7–6
Altera Corporation
Stratix Device Handbook, Volume 2
September 2004
Finite Impulse Response (FIR) Filters
FIR Filter Background
Digital communications systems use FIR filters for a variety of functions,
including waveform shaping, anti-aliasing, band selection,
decimation/interpolation, and low pass filtering. The basic structure of a
FIR filter consists of a series of multiplications followed by an addition.
The following equation represents an FIR filter operation:
where:
x(n) represents the sequence of input samples
h(n) represents the filter coefficients
L is the number of filter taps
Figure 7–2. Basic FIR Filter
This example filter in
Figure 7–2 uses the input values at eight different
time instants to produce an output. Hence, it is an 8-tap filter. Each
register provides a unit sample delay. The delayed inputs are multiplied
with their respective filter coefficients and added together to produce the
output. The width of the output bus depends on the number of taps and
the bit width of the input and coefficients.
yn
()
xn
() hn
()
=
yn
()
xn i
–
()hi
()
i0
=
L1
–
∑
=
x(n)
y(n)
h(2)
h(1)
h(3)
h(4)
h(5)
h(6)
h(7)
h(0)