Audio Engineering

474 Chapter 15

Delay

z^1

Delay

z^2









X(n) Y(n)

a 1 b 1

a 2 b 2

a 3 b 3

Gain dB

g dB

0 dB

Q

fQ f

s

Frequency

(c)

Figure 15.17(c) : To achieve the fl exibility of signal control, which analogue equalizers

exhibit in conventional mixing desks, an IIR fi lter can be used. Shown here it requires two

single-sample value delay elements and six multiplying operations each time it is presented

with an input sample value. We have symbolized the delay elements by using the z ^1

notation, which is used when digital fi lter structures are formally analyzed. The output

sequence can be expressed as bY11 21213232nnn na X a Xb Y a Xn nb Y.

The use ofz^1 notation allows us to express this difference or recurrence equation as

bYz11 2n ^0 aX zn^0 aX znn n n^1 bYz 2 1 aX z 3 2 bYz 3 2. The transfer function of

the structure is the ratio of the output over the input, just as it is in the case of an analogue

system. In this case the input and output happen to be sequences of numbers, and the

transfer function is indicated by the notation H(z): 

(Continued)