Circulant and skew-circulant matrices as new normal-form realization of IIR digital filters

Normal-form fixed-point state-space realization of IIR (infinite-impulse response) filters are known to be free from both overflow oscillations and roundoff limit cycles, provided magnitude truncation arithmetic is used together with two's-complement overflow features. Two normal-form realizations are derived that utilize circulant and skew-circulant matrices as their state transition matrices. The advantage of these realizations is that the A-matrix has only N (rather than N2) distinct elements and is amenable to efficient memory-oriented implementation. The problem of scaling the internal signals in these structures is addressed, and it is shown that an approximate solution can be obtained through a numerical optimization method. Several numerical examples are included

A new approach to the realization of low-sensitivity IIR digital filters

A new implementation of an IIR digital filter transfer function is presented that is structurally passive and, hence, has extremely low pass-band sensitivity. The structure is based on a simple parallel interconnection of two all-pass sections, with each section implemented in a structurally lossless manner. The structure shares a number of properties in common with wave lattice digital filters. Computer simulation results verifying the low-sensitivity feature are included, along with results on roundoff noise/dynamic range interaction. A large number of alternatives is available for the implementation of the all-pass sections, giving rise to the well-known wave lattice digital filters as a specific instance of the implementation

Optimal design of linear phase FIR digital filters with very flat passbands and equiripple stopbands

A new technique is presented for the design of digital FIR filters, with a prescribed degree of flatness in the passband, and a prescribed (equiripple) attenuation in the stopband. The design is based entirely on an appropriate use of the well-known Reméz-exchange algorithm for the design of weighted Chebyshev FIR filters. The extreme versatility of this algorithm is combined with certain "maximally flat" FIR filter building blocks, in order to generate a wide family of filters. The design technique directly leads to structures that have low passband sensitivity properties

Roundoff noise minimization in a modified direct-form delta operator IIR structure

Among various direct-form delta operator realized filter structures, the delta transposed direct-form II (δDFIIt) has been shown to produce the lowest roundoff noise gain in finite wordlength implementations. Recent analyses focus on the optimization of the free parameter Δ of the delta operator, with scaling of the structure to prevent arithmetic overflow. This paper proposes a modified δDFIIt second-order section in which the Δs and filter coefficients at different branches are separately scaled to achieve improved roundoff noise gain minimization. Expressions for the filter coefficients are derived, and reduction of roundoff noise gain is verified by numerical examples.published_or_final_versio

INVESTIGATION OF ROUNDOFF NOISE IN IIR DIGITAL FILTERS USING MATLAB

As technology increases, more and more devices are becoming digital. The typical purpose of a digital filter is to detect unwanted signals and noise and remove them by filtering. The infinite impulse response (IIR) filter is also called a recursive filter because of the feedback necessary during implementation. A filter can be expressed as a cascade of second-order sections (SOS). For N sections, there are (N!) ways to pair the poles and zeros. There are also (N!) ways to order the resulting second-order sections, for a total of (N!)2 different filter configurations for implementation. In this thesis, for a 6th order filter with three second-order sections, there are (3!)2 or 36 different ordering and pairings. Jackson\u27s proposed a few rules for the pairing of the poles and zeros and the ordering of the second-order sections. These rules were investigated using MATLAB for Butterworth, Chebyshev, and elliptic filter type. Three cutoff frequencies were used to represent the low, mid, and high cutoff frequencies. The value of the low cutoff frequency is .2π. The value of the mid cutoff frequency is .5π. The value of the high cutoff frequency is .8π. The filters were also implemented for both DF1 and DF2. A broad new \u27rule\u27 was not created but a few detailed \u27rules\u27 were suggested depending on the filter type and direct-form implementation

Finite worldlength effects in fixed-point implementations of linear systems

Thesis (M.Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1998.Includes bibliographical references (p. 173-194).by Vinay Mohta.M.Eng