샘플링 커널 기반의 IFIR 구조를 가진 주파수 재구성이 가능한 선형 위상 필터

Abstract

The Parks-McClellan algorithm is probably the most widely used FIR filter design method. However, a large number of filter coefficients is required to design sharp FIR filters by using the Parks-McClellan method. Additionally, increased filter coefficients result in more demanding calculations, stressing computational resources, and motivating researches to overcome this drawback. There are traditionally two main approaches to reduction of overall computations in FIR filter categories: interpolated FIR (IFIR) and frequency-response masking (FRM) methods. They have attracted much attention due to their significant advantages in computational burden; however, the design procedures for these filters are much more complicated than the traditional approaches since several subfilters and multiple cascade structures are involved in the filter structure. Additionally, further efforts should be added in case of the FRM structure to maintain the linear-phase property. In the IFIR and FRM methods, all subfilters in the design of such filters should be separately and uniquely designed using the filter design algorithm such as the Parks-McClellan method, which are complex and can require long run times every time a new filter specification is given. Therefore, if there is no filter design software (e.g., Filter Design and Analysis Tool of MATLAB program) in the field or electronic devices, users as well as DSP engineers cannot easily deal with changing filter specifications. Moreover, this problem may be a cause of the primary difficulty in frequency reconfigurable implementations. A simple method is presented in this dissertation for transforming conventional computationally efficient FIR filters into filters with the frequency reconfigurable structure, while maintaining phase linearity. This dissertation makes two key contributions. Firstly, closed-form equations (i.e., linear-phase sharp transition FIR lowpass filter design using the sampling kernel) have been formulated to the traditional IFIR structure. It is shown that this scheme reduces the computational cost from that of an FIR filter designed by the Parks-McClellan approach. More specifically, only 15% to 50% of the number of multipliers of the conventional Parks-McClellan approach is required in the proposed structure. Secondly, generalized sampling kernels with the complementary filter concept are derived and utilized to allow a great flexibility in various filter designs and applications. This dissertation subsequently includes the generalization of sampling kernels with the rational scaling factor. Finally, it is demonstrated that the proposed filter design approach is advantageous for use in various applications.