Linear periodic systems and multirate filter design

Results on multistage multirate digital filter design indicate most of the stages can be designed to control aliasing with only slight regard for the passband which is controlled by a single stage compensator. Because of this, the aliasing controlling stages can be made very simple. This paper considers comb filter structures for decimators and interpolators in multistage structures. Design procedures are developed and examples shown that have a very low multiplication rate, very few filter coefficients, low storage requirements, and a simple structure.

This paper describes the design of multirate filters used for the sample rate reduction of digital signals and their implementation on mixed-signal integrated circuits. Reaching target specifications of power, speed and silicon area as well as realizing multi-mode operation presents challenges. Possible solutions are discussed particularly for those filter stages which operate at the high sample rates and are illustrated in examples.

Sampling rate alteration is a problem that often arises in a modern sampled-data signal processing [1]. Very important parts of these systems are multirate filters. In this paper a method for design of VIS-SC multirate filters with retrieving the reflected pseudopower, is presented. Retrieving of the reflected pseudopower was first proposed for multirate wave digital filters [2,3,4,5]. It was shown that this idea leads to many advantages [2,4,6].

One ideal performance of this design is in the areas of decimation where a decimation factor of 10, 45-order and pass band ripple of 1dB and interpolation of sampled rates where a sinusoidal signal input produced a ripple free output with interpolation factor of 10, 52-order and stopband attenuation of 60dB. Owing to the multiple samples of filter length of 200, the filter performed down sampling preceded with filtering as well as up sampling preceded with filtering, hence multi-rate filter by allowing a low threshold of frequency of to be passed, blocking a high threshold of and vice versa. There was resampled output increased to 150% preceded by filtering. The filter coefficients for low pass and high pass Digital FIR filter, through the least square regression method, parks McClellan Algorithm and window methods were employed for easy optimization. More so, there was creation of 2-4-5 filter channel banks through the 2nd-level convolution of their down sampling and up sampling filtering techniques during the multi-irate filtering to ensure the design of error-free Digital FIR Filter using MATLAB File editor(M-File) and tool boxes for writing the C-programming of the design. In the analysis, the mean and standard deviation of the low pass Digital FIR Filter output during decimation and interpolation are (0.26, 6.13) and (0.004,1.22) respectively.

In this article, a “Backward in Time Observer” has been designed for linear systems having time delays in output measurements and differences in the sampling rate of input and output measurements. With the proposed observer we are able to recover the performance of the system with no time delay and an equal sampling rate of input and output measurements. Different observers have been designed for time delayed systems by the researcher, but multi-rate time delayed systems have not been discussed so far, hence our proposed observer is able to cater for both of these problems in the system. The proposed observer is simulated for the seeker system of the missile for verification and illustration. Seeker system of missile is a linear time-invariant system having time delay in output measurement. Furthermore, the output measurement through IR camera of the seeker system has a lower sampling rate than its input signal from the gyro.

The conventional signal reconstruction problem of multirate systems with channel noises can be cast as a robust multirate deconvolution design problem. We investigate a unified minimax approach for the robust deconvolution design of multirate systems. We discuss two typical multirate systems: the multirate filter bank system and the transmultiplexer system. We consider transmission noises resulting from quantization coding errors or external noises. The deconvolution filters for these systems that we derive are all IIR filters. The keypoint is converting the original robust deconvolution design problem to an equivalent minimax matching problem via polyphase decomposition and noble identities. Then, in spite of the presence of input signals and channel noises, we can solve this minimax matching problem by an optimization technique. The proposed method can be interpreted as designing an optimal multirate deconvolution filter such that the worst-case multirate system reconstruction error is minimized over all possible inputs and noises from the energy perspective. Therefore, our proposed design method is more robust than the conventional design method for multirate systems in the presence of uncertain input signals and channel noises. We present several numerical examples that show the good performance of our design method.

This paper considers robust fault‐detection problems for linear discrete time systems. It is shown that the optimal robust detection filters for several well‐recognized robust fault‐detection problems, such asℋ−/ℋ∞,ℋ2/ℋ∞, andℋ∞/ℋ∞problems, are the same and can be obtained by solving a standard algebraic Riccati equatio n. Optimal filters are also derived for many other optimization criteria and it is shown that some well‐studied and seeming‐sensible optimization criteria for fault‐detection filter design could lead to (optimal) but useless fault‐detection filters.

Multirate control: A new approach

Sample and hold functions have been described for periodic linear system control applications where they are used to assign the eigenvalues of the system monodromy matrix. If the system is controllable in one period it was shown that the complete monodromy matrix can be assigned. In this paper we apply these methods to non periodic continuous time linear systems. When the system is controllable across each sampling interval, the state transition matrix associated with each interval can be completely assigned with full state feedback. Thus the resulting closed loop system resembles a closed loop periodic system whose monodromy matrix is completely specified.

The problem of intermittent fault (IF) detection is studied for a class of linear discrete-time stochastic systems with unknown disturbance under the influence of a class of networked phenomena by using the moving horizon estimation (MHE). Aiming to normalise the transmission of data in network systems, the Round-Robin (RR) protocol is introduced for linear discrete-time stochastic systems, so the system is converted to a linear periodic system. By using the lifting technique and superposition principle, the linear periodic discrete-time system is transformed into a linear discrete time-invariant system. An MHE strategy is developed to cope with unknown disturbance by introducing provisional estimates of external unknown disturbances. By utilizing the moving horizon estimator, a scalar residual decoupled from the unknown disturbance is designed. Finally, the effectiveness of the proposed method is verified by a simulation example.

