Eigenfilters: A new approach to least-squares FIR filter design and applications including Nyquist filters

Abstract

Abstract-A new method of designing linear-phase FIR filters is proposed by minimizing a quadratic measure of the error in the passband and stopband. The method is based on the computation of an eigenvector of an appropriate real, symmetric, and positive-definite matrix. The proposed design procedure is general enough to incorporate both time-and frequency-domain constraints. For example, Nyquist filters can be easily designed using this approach. The design time for the new method is comparable to that of Remez exchange techniques. The passband and stopband errors in the frequency domain can be made eqniripple by an iterative process, which involves feeding back the approximation error at each iteration. Several numerical design exahples and comparisons to existing methods are presented, which demonstrate the usefulness of the present approach.

On Parallelepiped-Shaped Passbands for Multidimensional Nonseparable ${\bf M}$th-Band Low-Pass Filters

“…Various methods for the design of 1-D th-band filters have been proposed [4], [6]- [10], [15], [16]. Now consider the multidimensional ( -D) case.…”

“…We use the eigenfilter design method [4], [5] for all the designs. For imposing the th-band constraint on the filter, we use the technique discussed in [4], [5].…”

Eigenfilter Approach to the Design of One-Dimensional and Multidimensional Two-Channel Linear-Phase FIR Perfect Reconstruction Filter Banks

“…This approach can be used for the design of 1-D, as well as nonseparable MD, two-channel filter banks. Although the eigenfilter method and its extensions have been effectively used for the design of 1-D and MD filters [11], [12], [20], [21], [25], the eigenfilter method has not been applied to the problem of filter-bank design. Our method consists of first designing the low-pass analysis filter.…”

“…REVIEW OF THE EIGENFILTER DESIGN METHOD [11], [12] In this section, we briefly review the eigenfilter design method, as it applies to the design of zero-phase FIR filters [11], [12]. We will first review the 1-D case and then review the extensions of the method to the MD case.…”

Noise optimized eigenfilter design of time-domain equalizers for DMT systems

“…Combining (7) and (10), we obtain from (1), The vector opt is referred to as an eigenfilter [9,6] as its elements are filter coefficients derived from an eigenvector of a matrix. We now proceed to show that the FSE is simply a special case of the structure in Figure 1.…”