Digital Signal Processing Reference
In-Depth Information
Figure 4.1. Examples of median
lter patterns.
4.2 FIR Filters
Scaling, or changing image resolution, is an application which
requires linear filtering. When upsampling, or increasing resolu-
tion, a FIR filter is normally used to perform the interpolation.
When downsampling, the image is often low-pass filtered first to
remove the higher spatial frequencies that may alias with reduced
resolution.
4.3 FIR Filter Construction
Let's begin with how to construct a FIR filter. A FIR filter is
built of multipliers and adders, can be implemented in hardware
or software, and run in a serial fashion, parallel fashion, or some
combination. We will focus on the parallel implementation,
because it's the most straightforward to understand.
A key property of an FIR filter is the number of taps or
multipliers required to compute each output. In a parallel
implementation, the number of taps equals the number of
multipliers. In a serial implementation, one multiplier is used to
perform the multiple operations sequentially for each output.
Assuming single clock-cycle multipliers, a parallel FIR filter can
produce one output each clock-cycle, and a serial FIR filter would
require N clock-cycles to produce each output, where N is the
number of filter taps.
Figure 4.2
shows a small 5-tap parallel filter.
The inputs and outputs of the FIR filter are sampled data. For
simplicity, we will assume that the inputs, outputs and filter
coefficients C
m
are all real numbers. The input data streamwill be
denoted as x
k
, and the output y
k
. The “k” subscript is used to
identify the sequence of data. For example, x
k
þ
1
follows x
k
, and
x
k
1
precedes x
k
. For the purpose of defining a steady state
response, we often assume that the data streams are infinitely
long in time, or that k extends from
N
to
þ
N
.
