Design of Multi-Band Digital Filters and Full-Band Digital Differentiators Without Frequency Sampling and Iterative Optimization

Abstract

Most design problems of digital filters (or differentiators) are formulated with a set of grid point in the frequency region (frequency sampling). These problems are usually difficult to solve, and often require iterative optimization. The objective of this paper is to provide an efficient and simplified design approach to multi-band filters (including low-pass filters or high-pass filters) as well as full-band differentiators. The proposed method does not require frequency sampling and iterative optimization to compute the coefficients of the filters or that of the differentiators. The magnitude and phase specifications are simultaneously approximated, and the errors in the specified frequency bands are controlled by using frequency-weighting factors. In addition, a maximum pole radius, which corresponds to a stability margin, can be specified to robustly ensure the stability of the filters or the differentiators. To evaluate the efficiency of proposed method, we compare the proposed method with several established methods. Simulation results show that, although the propose method does not utilize frequency sampling and iterative optimization, the designed filters and differentiators have sufficient performance.

A System Identification Based Approach for Design of IIR Digital Filters with Robust Stability

“…Based on the difference of impulse responses, digital filters can be categorized into two classes [1]: finite impulse response (FIR) filters [2]- [4] and infinite impulse response (IIR) filters [5]- [16]. Although the stability of FIR filters can be guaranteed, the order of FIR filters is generally higher than that of IIR filters.…”

“…highpass, bandpass and bandstop), a transformation from the lowpass prototype filter to the desired one is needed. Also, many other direct methods (without prototype filters) for designing IIR filters have been proposed [5]- [16]. As we wrote before, the design problem of the IIR filters has a non-linearity caused by the existence of the denominator polynomial and the pole constraints (stability condition).…”

“…In [16], the cost function is finally expressed in the quadratic form by using the cost function proposed by Mullis and Roberts [5]. Accordingly, the method of [16] can obtain a solution (filter coefficients) without any iterative optimization.…”

“…Accordingly, the method of [16] can obtain a solution (filter coefficients) without any iterative optimization. In [16], the desired response is fixed to typical responses such as multi-band response and full-band differentiation. Also, the weighting function is a piecewise positive constant value and prescribed phase characteristic (constant group delay) in the passband.…”

“…First, we present the problem formulation in Section 2. Next, we shortly introduce the existing method [16] in Section 3. The proposed method is presented in Section 4.…”