Fractionally-addressed delay lines

While traditional implementations of variable-length digital delay lines are based on a circular buffer accessed by two pointers, we propose an implementation where a single fractional pointer is used both for read and write operations. On modern general-purpose architectures, the proposed method is nearly as efficient as the popularinterpolated circular buffer, and it behaves well for delay-length modulations commonly found in digital audio effects. The physical interpretation of the new implementation shows that it is suitable for simulating tension or density modulations in wave-propagating media.Comment: 11 pages, 19 figures, to be published in IEEE Transactions on Speech and Audio Processing Corrected ACM-clas

Digital Filters

The new technology advances provide that a great number of system signals can be easily measured with a low cost. The main problem is that usually only a fraction of the signal is useful for different purposes, for example maintenance, DVD-recorders, computers, electric/electronic circuits, econometric, optimization, etc. Digital filters are the most versatile, practical and effective methods for extracting the information necessary from the signal. They can be dynamic, so they can be automatically or manually adjusted to the external and internal conditions. Presented in this book are the most advanced digital filters including different case studies and the most relevant literature

Maximum-likelihood estimation of delta-domain model parameters from noisy output signals

Fast sampling is desirable to describe signal transmission through wide-bandwidth systems. The delta-operator provides an ideal discrete-time modeling description for such fast-sampled systems. However, the estimation of delta-domain model parameters is usually biased by directly applying the delta-transformations to a sampled signal corrupted by additive measurement noise. This problem is solved here by expectation-maximization, where the delta-transformations of the true signal are estimated and then used to obtain the model parameters. The method is demonstrated on a numerical example to improve on the accuracy of using a shift operator approach when the sample rate is fast

FIR Filter Design Using Distributed Maximal Flatness Method

In the paper a novel method for filter design based on the distributed maximal flatness method is presented. The proposed approach is based on the method used to design the most common FIR fractional delay filter – the maximally flat filter. The MF filter demonstrates excellent performance but only in a relatively narrow frequency range around zero frequency but its magnitude response is no greater than one. This ,,passiveness” is the reason why despite of its narrow band of accurate approximation, the maximally flat filter is widely used in applications in which the adjustable delay is required in feedback loop. In the proposed method the maximal flatness conditions forced in standard approach at zero frequency are spread over the desired band of interest. In the result FIR filters are designed with width of the approximation band adjusted according to needs of the designer. Moreover a weighting function can be applied to the error function allowing for designs differing in error characteristics. Apart from the design of fractional delay filters the method is presented on the example of differentiator, raised cosine and square root raised cosine FIR filters. Additionally, the proposed method can be readily adapted for variable fractional delay filter design regardless of the filter type.

Pascal-Interpolation-Based Noninteger Delay Filter and Low-Complexity Realization

This paper proposes a new method for designing the polynomial-interpolation-type noninteger-delay filter with a new structure formulation. Since the design formulation and the new realization structure are based on the discrete Pascal transform (DPT) and Pascal interpolation, we call the resulting filter Pascal noninteger-delay filter. The kth-order Pascal polynomial is used to pass through the given (k+1) data points in achieving the kth-order Pascal filter. The Pascal noninteger-delay filter is a real-time filter that consists of two sections, which can be realized into the front-section and the back-section. The front-section contains multiplication-free digital filters, and the number of multiplications in the back-section just linearly increases as order becomes high. Since the new Pascal filter has low complexity and structure can adjust non-integer delay online, it is more suited for fast delay tuning. Consequently, the polynomial-interpolation-type delay filter can be achieved by using the Pascal approach with high efficiency and low-complexity structure

H^∞-Optimal Fractional Delay Filters

Fractional delay filters are digital filters to delay discrete-time signals by a fraction of the sampling period. Since the delay is fractional, the intersample behavior of the original analog signal becomes crucial. In contrast to the conventional designs based on the Shannon sampling theorem with the band-limiting hypothesis, the present paper proposes a new approach based on the modern sampled-data $H^{infty}$ optimization that aims at restoring the intersample behavior beyond the Nyquist frequency. By using the lifting transform or continuous-time blocking the design problem is equivalently reduced to a discrete-time $H^{infty}$ optimization, which can be effectively solved by numerical computation softwares. Moreover, a closed-form solution is obtained under an assumption on the original analog signals. Design examples are given to illustrate the advantage of the proposed method