Multirate Filter Research Articles

Suppression of Residual Vibration of Mechanical Resonance beyond the Nyquist Frequency

In sampled-data positioning control systems, the vibrations caused by the mechanical resonances around a sampling frequency are not only the difficult to observe but readily excited by the control input in transient-state characteristics. To address this problem, we developed a control method that can suppress the zero-order-hold induced residual vibration in the sampled-data positioning control system. The study is on a shock response spectrum (SRS) analysis that handles the transient-state characteristics of mechanical resonances. The control method uses multi-rate notch filters that modify the acceleration input signals beyond the Nyquist frequency. We designed the notch filter based on the SRS analysis because the frequency response on the Bode diagram was not suitable for analyzing transient characteristics. The results of SRS analyses showed that the multi-rate notch filter was able to decrease the amplitude of residual vibrations caused by the mechanical resonances around the sampling frequency. To demonstrate the validity of the proposed method, simulations were conducted on a sampled-data positioning control system.

Fast parallel algorithms for discrete Gabor expansion and transform based on multirate filtering

The Gabor transform has long been recognized as a very useful tool for the joint time and frequency analysis in signal processing. Its real time applications, however, were limited due to the high computational complexity of the Gabor transform algorithms. In this paper, some novel and fast parallel algorithms for the finite discrete Gabor expansion and transform are presented based on multirate filtering. An analysis filter bank is designed for the finite discrete Gabor transform (DGT) and a synthesis filter bank is designed for the finite discrete Gabor expansion (DGE). Each of the parallel channels in the two filter banks has a unified structure and can apply the FFT and the IFFT to reduce its computational load. The computational complexity of each parallel channel does not change as the oversampling rate increases. In fact, it is very low and depends only on the length of the input discrete signal and the number of the Gabor frequency sampling points. The computational complexity of the proposed parallel algorithms is analyzed and compared with that of the major existing parallel algorithms for the finite DGT and DGE. The results indicate that the proposed parallel algorithms for the finite DGT and DGE based on multirate filtering are very attractive for real time signal processing.

Multistage Implementation of Multirate CIC Filters

In this paper a multistage multirate CIC filter has been compared with a FIR Filter. FIR filters are widely used in implementation of Digital Filters, but with some disadvantages like higher number of computational coefficients requirement and less computational speed. In this work we have shown that CIC filters are better choice than the single stage CIC or FIR Filters for multirate filtering structures and further improvement can be made by cascading different stages of CIC Filters.

Performance evaluation of multirate filters for digital down converters

For achieving maximum signal transfer without any noise in all available communication systems, the frequency of the processor is synchronized with the sampling rate of the signal. The use of multirate filtering allows designers to achieve this. In this paper, the multirate filters with and without compensation have been implemented very effectively using FPGA (field programmable gate arrays). Also, comparison of FIR (finite impulse response) filters and differential delay farrow filters has been done for different sampling frequencies. The proposed filter structures have wide applications in the designing of sample rate converters, analog to digital converter, decimators and interpolators. It can be concluded from the design results that the proposed structures can be used efficiently in the designing of any communication system. Key words: Multirate filters, compensation, DDC (digital down converter), WiMax (worldwide interoperability for microwave access), FPGA (field programmable gate arrays).

Minimizing the Effect of Sampling Jitters in Wireless Sensor Networks

A wireless sensor network (WSN) consists of low-cost and energy-limited sensors to measure a distributed phenomenon. The finite energy constraint limits the synchronization of sensors at every sampling instant which introduces sampling jitters. In this letter, we model sampling jitters using fractional delay transfer functions. The WSN is modeled using a hybrid multirate filter bank where the objective is to design discrete-time, causal and stable synthesis filters to minimize the effect of sampling jitters. Using a norm-invariant discretization, the hybrid and multirate problem is reduced to a model-matching H2 optimization problem involving linear time-invariant and discrete-time systems. A numerical example is also presented to show the effectiveness of the proposed approach.

