Pipelined VLSI recursive filter architectures using scattered look-ahead and decomposition

A new look-ahead (LA) scheme, distributed look-ahead (DLA), is proposed for pipelined implementation of recursive digital filters. It is established that, in the case of many recursive filters, DLA can provide equivalent and stable implementation with reduced multiplication and latch complexities, and higher area-efficiency. It also produces outputs with reduced delays, when compared with some existing LA schemes. Stability regions for the proposed scheme are also well defined. Next, a time-domain approximation method is proposed for direct design of pipelined recursive filters that can achieve superior match with reduced pipelined filter orders.

A new look-ahead (LA) scheme, referred to as distributed look-ahead (DLA), is proposed for pipelined implementation of recursive digital filters. It is established that in case of many recursive filters, DLA can provide equivalent and stable implementation with reduced pipeline delay and hardware, when compared with existing look-ahead schemes.

A look-ahead approach (referred to as scattered look-ahead) to pipeline recursive loops is introduced in a way that guarantees stability. A decomposition technique is proposed to implement the nonrecursive portion (generated due to the scattered look-ahead process) in a decomposed manner to obtain concurrent stable pipelined realizations of logarithmic implementation complexity with respect to the number of loop pipeline stages (as opposed to linear). The upper bound on the roundoff error in these pipelined filters is shown to improve with an increase in the number of loop pipeline stages. Efficient pipelined realizations are studied of both direct-form and state-space-form recursive digital filters. Based on the scattered look-ahead technique, fully pipelined and fully hardware efficient linear bidirectional systolic arrays for recursive digital filters are presented. The decomposition technique is extended to time-varying recursive systems. >

This paper presents a new Recursive Digital Filter (RDF) architecture for discrete time filters. This novel architecture allows decomposition of any discrete time filter into recursive filter of multiple order systematically. This decomposition results in reduction of the hardware when compared to conventional implementation. This hardware complexity reduction is feasible for both fixed and programmable filter coefficients. As an illustrative example, the hardware reduction is demonstrated for a programmable 100 tap symmetric FIR filter. Here, the complexity is quantified in terms of number of multipliers and adders with specific bit widths needed. Matlab numerical results are provided to compare the performance between the conventional and RDF implementation. The resources utilized in both architectures (conventional as well as RDF) are compared for Xilinx Kintex-7 FPGA device.

This paper presents a general lattice structure for the realization of two-dimensional (2-D) recursive digital filters. We employ two basic lattice sections to realize 2-D recursive digital filters with general coefficient support regions like a nonsymmetric half-plane (NSHP) support region. The matrix representations for the basic lattice sections are proposed and used to derive the transfer functions of the realized 2-D digital lattice filters. We use the Roesser state space model to verify the minimal realization of the proposed 2-D recursive digital lattice filter.

The design of pipelined recursive filter with existing Look-ahead CLA and SLA scheme, A new LA scheme, referred to as DLA, is proposed for pipelined implementation of recursive Digital filters. It is established that in case of many recursive filters, DLA can provide equivalent and stable implementation with reduced pipeline delay and hardware, when compared with existing Look-Ahead schemes, comparison between DLA and SLA scheme.

Abstract. This study compares baseflow estimates using chemical mass balance, local minimum methods, and recursive digital filters in the upper reaches of the Barwon River, southeast Australia. During the early stages of high-discharge events, the chemical mass balance overestimates groundwater inflows, probably due to flushing of saline water from wetlands and marshes, soils, or the unsaturated zone. Overall, however, estimates of baseflow from the local minimum and recursive digital filters are higher than those based on chemical mass balance using Cl calculated from continuous electrical conductivity measurements. Between 2001 and 2011, the baseflow contribution to the upper Barwon River calculated using chemical mass balance is between 12 and 25% of the annual discharge with a net baseflow contribution of 16% of total discharge. Recursive digital filters predict higher baseflow contributions of 19 to 52% of discharge annually with a net baseflow contribution between 2001 and 2011 of 35% of total discharge. These estimates are similar to those from the local minimum method (16 to 45% of annual discharge and 26% of total discharge). These differences most probably reflect how the different techniques characterise baseflow. The local minimum and recursive digital filters probably aggregate much of the water from delayed sources as baseflow. However, as many delayed transient water stores (such as bank return flow, floodplain storage, or interflow) are likely to be geochemically similar to surface runoff, chemical mass balance calculations aggregate them with the surface runoff component. The difference between the estimates is greatest following periods of high discharge in winter, implying that these transient stores of water feed the river for several weeks to months at that time. Cl vs. discharge variations during individual flow events also demonstrate that inflows of high-salinity older water occurs on the rising limbs of hydrographs followed by inflows of low-salinity water from the transient stores as discharge falls. The joint use of complementary techniques allows a better understanding of the different components of water that contribute to river flow, which is important for the management and protection of water resources.

