Low Coefficient Sensitivity Research Articles

Mel Log Spectrum Approximation (MLSA) filter for speech synthesis

AbstractThe spectral envelope of speech can be represented efficiently by the log magnitude spectrum on the nonlinear frequency scale, which is close to mel scale (called mel‐log spectrum). the mel cepstrum defined by its Fourier coefficients is also considered to have a suitable property as the parameter to represent the spectral envelope. So far, no satisfactory filter has been reported for the synthesis approximating the mel‐log spectrum. This paper presents a method of constructing the mel‐log spectrum approximation (MLSA) filter, which has a relatively simple structure and a low coefficient sensitivity, together with a design example of MLSA filter for speech synthesis. the transfer function of MLSA filter is represented by Padé approximation, which approximates the exponential of the transfer function of the filter (so‐called basic filter). Since the transfer function of the basic filter is represented by a polynomial with the transfer function of the first‐order all‐pass filter as the variable, it is necessary in the realization of the filter to delete from the feedback loop the path without a delay. By the construction method of MLSA filter shown in this paper, the path without delay can easily be deleted from the feedback loop in the MLSA filter. the obtained MLSA filter is of relatively simple structure and has low coefficient sensitivity. the quantization characteristics of the coefficient are also satisfactory.

Applications of wave digital filters to branching filters with low coefficient sensitivity

AbstractWave digital filters made to imitate the behavior of doubly terminated lossless filters (resistance terminated reactance circuits) are a class of digital filters with low coefficient sensitivity. A wave digital filter can realize not only an input‐output transfer function, but also an input reflection coefficient of the doubly terminated lossless filter. However, so far, almost no consideration has been given to the realization of the reflection coefficient by wave digital filters. This paper shows that wave digital filters can be applied to branching filters, narrowband eliminate filters and multibranching filters by utilizing two transfer functions of wave digital filters. Some examples show that these filters composed of wave digital filters can be realized with fewer multipliers and have low coefficient sensitivity properties.

Wave digital filters for second and fourth order basic reactance sections

AbstractOne way to realize a low coefficient sensitivity digital filter is to simulate a resistively terminated LC ladder network. This is called a wave digital filter. However, the transfer functions realized with a resistively terminated LC ladder network are limited. A resistively terminated reactance network realizing an arbitrary transfer function may be synthesized by cascading basic reactance sections. In this paper, we use Brune, Types C, E and D sections with 2‐wire lines as the models for the basic reactance section. These basic sections are represented using modal decomposition by equivalent circuits made of ideal transforming networks (including gyrators for nonreciprocal circuits) and uncoupled lossless lines. Then we derive basic wave digital filters of reciprocal and nonreciprocal second‐order sections and reciprocal fourth‐order sections. the digital filters realized from the basic wave digital filters in the present method do not correspond exactly to the original analog circuit as long as they are constructed with multipliers with finite word length; however, they become low coefficient sensitivity digital filters with as good performance as the wave digital ladder filters.

The Normal Lattice-A Cascade Digital Filter Structure

A normal lattice is defined as a cascade of two-input two-output second-order normal form digital filter modules. An analysis of this structure is presented along with an iterative algorithm for constructing the system eigenvectors, a scaling algorithm, and an explicit expression for roundoff noise gain. These expressions and algorithms provide an explicit design procedure for realizing arbitrary rational transfer functions for single-input single-output filters. Comparisons with other digital filter structures show that the normal lattice has very low roundoff noise and low coefficient sensitivity in realizations of narrow-band filters. This structure is also well adapted to the realization of complex filters.

A design of single‐tuned bandpass filters using charge transfer device

AbstractIn accordance with the recent tendency of miniaturizing failure with active elements, the non recursive transversal CTD (Charge Transfer Device) filters and the recursive CTD filters by means of the signal delay effect of CTD's have been analyzed and constructed. Comparing the latter with the former, a faster frequency response can be realized with less order although there exists a stability problem due to the poles produced by the recursive loop of the circuit. The recursive circuit is suitable in realizing a high‐Q single‐tuned bandpass filter. In this paper, a design method for the single‐tuned bandpass filter with CTD having higher stability against Q variation than that of the conventional second‐order CTD filters [6, 7] is presented. Assuming a pole and a zero which can move along the prescribed closed loci on the Z‐plane depending on the input frequency, the low coefficient sensitivity transfer function is obtained and an economical canonic form circuit is realized. A consideration on the proposed concept that poles and zeros can move corresponding to the input frequencies is presented in the Appendix and the experimental confirmation is shown.

Optimal synthesis of second-order state-space structures for digital filters

Sufficient conditions are derived for a second-order statespace digital filter with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L_2</tex> scaling to be optimal with respect to output roundoff noise; and from these, a simple synthesis procedure is developed. Parallel-form designs produced by this method are equivalent to the block-optimal designs of Mullis and Roberts. The corresponding cascadeform designs are not equivalent, but they are shown, by example, to be quite close in performance. It is also shown that the coefficient sensitivities of this structure are closely related to its noise performance. Hence, the optimal design has low-coefficient sensitivity properties, and any other low-sensitivity design is a good candidate for near-optimal noise performance. The uniform-grid structure of Rader and Gold is an interesting and useful case in point.

A direct approximation technique of log magnitude response for digital filters

A new direct approximation technique of log magnitude response for digital filters is presented in this paper. The facts that the log magnitude response of digital filters can be expanded into Fourier series and a fairly accurate cosine type log magnitude response can be realized by the elemental digital filter presented in this paper are used in the present technique. The system functions obtained by this method provide the best mean-square approximation to an arbitrarily prescribed log magnitude response. The resulting digital filters are realized in the cascade form of the elemental digital filters, and they give relatively low coefficient sensitivity. The elemental filter is recursive but its form is very simple. Its coefficients are easily obtained by the cepstrum of the impulse response which is the Fourier transform of the desired log magnitude response. This method is very powerful in the realization of digital filters for speech synthesis filters with complicated log magnitude responses.

Floating-point coefficient sensitivity and roundoff noise of recursive digital filters realized in ladder structures

Coefficient sensitivity and roundoff error with floatingpoint rounding have been investigated for several digital ladder filter structures. It is found that in all the cases studied, the ladder structures first proposed by Fettweis show a much lower coefficient sensitivity. In this paper, a hybrid cascade structure is proposed and synthesized. Its coefficient sensitivity is found to be between a conventional cascade structure and the ladder structures. Roundoff error is also investigated by extensive simulation. The new Fettweis ladder structure is found to exhibit the lowest roundoff error. This result is in agreement with the theoretical study which indicates that digital filters which exhibit reduced attenuation sensitivity tend to have less roundoff error.

Digital formant speech synthesis utilizing wave digital filters

Digital computer processing of speech is of much current interest. This paper examines the synthesis of speech utilizing the wave digital filter which has been shown to have low coefficient sensitivity properties and to generate smaller roundoff error than conventional filters. Also examined is the coefficient quantization in the digital formant speech synthesis model and how implementation with the wave filter may serve as a better alternative. Simulation and generation of speech confirm the feasibility and corresponding advantages of implementation with the wave digital filter compared to conventional filters.