Abstract
The conventional polyphase architecture for linear-phase finite impulse response (FIR) filter loses its coefficient symmetry property due to the inefficient arrangement of the filter coefficients among its subfilters. Although, existing polyphase structures can avail the benefits of coefficient symmetry property, at the cost of versatility and complex subfilters arrangement of the conventional polyphase structure. To address these issues, in this paper, we first present the mathematical expressions for inherent characteristics of the conventional polyphase structure. Thereafter, we use these expressions to develop a generalized mathematical framework which exploits coefficient symmetry by retaining the direct use of conventional FIR filter coefficients. Further, the transfer function expressions for the proposed Type-1/transposed Type-1 polyphase structures using coefficient symmetry are derived. The proposed structures can reduce the requirement of multiplier units in polyphase FIR filters by half. We also demonstrate the decimator design using the proposed Type-1 polyphase structure and the interpolator design using the proposed transposed Type-1 polyphase structure. Moreover, the phase and magnitude characteristics of the proposed Type-1/transposed Type-1 polyphase structures are presented. It is revealed via numerical examples that all subfilters of the proposed symmetric polyphase structure possess linear-phase characteristics.
Highlights
The communication technologies, such as Internet of Things (IoT), cognitive radio, and cooperative communication have gradually emerged; reflecting a large diversity of application domains and signal processing requirements
Different from the existing work in the literature [18]–[24], whose characteristics are summarized in Table 1, in this paper, we propose a novel approach for exploiting the coefficient symmetry in the conventional polyphase structure
MATHEMATICAL PRELIMINARIES PERTAINING TO THE CONVENTIONAL POLYPHASE finite impulse response (FIR) FILTER In order to build a robust mathematical framework which can lead to the development of symmetric polyphase FIR filter, we study various characteristics of conventional polyphase FIR filter and express their mathematical expressions in the sequel
Summary
The communication technologies, such as Internet of Things (IoT), cognitive radio, and cooperative communication have gradually emerged; reflecting a large diversity of application domains and signal processing requirements. The conventional polyphase based multirate systems can find their applicability in designing of filter banks. Replicating the conventional polyphase filter in parallel branches with lower complexity using fast FIR algorithm (FFA) [15], and modifying the perfect reconstruction filter banks [16] are well known approaches for designing such systems. Such approaches involve additional arrangement of the subfilters by incorporating extra adders over the conventional polyphase structure or pre-calculation of the filter coefficients. We refer this additional processing as pre/post processing
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