Multiplicative Finite Impulse Response Filter Research Articles

Multi-Objective Sparsity Maximum Mode De-Composition: A New Method for Rotating Machine Fault Diagnosis on High-Speed Train Axle Box

Signal decomposition techniques generally have two limitations. First, for adaptive correlated kurtogram (ACK) and variational mode decomposition (VMD), etc., the definition of the decomposition target has no direct relationship with the features of fault impacts, i.e., the decomposition is not guided by the health indices used to characterize bearing faults, resulting in fault impacts cannot be completely separated from vibration data. Second, it is hard to accurately determine the decomposition stop parameter (the number of final output modes), resulting in frequent over- or under-decomposition. All these are not conducive to bearing fault detection in engineering practice. In this paper, a new decomposition method, multi-objective sparse maximum mode decomposition (MOSMMD), is proposed. Firstly, by analyzing the Fourier spectrum of vibration data, MOSMMD constructs multiple finite impulse response filters covering different frequency bands to obtain initial candidate modes. Then, aiming at maximizing <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L2</i> / <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L1</i> norm of envelope spectrum (ES), the upper and lower cutoff frequencies of each filter are adjusted adaptively through iterative optimization, and the frequency bands covered by each mode are adjusted accordingly. Finally, by using that fault feature harmonics have periodic natures in ES, the redundant modes are eliminated and only the modes with obvious fault features are output. Compared with VMD and ACK, the decomposition target of MO-SMMD is directly related to the fault features, i.e., cyclostationarity of fault impacts, which makes the extraction of fault impacts more accurate. Moreover, the number of final output modes of MOSMMD is determined adaptively and does not need to be set in advance as an input parameter. Also, MOSMMD can decompose fault modes from vibration data without prior fault information, even when processing concurrent fault signals. Simulation and experiments demonstrate the superiority of the proposed MOSMMD.

Reducing the Number of Elements in the Synthesis of a Broadband Linear Array With Multiple Simultaneous Frequency-Invariant Beam Patterns

The problem of reducing the number of elements in a broadband linear array with multiple simultaneous crossover frequency-invariant (FI) patterns is considered. Different from the single FI pattern array case, every element channel in the multiple FI pattern array is divided and followed by multiple finite-impulse-response (FIR) filters, and each of the multiple FIR filters has a set of coefficients. In this situation, a collective filter coefficient vector and its energy bound are introduced for each element, and then the problem of reducing the number of elements is transformed as minimizing the number of active collective filter coefficient vectors. In addition, the radiation characteristics including beam pointing direction, mainlobe FI property, sidelobe level, and space-frequency notching requirement for each of the multiple patterns can be formulated as multiple convex constraints. The whole synthesis method is implemented by performing an iterative second-order cone programming (SOCP). This method can be considered as a significant extension of the original SOCP for synthesizing broadband sparse array with single FI pattern. Numerical synthesis results show that the proposed method by synthesizing multiple discretized crossover FI patterns can save more elements than the original iterative SOCP by using a single continuously scannable FI pattern for covering the same space range. Moreover, even for multiple FI-patterns case with complicated space-frequency notching, the proposed method is still effective in the reduction of the number of elements.

Reconfigurable filter bank structures for low complexity digital channelizer using fractional interpolation and MFIR filters with cosine modulation

A low complexity digital reconfigurable filter bank structure which is suitable for digital channelizers in software defined radio is proposed in this paper. In order to get a sharp transition width with low hardware complexity, multiplicative finite impulse response (MFIR) filter is used as the prototype filter in the proposed structure. A masking stage and a channel generation stage constitute the two stages of the proposed structure. In the masking stage, 5 sub-bands are generated by performing cosine modulation technique on the prototype filter. In the channel generation stage, different channels are generated by doing spectral addition/subtraction operations on the interpolated versions of the MFIR filter. Hence, the basic techniques used in the proposed structure are, cosine modulation and fractional interpolation technique. By adjusting a 3-bit control signal, different regions and channels, generated by the two stages, can be obtained. The proposed structure has a hardware complexity, which is much lesser than that of the state-of-the art techniques used for SDR channelizers. The number of channels generated using the proposed structure is also more. The main advantage of the proposed structure is that the hardware complexity of the proposed structure remains the same even if the number of channels is increased.

Multiplicative finite impulse response filters: implementations and applications using field programmable gate arrays

This paper describes how modern field programmable gate array (FPGA) technology can be used to build practical and efficient multiplicative finite impulse response (MFIR) filters with low-pass, high-pass, band-pass and band-stop characteristics. This paper explains how MFIR structures can be built with or without linear phase characteristics and implemented efficiently on modern FPGA architectures using fixed-point arithmetic without incurring stability problems or limit cycles which commonly occur when using equivalent infinite impulse response structures. These properties have a particular importance for applications such as tunable resonators, narrow band rejectors and linear phase filters which have demanding, narrow transition band requirements. The results presented in this paper indicate that MFIR filters are, for some applications, a viable alternative to existing filter structures when implemented on an FPGA.

Round-Off Noise of Multiplicative FIR Filters Implemented on an FPGA Platform

The paper analyzes the effects of round-off noise on Multiplicative Finite Impulse Response (MFIR) filters used to approximate the behavior of pole filters. General expressions to calculate the signal to round-off noise ratio of a cascade structure of Finite Impulse Response (FIR) filters are obtained and applied on the special case of MFIR filters. The analysis is based on fixed-point implementations, which are most common in digital signal processing algorithms implemented in Field-Programmable Gate-Array (FPGA) technology. Three well known scaling methods, i.e., L2 bound; infinity bound and absolute bound scaling are considered and compared. The paper shows that the ordering of the MFIR stages, in combination with the scaling methods, have an important impact on the round-off noise. An optimal ordering of the stages for a chosen scaling method can improve the round-off noise performance by 20 dB.

2-D generalized MFIR filters

An efficient structure for 2-D linear phase FIR (finite-impulse response) filters is introduced. The structure is the 2-D counterpart of the 1-D MFIR (multiplicative FIR) filters. It is shown that this structure is capable of satisfying tight specifications with a significantly reduced number of coefficients. The performance improves for tighter specifications with centered transition bands. The filter coefficients are obtained by minimizing an l/sub p/ error function. It is shown that the optimization problem is readily broken up into a set of simpler subproblems. For the special case of p=2, these subproblems reduce to simple matrix inversions. Increasing the filter order does not affect the problem complexity since it only requires an increase in the number of matrix inversions needed. Examples illustrating the capabilities of this structure and comparisons with other approaches are given. >

Multiple FIR filters on a finite ring

Efficient design techniques for implementing a bank of recursive FIR (finite-impulse response) filters are introduced. The bank of filters is transformed to an equivalent single recursive FIR filter on a finite ring, using the integer residue ring isomorphism directly derived from the Chinese remainder theorem. This equivalent filter provides an efficient implementation scheme on a general-purpose computer. Design schemes are described for bank sizes ranging from two to five. Proper choices of moduli numbers and the residue arithmetics are presented, along with the efficient Chinese remainder transform algorithms for the chosen moduli. >