Timing Mismatch Compensation in Time-Interleaved ADCs Based on Multichannel Lagrange Polynomial Interpolation

In this paper, the timing mismatch compensation problem in the implementation of a time-interleaved analog-to-digital converter (TIADC) is investigated. The investigation leads to a novel multichannel Lagrange polynomial interpolation timing-mismatch compensation algorithm (MLPI-TMCA). A multichannel Lagrange compensation filter (MLCF) in the form of a finite-impulse response (FIR) filter is also developed for real-time implementation. The design of the compensation system is done in three steps. First, the coefficients of the MLCF are computed based on the mismatch parameters of the TIADC. Second, an Nth order FIR filtering process is performed for each sub-ADC. Third, a multiplexer is used to combine the output of each compensation filter in an orderly manner into the final compensated output signal. The computational complexity of this timing mismatch compensation system is of order N. Computer simulation results showed that MLPI-TMCA is computationally efficient and not sensitive to timing mismatch fluctuations. The actual implementation of a four-channel 320-MHz 12-bit TIADC showed that the MLPI-TMCA is able to efficiently compensate the timing mismatch in a real-time manner and produced about 30-dB spurious-free dynamic range (SFDR) enhancement when the input signal frequency is 70 MHz, whereas the multirate filter banks compensation method produced about 19 dB of SFDR enhancement under the same condition. Thus, the MLPI-TMCA and its multichannel filter implementation provides a good solution for TIADC real-time timing mismatch compensation and may be employed in TIADC chip design due to its implementation advantages.

Multirate Asynchronous State and Parameter Estimation for Centrifugal Compressors

AbstractA number of strategies for state and parameter estimation for a centrifugal compressor system are investigated using a nonlinear dynamical model. It is found that high frequency measurements can be combined with lower frequency measurements to achieve high fidelity state estimation for stable equilibria, limit cycles, as well as transients using either a multirate discrete extended Kalman filter or a data fusion based algorithm with one independent estimator per measurement. When there is a change in one of the parameters of the system only a filter designed to adapt to such changes produces estimates with acceptable errors for a locally stable equilibrium.

Editorial: Advanced techniques on multirate signal processing for digital information processing

Multirate signal processing has become a key topic enabling efficient techniques for digital information processing in a variety of applications such as digital transceivers s for wireless as well as satellite communication systems, digital broadcasting, high performance audio and video, multimedia services, and signal compression. In the wireless communications arena, multirate signal processing techniques provide effective means to implement flexible receiver channelisation filtering and sampling rate conversion for software and cognitive radio digital frontends. As far as multimedia signal processing is concerned, recent techniques relying on multirate filter banks have resulted in improved subband coding techniques reflected in the JPEG-2000 multimedia standard, as well as on some modern audio compression formats such as MP3, AAC3 and ATRAC3plus, to cite but a few.

An integrated visual-inertial technique for structural displacement and velocity measurement

Measuring displacement response for civil structures is very important for assessing their performance, safety and integrity. Recently, video-based techniques that utilize low-cost high-resolution digital cameras have been developed for such an application. These techniques however have relatively low sampling frequency and the results are usually contaminated with noises. In this study, an integrated visual-inertial measurement method that combines a monocular videogrammetric displacement measurement technique and a collocated accelerometer is proposed for displacement and velocity measurement of civil engineering structures. The monocular videogrammetric technique extracts three-dimensional translation and rotation of a planar target from an image sequence recorded by one camera. The obtained displacement is then fused with acceleration measured from a collocated accelerometer using a multi-rate Kalman filter with smoothing technique. This data fusion not only can improve the accuracy and the frequency bandwidth of displacement measurement but also provide estimate for velocity. The proposed measurement technique is illustrated by a shake table test and a pedestrian bridge test. Results show that the fusion of displacement and acceleration can mitigate their respective limitations and produce more accurate displacement and velocity responses with a broader frequency bandwidth.

