R. P. Ramachandran and P. Kabal

"Minimax
Design of Factorable Nyquist Filters for Data Transmission", *Signal
Processing*, vol. 18, no. 3, pp. 327-339, Nov. 1989.

The use of Nyquist filters in data transmission systems is important in avoiding intersymbol interference. Moreover, the Nyquist filters should be factorable into lowpass transmitter/receiver filter pairs. Here, the design problem is formulated so as to generate zero-phase FIR lowpass Nyquist filters that can be split into minimum and maximum phase parts. Two factorable minimax design methods are given. These methods use the McClellan-Parks algorithm as a first step to control the stopband behaviour. The time domain constraints, imposed by solving a linear system of equations, determine the passband response. The final filter exhibits equiripple stopband behaviour. The advantages of these methods are that the minimum and maximum phase parts are obtained without direct factorization and that arbitrary frequency weighting can be easily incorporated to allow for a nonequiripple behaviour. Design examples depict both equiripple and nonequiripple magnitude responses. The new design approach is compared with other methods in terms of both magnitude and group delay behaviour. Finally, a practical design that conforms to a CCITT voice band modem specification is shown.

P. Kabal and R. P. Ramachandran

"Joint
Optimization of Linear Predictors in Speech Coders", *IEEE Trans.
Acoustics, Speech, Signal Processing*, vol. 37, no. 5, pp. 642-650, May 1989.

Low bit rate speech coders often employ both formant and pitch filters to remove near-sample and distant-sample redundancies in the speech signal. The coefficients of these predictors are usually determined for one prediction filter and then for the other (a sequential solution). This paper deals with formant and pitch predictors which are jointly optimized. The first configuration considered is a combination prediction error filter (in either a transversal or lattice form) that performs the function of both a formant and a pitch filter. Although a transversal combination filter outperforms the conventional F-P (formant followed by pitch) sequential solution, the combination filter exhibits a high incidence of nonminimum phase filters. For an F-P cascade connection, combined solutions and iterated sequential solutions are found. They yield high prediction gains than the conventional F-P sequential solution. Furthermore, a practical implementation of the iterated sequential solution is developed such that both the formant and pitch filters are minimum phase. This implementation leads to decoded speech of higher perceptual quality than the conventional sequential solution.

R. P. Ramachandran and P. Kabal

"Pitch
Prediction Filters in Speech Coding", *IEEE Trans. Acoustics, Speech,
Signal Processing*, vol. 37, no. 4, pp. 467-478, April 1989.

Prediction error filters which combine short-time prediction (formant prediction) with long-time prediction (pitch prediction) in a cascade connection are examined. A number of different solution methods (autocorrelation, covariance, Burg) and implementations (transversal and lattice) are considered. It is found that the F-P cascade (formant filter before the pitch filter) outperforms the P-F cascade for both transversal- and lattice-structured predictors. The performances of the transversal and lattice forms are similar. The solution method that yields a transversal structure requires a stability test and, if necessary a consequent stabilization. The lattice form allows for a solution which ensures a stable synthesis filter. Simplified solution methods are shown to be applicable for the pitch filter (multitap case) in an F-P cascade. Furthermore, new methods to estimate the appropriate pitch lag for a pitch filter are proposed for both transversal and lattice structures. These methods perform essentially as well as an exhaustive search in an F-P cascade. Finally, the two cascade forms are implemented as part of an APC coder to evaluate their relative subjective performance.

"Parameter
Coding for CELP: Channel Error Considerations", *Proc. IEEE Workshop Speech Coding* (Vancouver,
BC), p. 26, Sept. 1989.

"Digital Speech Coding: New Algorithms and
New Applications", *Canadian Conf. Electrical, Computer
Engineering* (Montreal, QC), Sept. 1989.

R. P. Ramachandran and P. Kabal

"Minimax
Design of Factorable Nyquist Filters", *Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing* (Glasgow, Scotland), pp. 1247-1250, May
1989.

The use of Nyquist filters in data transmission systems is important in avoiding intersymbol interference. Moreover, the Nyquist filters should be factorable into lowpass transmitter/receiver filter pairs. Here, the design problem is formulated so as to generate zero-phase FIR lowpass Nyquist filters that can be split into minimum and maximum phase parts. Two factorable minimax design methods are given. These methods use the McClellan-Parks algorithm as a first step to control the stopband behaviour. The time domain constraints, imposed by solving a linear system of equations, determine the passband response. The final filter exhibits equiripple stopband behaviour. The advantages of these methods are that the minimum and maximum phase parts are obtained without direct factorization and that arbitrary frequency weighting can be easily incorporated to allow for a nonequiripple behaviour. The new design approach is compared with other methods. Finally a practical design that conforms to a CCITT voice band modem specification is shown.

Paper titles.