Method for a highly efficient and scalable architecture for
multitap 1-D filter to implement triangular and rectangular windows
Disclosed is a method for a highly efficient and scalable
architecture for multitap one-dimensional (1-D) filter to implement triangular
and rectangular windows. Benefits include improved
performance and improved design flexibility.
Background
Digital filters are
used in a variety of digital signal processing (DSP) and image-processing
applications. Of several different kinds of filters, linear finite impulse
response (FIR) filters are quite popular. They have some significant
properties, including ease of design and analysis, linear phase
characteristics, and ease of implementation.
General description
The disclosed method
uses a highly efficient and scalable implementation of one class of multitap
filters commonly called rectangular filters and triangular filters. The reasons
for using these filters are their widespread use in DSP and image processing
applications and ease of implementation. These filters do not require the use
of a multiplier accumulator (MAC). A general purpose CPU with a simple ADD
instruction could be used to implement the function. Another reason for
considering these specific filter algorithms is that the image path supports
1-D and 2‑D filters.
Advantages
Some implementations
of the disclosed structure and method provide one or more of the following
advantages:
• Improved performance
due to improved processing efficiency
• Improved performance
due to reduced bandwidth requirements
• Improved design
flexibility due to improved scalability
Detailed description
The disclosed
method is a highly efficient and scalable computing structure that implements
triangular and rectangular filter that form the basis for implementing an image
path.
Digital filters are
usually based on the relationship between the input sequence x(n) and
the output sequence y(n) (see Figure 1). Equation (1) is the linear
constant coefficient difference equation. Specifically, for FIR filters, all ak
in (1) are zero. Therefore, equation (1) reduces to equation (2) (see Figure
2).
The output of the FIR
filter is essentially the weighted sum of present and previous inputs to the
filter. The nature of coefficients bk determines
the type of filter. The rectangular filter is characterized by equation (3)
(see Figure 3), where k ranges
from 0 to (T-1).
The coefficient or
window function for the 9-tap rectangular filter is illustrated (see Figure 4).
In a similar manner, 9-tap triangular filter is defined as a filter with
coefficients that form triangular window (see Figure 5). The coefficients of
the 9-tap triangular filter are given by 1, 2, 3, 4, 5, 4, 3, 2 and 1. This
example assumes that the
application is image processing and that the input sequence is
essentially pixel values.
In general, the filter comp...
