<title>Roundoff noise of the cascade structure implementation for the filters designed by McClellan transformations</title>

Abstract

ABSTRACT Because of the easiness of design and efficiency of Implementation, the McClellan transform is by far the most popular and successful method to design multi-dimensional finite impulse response filters for Image Processing. The filters can be implemented efficiently by the directed structure, cascade structure and Chebyshev structure with operators required proportional to N not to N**2. The Chebyshev structure has the best roundoff noise performance, but it has the drawback of large storage required and more complicated architecture. Although the output roundoff noise of the cascade structure is larger than that of the chebyshev structure, they are very close. In this paper we find that the output roundoff noise of the cascade structure can be further reduced and the result structure still has the same efficient implementation. We provide two methods to reduce the output roundoff noise: (1) Utilize the full dynamic range of each stage, and (2) Reduce the possible noise source in each stage. The cascade structure has the advantage of low sensitivity and inherent pipelinability. Also it is very suitable to be implemented by nowadays modular image processing hardware. So with the output roundoff noise reduced, the cascade structure will prove itself to be a suitable structure for the fixed-point implementation of the filters designed by McClellan transformations.