Altera Corporation 7–41
September 2004 Stratix Device Handbook, Volume 2
Implementing High Performance DSP Functions in Stratix & Stratix GX Devices
Through the use of integer feedforward multiplies, which can be
implemented by combining addition, shifting, and complimenting
operations, a Butterworth filter’s transfer function biquad can be
optimized for logic synthesis. The most efficient transformation is that of
an all pole filter. This is because there is a unique relationship between the
feedforward integer coefficients of the filter represented as:
As can be seen by this equation, the z
-1
coefficient in the numerator
(representing the feedforward path) is twice the other two operands (z
-2
and 1). This is always the case in the transformation from the frequency
to the digital domain. This represents the normalized response, which is
faster and smaller to implement in hardware than real multipliers. It
introduces a scaling factor as well, but this can be corrected at the end of
the cascade chain through a single multiply.
Figure 7–24 shows how a Butterworth filter biquad is implemented in a
Stratix or Stratix GX device.
Hz()
12z
1–
z
2–
++
1b
1
z
1–
b
2
z
2–
++
-------------------------------------------=
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