Alfonso Fernandez-Vazquez

A new method for the design of IIR filters with flat magnitude response

This paper presents a new direct design of infinite-impulse response (IIR) filters with a flat magnitude response in both passband and stopband (Butterworth filters). The design specifications are passband and stopband frequencies and passband droop and stopband attenuation. The approach is based on an allpass filter with flatness at frequency points omega=0 and omega=pi. Depending on the parity of the IIR filter order, the allpass filter is either real or complex. However, in both cases, the resulting IIR filter is real

Design of complex allpass filters

The paper presents the design of complex allpass filters that satisfy a desired degree of flatness and a desired phase at any specified frequency point. The set of linear equations are derived based on the specifications of the flatness and the values of the phase at the given frequency points. The filter coefficients are obtained by solving this set of equations.

A New Method for Designing Flat Shelving and Peaking Filters Based on Allpass Filters

Two most commonly IIR filters used in audio equalization are shelving filters and peaking filters. Traditional design of shelving and peaking filters is based on the design of analog filters, mainly Butterworth filters, and bilinear transformation. In this way, it is well known the design of first order shelving filters and second order peaking filters. Additionally, the resulting filter can be efficiently implemented using allpass filter structures with a low sensitivity to the filter quantization and a low noise level. In this paper, we present a direct design of high order shelving and peaking filters with flat magnitude response in both passband and stop-band. The design is reduced to the design of one digital allpass filter with real coefficients. Using this allpass filter, we obtain two stable and real allpass filters, which are used to implement the resulting shelving and peaking filters. Additionally, closed form equations for the pole/zero computations are given. In contrast with others proposed methods, the design parameters for the shelving filter are the gains KBdB and KcdB at omega=0 and omega=pi, respectively, the passband droop Ap, stopband attenuation As, passband frequency omegap, and stopband frequency omega s, while for the peaking filter we have the gains KBdB and KcdB, the passband and stopband attenuation Ap and As, passband width Wp, stopband width Ws, and the central frequency omega0. The proposed method is illustrated by means of examples. Finally, the appendix shows the MATLAB function ShelvingEq.m, which implements the proposed method for the design of shelving filters

Design of wavelet filters based on digital complex allpass filters

A method for designing IIR complex wavelet filters based on complex allpass filters, that are maximally flat at /spl omega/=0 is presented. This allpass filter is obtained from a complex all-pole filter with a desired flatness at /spl omega/=0. The parameters of the complex allpass filter design are the order of the filter, N, the degree of flatness, K, and the phase, /spl phi//sub 0/, at /spl omega/=0. The real and imaginary parts of the filter coefficients are computed from the proposed iterative equations.

Multiplierless two-stage comb structure with an improved magnitude characteristic

This paper presents a simple multiplierless two-stage comb decimation filter. The filter exhibits an improved magnitude characteristic in both pass band and comb folding bands. The attenuation in folding bands is increased by inserting additional zeros into comb folding bands, which are provided by two additional combs at the second stage. The comb pass band droop is decreased by cascading a simple compensator at low rate. The corresponding structure is simple and can be implemented either in nonrecursive or recursive form as CIC (Cascaded-Integrator-Comb) filter. The comparisons with some existing comb-based decimation filters demonstrate benefits of the proposed method.

Passband-droop compensation of modified non-recursive comb filter

This paper presents the passband-droop compensation of a modified non-recursive comb filter where the decimation factor is a power of two. The modified non-recursive comb filter is introduced to improve the alias reduction in the first folding band while keeping a low power characteristic of a non-recursive comb structure. The compensation filter is a multiplierless filter which works at low rate. The parameter of the filter depends on the cascade of filters in the last stage of the modified comb filter and does not depend on the decimation factor. In such way it is not necessary to redesign the compensation filter for new parameters.

Design of Real and Complex Linear-Phase IIR Modified QMF Banks

A design of linear-phase IIR (infinite impulse response) modified QMF banks including both real and complex valued coefficients is proposed. This design is based on parallel structure of two complex allpass filters. We first introduce a complex analog allpass filter, designed using elliptic functions and the PR (perfect reconstruction) conditions. We use bilinear transformation to obtain the digital counterpart of this analog allpass filter. Depending on the parity of the order N of the complex allpass filter, the resulting IIR filters in the filter bank can be either real or complex. If N is even, the IIR filters are real, otherwise they are complex. Using complex IIR analysis filters, the corresponding magnitude responses have an extra zero around omega = 3pi/2. The method is illustrated by means of examples

The design of M-channel linear phase wavelet-like filter banks

This paper investigates M-channel linear-phase (LP) wavelet-like filter banks. The term ldquowavelet-likerdquo is justified because the filter bank is of near-perfect-reconstruction (NPR). We firstly derive some conditions for designing M-channel LP NPR filter banks and then propose a design method of wavelet-like filter banks. The proposed wavelet-like filter bank is obtained by imposing regularity constraints on the LP NPR filter bank. By using some simple algebraic transformations, we convert the original filter into the wavelet-like filter without nonlinear optimization. With this method, we not only preserve the desired LP property, but also obtain good NPR property as the original NPR filter bank, such as high stopband attenuation. Finally, examples show that LP wavelet-like filter banks with even and odd numbers of channels are capable of achieving different degrees of regularity.

Direct Design of Infinite Impulse Response Filters Based on Allpole Filters

This chapter presents a new framework to design different types of IIR filters based on the general technique for maximally flat allpole filter design. The resulting allpole filters have some desired characteristics, i.e., desired degree of flatness and group delay, and the desired phase response at any prescribed set of frequency points. Those characteristics are important to define the corresponding IIR filters. The design includes both real and complex cases. In that way we develop a direct design method for linear-phase Butterworth-like filters, using the same specification as in traditional analog-based IIR filter design. The design includes the design of lowpass filters as well as highpass filters. The designed filters can be either real or complex. The design of liner-phase two-band filter banks is also discussed. Additionally, we discussed the designs of some special filters such as Butterworth-like filters with improved group delay, complex wavelet filters, and fractional Hilbert transformers. Finally, we addressed a new design of IIR filters based on three allpass filters. As a result we propose a new design of lowpass filters with a desired characteristic based on the complex allpole filters. Closed form equations for the computation of the filter coefficients are provided. All design techniques are illustrated with examples.

On the design of high order digital audio equalizers

This paper presents a new approach for designing high order digital audio equalizer filters. The new design is based on odd order analog allpass filters and bilinear transformation. The analog allpass filters are designed using Butterworth, Chebyshev I, Chebyshev II and elliptic polynomials. The new design results in an efficient structure, i.e., a parallel connection of two stable allpass filters.