Infinite Impulse Response All-pass Filters Research Articles

Design of IIR full-band differentiators with improved nearly linear phase

Linear, or almost linear phase in the design of digital differentiators depends both on the method of calculation of the filter coefficients and the adopted structural design. Acknowledging the importance of this design objective, we developed a method to derive infinite impulse response differentiators which tackles it from both perspectives and yields improved characteristics compared to our previous design. We have replaced the differentiator structure comprising an all-pass filter and a delay line with a configuration of two infinite impulse response all-pass filters. Furthermore, we provide a procedure for determining an improved initial solution to the optimization of filter coefficients, as well as a procedure for improving the differentiator's magnitude response. The final solution exhibits considerably lower error at low frequencies and is thus suitable for the common scenario where the relevant spectral content decreases with frequency. The proposed filters of third and fifth order outperform many existing solutions in literature, especially in terms of the phase characteristic and time-domain performance.

Design of nearly linear‐phase double notch digital filters with close notch frequencies

In this study, the authors present a new procedure for the synthesis of the nearly linear-phase infinite impulse response (IIR) filters with two close notch frequencies based on all-pass filter application. The filter is obtained using a parallel connection of the delay line and IIR all-pass filter with a piecewise approximately linear phase. The desired magnitude characteristic is achieved by equiripple approximation of the all-pass filter phase. The magnitude characteristic is equiripple in all passbands. The proposed method is also suitable for the synthesis of complementary filters for extraction of the signal components at prescribed frequencies. The initial solution for the arbitrary order of an all-pass filter is proposed, which attains a sufficient number of phase error extrema. All phase error minima and maxima corresponding to the initial solution have almost identical values, excluding the ones near notch frequencies. As a result, the method exhibits fast and strong convergence. The described method can also be applied for the design of multiple notch filters with two very close notch frequencies.

Design of IIR All-Pass Filters Using a Neural-Based Learning Algorithm

Least-squares design of infinite impulse response all-pass filter can be formulated as an eigenvector solving problem based on the Rayleigh principle. The eigenfilter is designed by solving a single eigenvector corresponding to the smallest eigenvalue of a real, symmetric, and positive-definite matrix. This paper proposes a minor component analysis-based neural learning algorithm for designing eigenfilter. By appropriately mapping the associated all-pass filter specifications to the simple neural model enables the filter coefficients to be derived from the neural weights. The neural weights eventually approach the optimal filter coefficients of the eigenfilter when the neural model achieves convergence. The proposed neural learning algorithm is demonstrated from simulation results to converge rapidly and achieve accurate performance of eigenfilter design.

An Improved All-Pass Filter Design Using Closed-Form Toeplitz-plus-Hankel Matrix

The least-squares design of infinite impulse response all-pass filter can be formulated as to solve a system of linear equations without directly computing a matrix inversion. The set of linear equations associated matrix is further expressed as a Toeplitz-plus-Hankel matrix such that the optimal filter coefficients are efficiently solved by employing a robust Cholesky decomposition or the split Levinson technique. This paper proposes closed-form expressions for efficiently computing Toeplitz-plus-Hankel matrix based on trigonometric identities. The closed-form expressions of the Toeplitz-plus-Hankel matrix can be directly evaluated as the passband edges are specified without sampling the frequency band as that of the previous computing-efficiency algorithm. The proposed new and simpler closed-form expressions are indicated from simulation results to accurately improve the design performance as well as achieve computational efficiency.

Design of Two-Channel Quadrature Mirror Filter Banks Using Minor Component Analysis Algorithm

The design of two-channel quadrature mirror filter banks can be constructed based on real infinite impulse response (IIR) all-pass digital filters without yielding magnitude distortion. The design problem is first formulated as a phase optimization using IIR all-pass filters in the least-squares sense. Then the nonlinear phase optimization is further converted into solving an eigenproblem of an appropriate real, symmetric, and positive-definite matrix. In this paper, the minor component analysis algorithm based on the neural learning rule is exploited to the design of eigenfilter. When the learning algorithm achieves convergence, the weights of the neural system approximate the smallest eigenvector, which are the optimal filter coefficients of the IIR all-pass filters. The simulation results confirm that the proposed neural-based method can achieve accurate performance by incorporating the simple neural model.

Design of a Sample-Rate Converter From CD to DAT Using Fractional Delay Allpass Filter

In sampling rate conversion between two different formats, the desired output sample values are the interpolated sample values at noninteger (or, integer) multiples of the original sampling period. In this brief, we present an efficient structure for sampling rate conversion from 44.1-kHz compact disc to 48-kHz digital audio tape formats. For efficient conversion, we propose a new infinite-impulse response (IIR) fractional delay filter based on Thiran-based IIR allpass filter. It is shown that the proposed method requires less hardware complexity and maintains high quality of signal-to-noise ratio compared with other methods

Design of two-channel linear-phase QMF banks based on real IIR all-pass filters

The design of two-channel linear-phase quadrature mirror filter (QMF) banks constructed by real infinite impulse response (IIR) digital all-pass filters is considered. The design problem is appropriately formulated to result in a simple optimisation problem. Using a variant of Karmarkar's algorithm, the optimisation problem can be efficiently solved through a frequency sampling and iterative approximation method to find the real coefficients for the IIR digital all-pass filters. The resulting two-channel QMF banks possess an approximately linear phase response without magnitude distortion. The effectiveness of the proposed technique is achieved by forming an appropriate Chebyshev approximation of the desired phase response and then finding its solution from a linear subspace in a few iterations. Finally, several simulation examples are presented for illustration and comparison.