| =

Figure 14.3.10(a)Preemphasis

filter characteristic.(b)Deempha-

sis filter characteristic.

z(t)

x + ε

x − ε

x

t

t 1 t 2 t 3

z(t 1 )

z(t 2 ) z(t^3 )

Figure 14.3.11Constant signalx

with noise fluctuations.

G=

x

√

Pout/Nout

(14.3.11)

By takingMdifferent samples ofz(t), the arithmetic average can be seen to be

zav=

1

M

(z 1 +z 2 +...+zM) (14.3.12)

If the samples are spaced in time by at least 1/Bseconds, then the noise-induced errors tend to
cancel out and the rms error ofzavbecomes

εM=ε/

√

M (14.3.13)

This averaging method amounts to reducing the bandwidth toB/M.
When the signal in question is a sinusoid whose amplitude is to be measured, averaging
techniques can also be used by utilizing a narrow bandpass filter, or a special processor known