Audio Engineering

Compact Disc 515

frequently than would be permitted by the notional “ cut-off ” frequency of the fi lter
will all have a coded equivalent to zero magnitude.) Each additional stage has the same
attenuation rate as a single-pole RC fi lter (–6 dB/octave), but with a strictly linear phase
characteristic, which leads to zero group delay.

This type of fi lter is known either as a “ transversal fi lter, ” from the way in which the
signal passes through it, or a “ fi nite impulse response ” (FIR) fi lter because of the
deliberate omission from its synthesized impulse response characteristics of later
contributions from the coeffi cient multipliers. (There is no point in adding further terms
to the A 1 ,... , An series when the values of these operators tend to zero.)

Some contemporary fi lters of this kind use 128 sequential “ taps ” to the transmission
chain, giving the equivalent of a –768-dB/octave low-pass fi lter. This demonstrates,
incidentally, the advantage of handling signals in the digital domain in that a 128-stage
analogue fi lter would be very complex and also have an unacceptably high thermal noise
background.

Output

Initial impulse

Time

Time

Filter delay Filter output

Figure 16.13 : Impulse response of low-pass FIR fi lter. Zeros are l/ f (^) s apart; cutoff
frequency  f (^) s /2.