of Microprocessors

DIGITAL FILTERING 501
frequency is low, the result is essentially the step response of the component.
Although few manfacturers care to admit it, hi-fi components act like
bandpass filters and the step response reveals a lot (in fact, everything) about
the "filter's" characteristics.
The same idea applies to the impulse response, but the test signal is a
very narrow pulse rather than a voltage step. In theory the pulse should have
zero width, infinite amplitude, and finite energy content. In practice, an
analog impulse has a width that is small in comparison to the fastest responding
element of.the filter under consideration and a height small enough to
avoid distortion. In a digital system, the impulse is quite simple: just a
single 1.0 sample surrounded by a sea of zeroes. The spectrum of an isolated
!'.O! · --a-b L
::liE 0· ~.. ~ 0lliJlllilllilll
~ TIME FREOUENCY
IMPULSE WAVEFORM
IMPULSE SPECTRUM
~ .0
:::>
~ •• e.
~ ...,...::.'----_.....-....,..:.~..
~ .'
• •
TIME
IMPULSE RESPONSE
WAVEFORM
~ ~
~~
,
~
FREQUENCY
IMPUlSE RESPONSE
SPECTRUM
.
~ .. e.
~ . .e.
:J • e.
11.~---