Magnitude modulation for VSAT's low back-off transmission

This paper addresses the problem of controlling the envelope's power peak of single carrier modulated signals, band limited by root-raised cosine (RRC) pulse shaping filters, in order to reduce power amplifier back-off for very small aperture terminals ground stations. Magnitude modulation (MM) is presented as a very efficient solution to the peak-to-average power ratio problem. This paper gives a detailed description of the MM concept and its recent evolutions. It starts by extending the look-up-table (LUT) based approach of the MM concept to M-ary constellations with M ≤ 16. The constellation and RRC symmetries are explored, allowing considerable reduction on LUT computation complexity and storage requirements. An effective multistage polyphase (MPMM) approach for the MM concept is then proposed. As opposed to traditional LUT-MM solutions, MM coefficients are computed in real-time by a low complexity multirate filter system. The back-off from high-power amplifier saturation is almost eliminated (reduction is greater than 95%) with just a 2-stage MPMM system even for very demanding roll-off cases (e.g., α = 0.1). Also, the MPMM is independent of modulation in use, allowing its easy application to constellations with M > 16.

A novel calibration approach of soft sensor based on multirate data fusion technology

In multirate chemical processes, soft sensor is commonly used for fast-rate quality estimations. As the kernel of soft sensor, modeling technique has drawn much attention from researchers. But most of the modeling methods have disadvantages of uncertain estimation errors and limited modeling capability. To these issues, soft sensor calibration is considered as an efficient alternative, which however is often ignored by researchers and the current application level is relatively low. A novel soft sensor calibration method is proposed in this paper. Under multirate sampling conditions, data fusion technology based on Kalman filter is introduced into soft sensor maintenance to integrate the soft sensor model estimations with process measurements. The performance of the algorithm is evaluated through simulations and a laboratory scale experiment. The factors that may influence the performance are also discussed in detail. The results demonstrate that the multirate Kalman filter approach is able to improve the accuracy and reliability of soft estimations, when the essential dynamics is included in the Kalman filtering model and the filter parameters are properly tuned.

Multirate DSP and its technique to reduce the cost of the analog signal conditioning filters

There are many reasons to change the sample rate of a sampled data signal. Here we discuss the two basic operations in a multirate system i.e. decreasing (decimation) and (increasing) the sampling rate of a signal. Also the use of multirate filters at the interfaces of continuous & sampled data which results in a cost reduction of the analog signal conditioning components as well as improvement of signal quality.

Design and Implementation of Low-Power ANSI S1.11 Filter Bank for Digital Hearing Aids

Due to well matching the frequency characteristics of human ears, ANSI S1.11 1/3-octave filter bank is popular in acoustic applications, such as acoustic analyzers and equalizers. It is also desirable in hearing aids because the famous hearing aid prescription formula, NAL-NL1, prescribes its gains at ANSI 1/3-octave frequencies. However, the high computation complexity limits its usage, in which the power consumption is a critical concern. To address this issue, a low-power design and implementation of ANSI S1.11 filter bank for digital hearing aids is present. We first develop the complexity-effective multirate FIR filter bank algorithm. And, a systematic coefficient design flow is elaborated for the proposed filter bank to minimize the order of the FIR filter thereof. In an 18-band digital hearing aid with 24-kHz sampling rate, the proposed algorithm saves about 96% of multiplications and additions, comparing that with a straightforward FIR filter bank. Moreover, various low-power VLSI design techniques are investigated in detail and applied on our design. The proposed complexity-effective ANSI S1.11 FIR filter bank has been implemented in the TSMC 0.13-μ m CMOS technology with an area-efficient architecture. The test chip consumes only 87 μW, which is 30%-79% of that of the others available in the literature. The proposed low-power ANSI 1/3-octave bank makes itself being able to precisely apply the prescribed gains obtained by NAL-NL1 prescription formula for hearing-impaired people.

