Fir Sc Filters90-03-26

In this paper, we review some basic definitions and properties of FIR filters. We also discusses different types of realizations of digital FIR filters and their uses in some typical applications. We then present some basic building blocks for SC filters. Of particular interest are static and dynamic memory SC circuits, based on SC integrators. These building blocks are the basis for many types of FIR SC filters: direct form, linear-phase direct form, transposed direct form, linear-phase direct form, complementary and half-band FIR filters. We propose several realization of FIR SC filters of which some possibly are new. However, these realizations only demonstrate the principle; they can and should be further improved by using strayinsensitive and offset compensated SC circuits. INTRODUCTION Digital filters can be categorized into two broad classes known as FIR (finite-impulse response) or IIR (infinite-impulse response) filters. The transfer function of an FIR filter of order N-1 is: H(z) = ∑ i=0 N-1 ci zi (1) The poles in the transfer function can only be placed at the origin of the z-plane for non-recursive algorithms. In recursive algorithms, some of the poles may be outside the origin, but these poles are always canceled by zeros. The zeros can be placed anywhere in the z-plane, but they are usually located on the unit circle. Of main interest is FIR filters with linear-phase for which the coefficients exhibits symmetry or antisymmetry [1, 3, 4]. However, in some cases, minimum-phase FIR filters are also used. When working with linear-phase FIR filters it is convenient to define the real function HR(ejωT). H(ejωT) = e-jωτg HR(ejωT) (2) where τg(ejωT) is the group delay of the filter. HR(ejωT) is the frequency response of a non-causal linear-phase filter. HR is often referred to as the zero-phase response. If the impulse response is symmetric, HR can be written: