Altera Corporation 7–39
September 2004 Stratix Device Handbook, Volume 2
Implementing High Performance DSP Functions in Stratix & Stratix GX Devices
Basic IIR Filter Implementation Results
Table 7–15 shows the results of implementing a 4
th
order IIR filter in a
Stratix device.
Basic IIR Filter Design Example
Download the 4
th
Order IIR Filter (iir.zip) design example from the
Design Examples section of the Altera web site at www.altera.com.
Butterworth IIR Filters
Butterworth filters are the most popular version of IIR analog filters.
These filters are also known as “maximally flat” because they have no
passband ripple. Additionally, they have a monotonic response in both
the stopband and the passband. Butterworth filters trade-off roll off
steepness for their no ripple characteristic. The distinguishing
Butterworth filter feature is its poles are arranged in a uniquely
symmetrical manner along a circle in the s-plane. The expression for the
Butterworth filter’s magnitude-squared function is as follows:
where:
ω
c
is the cut-off frequency
N is the filter order
The filter’s cutoff characteristics become sharper as N increases. If a
substitution is made such that jω = s, then the following equation is
derived:
Table 7–15. 4
th
Order IIR Filter Implementation Results
Part EP1S10F780C5
Utilization Lcell: 102/10570(<1%)
DSP Block 9-bit elements: 24/48 (50%)
Memory bits: 0/920448(0%)
Performance 73 MHz
Latency 4 clock cycles
H
c
jω()
2
1
1
jω
jω
c
-------
⎝⎠
⎛⎞
2N
+
----------------------------=
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