Generation of Filter Bank-Based Multicarrier Waveform Using Partial Synthesis and Time Domain Interpolation

Recently, multirate filter banks have been recognized as high performance signal processing tools that could significantly enhance the efficiency and flexibility of future wireless communications. Filter bank-based multicarrier (FBMC) modulation allows increasing the spectral efficiency of high data rate transmission, both through the lack of time domain guard periods and the reduced frequency domain guard bands. Further, the inherent frequency selectivity is regarded as a vital characteristic, which enables high quality radio scene analysis, necessary for successful deployment of dynamic spectrum access in the context of cognitive radio technology. When applied to multicarrier communications, the filter banks are operated in the so-called transmultiplexer configuration where typically equal-size synthesis and analysis filter banks are utilized at the transmitter and receiver, respectively. This paper presents a new approach to generate an FBMC signal waveform. We focus on contiguous narrowband subcarrier allocation, which is often encountered in uplink transmission. Instead of using a full-size M-subchannel synthesis filter bank, the proposed scheme relies on a cascade of a P-subchannel synthesis bank (P ≪ M), time domain interpolation, and a user-specific frequency shift. This method allows constructing a transmitter-receiver pair using synthesis and analysis filter banks of different sizes. The presented approach is shown to provide notable computational complexity savings over a wide range of practical user bandwidth allocations, when compared to the conventional implementation consisting of equally sized filter banks. Therefore, this novel scheme provides flexible and low-complexity synthesis of spectrally well-localized FBMC uplink waveforms, which show strong potential for future broadband mobile communications.

Identification of the secondary actuator dynamics at frequencies beyond the Nyquist Rate in Dual-Stage Actuator Hard Disk Drive systems

In Hard Disk Drive (HDD) head positioning control systems, the system output can be observed only at fixed finite time intervals. Identification of the plant dynamics embedded in such an inherently sampled-data system requires special considerations to avoid the aliasing effect caused by the sampling operation. In this paper, non-parametric algorithms to identify the secondary actuator dynamics in a Dual-Stage Actuator HDD system are investigated. Identification methods with continuous-time and discrete-time excitation input are proposed. In the discrete-time method, a multirate digital—analogue converter and multirate filters are employed to reduce the aliasing effect. Numerical simulation and experimental results are presented to show the effectiveness of the proposed methods.

Group Lifting Structures for Multirate Filter Banks I: Uniqueness of Lifting Factorizations

Group lifting structures are introduced to provide an algebraic framework for studying lifting factorizations of two-channel perfect reconstruction finite-impulse-response (FIR) filter banks. The lifting factorizations generated by a group lifting structure are characterized by Abelian groups of lower and upper triangular lifting matrices, an Abelian group of unimodular gain scaling matrices, and a set of base filter banks. Examples of group lifting structures are given for linear phase lifting factorizations of the two nontrivial classes of two-channel linear phase FIR filter banks, the whole- and half-sample symmetric classes, including both the reversible and irreversible cases. This covers the lifting specifications for whole-sample symmetric filter banks in Parts 1 and 2 of the ISO/IEC JPEG 2000 still image coding standard. The theory is used to address the uniqueness of lifting factorizations. With no constraints on the lifting process, it is shown that lifting factorizations are highly nonunique. When certain hypotheses developed in the paper are satisfied, however, lifting factorizations generated by a group lifting structure are shown to be unique. A companion paper applies the uniqueness results proven in this paper to the linear phase group lifting structures for whole- and half-sample symmetric filter banks.

Dead-reckoning sensor system and tracking algorithm for 3-D pipeline mapping

A dead-reckoning sensor system and a tracking algorithm for 3-D pipeline mapping are proposed for a tap water pipeline for which the diameter is small and the inner surface is rough due to pipe scales. The goals of this study are to overcome the performance limitations of small and low-grade sensors by combining various sensors with complementary functions and achieve robustness against a severe environment. A dead-reckoning sensor system consists of a small, low-cost micro electromechanical system inertial measurement unit (MEMS IMU) and an optical navigation sensor (used in laser mice). A tracking algorithm consists of a multi-rate extended Kalman filter (EKF) to fuse redundant and complementary data from the MEMS IMU and the optical navigation sensor and a geometry compensation method to reduce position estimation error using the end point of the pipeline. Two sets of experimental data have been obtained by driving a radio-controlled car equipped with the sensor system in a 3-D pipeline and on asphalt pavement. Our study can be used to estimate the path of a 3-D pipeline or mobile robots.

