EP1S80B956C7N Altera, EP1S80B956C7N Datasheet - Page 618

• Manufacturer Part Number: EP1S80B956C7N
• Description: IC STRATIX FPGA 80K LE 956-BGA
• Manufacturer: Altera
• Series: Stratix®r

Specifications of EP1S80B956C7N

• Number Of Logic Elements/cells: 79040
• Number Of Labs/clbs: 7904
• Total Ram Bits: 7427520
• Number Of I /o: 683
• Voltage - Supply: 1.425 V ~ 1.575 V
• Mounting Type: Surface Mount
• Operating Temperature: 0°C ~ 85°C
• Package / Case: 956-BGA
• Lead Free Status / RoHS Status: Lead free / RoHS Compliant
• Number Of Gates: -

Infinite Impulse Response (IIR) Filters
7–40
Stratix Device Handbook, Volume 2
with poles at:
There are 2N poles on the circle with a radius of
poles are evenly spaced at /N intervals along the circle. The poles chosen
for the implementation of the filter lie in the left half of the s-plane,
because these generate a stable, causal filter.
Each of the impulse invariance, the bilinear, and matched z transforms
can transform the Laplace transform of the Butterworth filter into the z-
transform.
■
■
■
Butterworth Filter Implementation
For digital designs, consideration must be made to optimize the IIR
biquad structure so that it maps optimally into logic. Because speed is
often a critical requirement, the goal is to reduce the number of
operations per biquad. It is possible to reduce the number of multipliers
needed in each biquad to just two.
Impulse invariance transforms take the inverse of the Laplace
transform to obtain the impulse response, then perform a
z-transform on the sampled impulse response. The impulse
invariance method can cause some aliasing.
The bilinear transform maps the entire j -axis in the s-plane to one
revolution of the unit circle in the z-plane. This is the most popular
method because it inherently eliminates aliasing.
The matched z-transform maps the poles and the zeros of the filter
directly from the s-plane to the z-plane. Usually, these transforms are
transparent to the user because several tools, such as MATLAB, exist
for determining the coefficients of the filter. The z-transform
generates the coefficients much like in the basic IIR filter discussed
earlier.
H
s
k
c
=
=
s H
1 –
c
c
e
s –
------- 2k
2N
------ -
2N
j
1
j
=
c
--------------------------- -
1
+
N 1
+
–
------ -
j
1
s
c
2N
for k=0,1,…,2N-1
c
in the s-plane. These
Altera Corporation
September 2004