Realisation of Digital Filters - Digital Signal Processing: A Practitioner's Approach - page 107

Figure 5.7 Fixed-point IIR filter

1

Floating-point filter

0.8

Fixed-point filter

0.6

0.4

0.2

0

0.04 0.06 0.08 0.1 0.12 0.14 0.16

Normalised frequency

Figure 5.8 Comparison of floating-point and fixed-point filters

5.5 Pipelining Filters
Often the throughput rate is more important than the latency in filter designs.
Pipelining is the art of positioning the hardware blocks such that the throughput rate
is maximised. Output results are available after every clock cycle.

5.5.1 Modelling Hardware Multipliers and Adders
We introduce

^

representing a multiplier. In
reality, all arithmetic operations take a finite amount of time, introducing a delay
into the system. Multiplication of two variables, say b 1 and u k , in hardware can be

þ representing a hardware adder and

^