Page 40 - Analog and Digital Filter Design

Introduction 37

TRUNCATED SI N(X)/X

w 1.5 1

TI ME
WI NDUW

TI ME

WINDOWED SlN(X)/X
ENVELOPE

1.5

I-
: 0.5
/
a 0 v
2 4.5
TI ME
Figure 1.16 (a-c)
Windowing a Truncated Time Domain Response

To make a practical filter, the peak in the sin(x)/x envelope cannot occur at time
equals zero, since producing an output signal before the input pulse has occurred
is impossible. Instead, the peak in the envelope is moved to midway along the
delay line. The first nonzero value in the sin(x)/,u envelope is taken from the input
to the delay line, and the last nonzero value is taken from the end of the delay
line.