Method for a highly efficient and scalable architecture for multitap 1-D filter to implement triangular and rectangular windows

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 a_k 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 b_k 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...