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

Fractional Delayer Utilizing Hermite Interpolation with Caratheodory Representation

Fractional delay is indispensable for many sorts of circuits and signal processing applications. Fractional delay filter (FDF) utilizing Hermite interpolation with an analog differentiator is a straightforward way to delay discrete signals. This method has a low time-domain error, but a complicated sampling module than the Shannon sampling scheme. A simplified scheme, which is based on Shannon sampling and utilizing Hermite interpolation with a digital differentiator, will lead a much higher time-domain error when the signal frequency approaches the Nyquist rate. In this letter, we propose a novel fractional delayer utilizing Hermite interpolation with Caratheodory representation. The samples of differential signal are obtained by Caratheodory representation from the samples of the original signal only. So, only one sampler is needed and the sampling module is simple. Simulation results for four types of signals demonstrate that the proposed method has significantly higher interpolation accuracy than Hermite interpolation with digital differentiator