This article presents the design and implementation of a low power FPGA-based optimal multiband filter with Spline function for denoising ECG signals. The proposed multiband filter design utilizes least mean square algorithm to determine the optimal filter coefficients for multiple frequency bands, while the Spline function is used to interpolate the filter coefficients within each band to achieve a smooth transition between adjacent bands. The experimental work is carried out with ECGID database and it shows that the proposed filter outperforms in terms of benchmark performance matrices SNR, MSE, CC and PRD. The filter is implemented on a low power FPGA platform, which allows for real-time processing of ECG signals with low power consumption. The experimental results are analyzed and compared for different architecture using the MATLAB and XILINX VIVADO tools. The serial architecture of proposed filter design is implemented on Artix 7 (XC7A35T) EDGE Board, utilizing 1932 LUT, 5299 FF, 1 DSP block and 0.158 W on-chip power. The experimental results indicate that the proposed filter design approach is efficient, effective, and suitable for implementation in compact biomedical devices.

PurposeVery large-scale integration (VLSI) digital signal processing became very popular and is predominantly used in several emerging applications. The optimal design of multirate filter with improvement in performance parameters such as less area, high speed and less power is the challenging task in most of the signal processing applications. This study aims to propose several effective multirate filter structures to accomplish sampling rate conversion.Design/methodology/approachThe multirate filter structures considered in this work are polyphase filter and coefficient symmetry-based finite impulse response filter. The symmetry scheme particularly brings down the complexity to significant extent. To bring improvement in speed, delay registers are inserted at appropriate path with the help of pipelining and retiming scheme.FindingsIn this paper, the three tasks have been considered. First, the polyphase coefficient symmetry and modified polyphase (MP) structure is designed. Second, the pipelining is applied to the polyphase structure and the obtained results are compared with the polyphase structure. In third, retiming is applied to the polyphase structure and the performance comparison is carried out. The structures are realized for various orders, and the comparative analysis is carried out with the filter order N = 12, 30, 42, 8, 11 and 24 and the results are stated. The performance of all the accomplished structures is analyzed using Altera Quartus with the family cyclone II, device EP2C70F672C6. The results show that the multirate filter using pipelining and retiming offers better performance when examining with the conventional structures. Retimed and pipelined MP structure achieves a speed enhancement of about 33.81% when examining with the conventional polyphase (CP) structure with retiming and pipelining for N = 24 and M = 5. Likewise, the 2/3 structure of pipelined coefficient symmetry approach offers area reduction of about 54.76% over 2/3 structure of pipelined polyphase approach for N = 30 with little reduction in power. The fine grain pipelined and retimed MP structure with N = 11 and M = 3 avails critical path delay reduction of about 28.15% when examining with the corresponding fine grain pipelined and retimed CP structure.Originality/valueThe proposed distinct structures offer better alternative to conventional structures because of the symmetric coefficients, performance enhancement using pipelining and retiming based rate conversion structures. The suggested structures can be used for achieving different rates in software radios.

Various optimum and sub-optimum filters have been added to the basic cross-correlator in order to enhance its time delay estimation capability in the presence of noise. These pre-detection filters include the Hannan-Thomson, the Eckart, the Smoothed Coherence Transform, some least-squares, and two optimum filters recently derived by the authors. Here, a quantitative comparison of all six filters has been conducted by extensive simulation for various input signal and noise ratio and signal and noise bandwidths. The results define the actual enhancement in time delay detection when using the optimum filters and the amount of performance degradation from the optimum for the other filters. The rank ordering of the filters is carried out. Histograms of the time delay estimates, their mean and variance are presented. Confirmation of analytical predictions is noted.

This paper presents an alternative approach for the design of linear phase digital high pass FIR filter using Particle Swarm Optimization with Constriction Factor and Inertia Weight Approach (PSOCFIWA). FIR filter design is a multi-modal optimization problem. The conventional gradient based optimization techniques are not efficient for digital filter design. Given the filter specifications to be realized, PSO algorithm generates a set of optimal filter coefficients and tries to meet the ideal frequency characteristic. In this paper, for the given problem, the realization of the optimal FIR high pass filters of different orders has been performed. The simulation results have been compared to those obtained by the well accepted evolutionary algorithm such as genetic algorithm (GA). The results justify that the proposed optimal filter design approach using PSOCFIWA outperforms GA, not only in the accuracy of the designed filter but also in the convergence speed and solution quality.

An analytic solution for real optimal filters is known, and the special case of optimal binary phase-only filters can be solved by a fast binning algorithm but no analytic solution is known. We establish a geometric solution for the design of optimal binary amplitude filters (OBAF's) and optimal binary phase-only filters (OBPOF's) for any object. The optimal filter is found in terms of maximizing the field strength at the origin in the correlation plane. We found that it is possible to construct a unique convex polygon by using an ordered set of phasors from the filter object's Fourier transform. This process leads eventually to an exact solution for the filter-design problem. We show that the maximum distance across the polygon divides the phasors into two groups: For the OBAF, it determines the group that is passed or blocked; for the OBPOF, it determines which group is passed with a zero or a pi phase shift. The shape of the convex polygon gives qualitative information on the criticalness and the tightness needed in the design process. It provides good insight into the binning-process algorithm and permits us to bound the error in the binning process. Design examples through computer simulation and applications in fingerprint identification are presented.