Guest Editorial: Low-Power Digital Filter Design Techniques and Their Applications

Welcome to this Special Issue on Low-Power Digital Filter Design Techniques and Their Applications. Digital filters are essential elements of many signal processing systems and everyday electronics such as radios, cell phones, and biomedical devices. With the ever-increasing popularity of portable devices in communication, medical, and audio/video systems, the computational efficiency and power consumption of digital filters have become increasingly a matter of concern, as digital filters usually involve a large number of arithmetic operations, especially for the finite impulse response (FIR) filters. While FIR filters do have merits in stability, linear phase property, and low coefficient sensitivity, they consume more power than their infinite impulse response (IIR) equivalents in general. There has been consistent effort to develop low-power techniques for FIR filters in the past half century, such as multirate filtering, subfilter approaches, and multiplierless filtering. In multirate filtering, arithmetic units are shifted to the lower frequency end, resulting in reduced power at low operation frequencies. In subfilter approaches, filters are connected in series and/or parallel to form a network, where the frequency responses of different frequency intervals are taken care of by different filters or filter pairs. The overall number of non-trivial coefficients can be significantly reduced by cleverly arranging the subfilters. A very successful subfilter structure is the frequency-response masking (FRM) structure, which was first proposed in 1986 by Y.C. Lim. In 1979 Lim pioneered multiplierless filter-

Efficient Image Enhancement Algorithm Using Multi-Rate Image Processing

This paper describes an efficient image enhancement method based on the Multi-Scale Retinex (MSR) approach for pre-processing of video applications. The processing amount is drastically reduced to 4 orders less than that of the original MSR, and 1 order less than the latest fast MSR method. For the efficient processing, our proposed method employs multi-stage and multi-rate filter processing which is constructed by a x-y separable and polyphase structure. In addition, the MSR association is effectively implemented during the above multi-stage processing. The method also modifies a weighting function for enhancement to improve color rendition of bright areas in an image. A variety of evaluation results show that the performance of our simplified method is similar to those of the original MSR, in terms of visual perception, contrast enhancement effects, and hue changes. Moreover, experimental results show that pre-processing of the proposed method contributes to clear foreground object separation.

On Bounds of Shift Variance in Two-Channel Multirate Filter Banks

Critically sampled multirate FIR filter banks exhibit periodically shift variant behavior caused by nonideal antialiasing filtering in the decimation stage. We assess their shift variance quantitatively by analysing changes in the output signal when the filter bank operator and shift operator are interchanged. We express these changes by a so-called commutator. We then derive a sharp upper bound for shift variance via the operator norm of the commutator, which is independent of the input signal. Its core is an eigensystem analysis carried out within a frequency domain formulation of the commutator, leading to a matrix norm which depends on frequency. This bound can be regarded as a worst case instance holding for all input signals. For two channel FIR filter banks with perfect reconstruction (PR), we show that the bound is predominantly determined by the structure of the filter bank rather than by the type of filters used. Moreover, the framework allows to identify the signals for which the upper bound is almost reached as so-called near maximizers of the frequency-dependent matrix norm. For unitary PR filter banks, these near maximizers are shown to be narrow-band signals. To complement this worst-case bound, we derive an additional bound on shift variance for input signals with given amplitude spectra, where we use wide-band model spectra instead of narrow-band signals. Like the operator norm, this additional bound is based on the above frequency-dependent matrix norm. We provide results for various critically sampled two-channel filter banks, such as quadrature mirror filters, PR conjugated quadrature filters, wavelets, and biorthogonal filters banks.