A new design approach for high-order active recursive filters is presented in this paper. The methodology is based upon a multi-cellular approach. Transfer functions of such filters result from a cascade association of unitary transfer functions. Consequently, the synthesis can be more easily performed. We illustrate our approach with the physical implementation of a composite four-cell active bandpass recursive filter, in the X-band with 5 dB gain and -40 dB out-of-band rejection. This filter results from the cascade association of four MMIC first order active recursive tunable filters.

This paper considers designing in the minimax sense complementary low-pass/high-pass approximately linear-phase recursive filters with variable magnitude characteristics. A filter structure based on the parallel connection of a delay and a variable fractional delay all-pass filter is proposed for implementing these filters. The filter optimization is performed in two basic steps. First, an initial filter is generated using a simple design scheme. Second, this filter is used as a start-up solution for further optimization being carried out by an efficient constrained nonlinear optimization algorithm. Examples are included for illustrating the efficiency of the proposed design scheme. In addition, the performance and the complexity of the proposed variable recursive digital filters are compared with those of the other variable recursive digital filters proposed in the literature. This comparison shows that the number of multipliers for the proposed filters is less than 30 percent compared with the other existing structures.

А new method of parallelization of computations with recursive equations, more efficient in terms of equipment costs, the method of nested auto-substitutions, is proposed in this paper. The new method was considered using an example of parallelization of computations in digital recursive filters, which are described by difference equations, where the result depends on both the input and output data. The speed of feeding input data to the input of a digital filter depends on the execution time of all computational operations specified by the difference equation, i.e. the next input sample can be fed and processed only after the processing of the previous sample has been completed. The reason is that the result of processing the next sample directly depends on the results of processing several previous samples. To feed data at a high rate, it is necessary to either use more powerful computing devices or provide parallelization of computations. Until now, the well-known method of sequential auto-substitutions has been used to parallelize computations described by recursive equations. This method allows correct introducing of pipeline registers into the feedback loops of a recursive filter and ensuring the use of high-performance computing nodes built on the pipeline principle. The method of sequential auto-substitutions has a linear function of growth of the number of operations depending on the level of parallelization of computations. A new method, the method of nested auto-substitutions, which can be used to parallelize calculations described by recursive equations, is proposed by authors. The proposed method also allows correct introducing of pipeline registers into feedback loops, but has a logarithmic function of growth of the number of operations depending on the level of parallelization. The new method is more efficient than the well-known method of sequential auto-substitutions. Its efficiency is proven in comparison with the well-known method of sequential auto-substitutions by example of parallelization in recursive filters of the first and second orders using the new method of nested auto-substitutions. Numerical simulation of processing random digital sequences by pipelined filter using the method of nested auto-substitutions confirmed matching with the results of processing the same digital sequences by a non-pipelined second-order prototype filter. During the simulation, all calculations were performed in single-precision floating-point data format according to the IEEE-754 standard.

There are many problems in science and engineering whose solution is applied in the design of Multi-Dimensional (MD) digital filters. Digital filtering finds an important position in the field of digital signal and image processing. Recently there had been a great deal of interest in the design and stability analysis of Two-Dimensional (2-D) recursive digital filters. The design techniques for stable One Dimensional (1-D) digital filters are relatively well developed; but their extension to 2-D had been tried with difficulties. The stability problem of 2D filters had been the subject of intensive research during the recent decades. The trend is towards finding sufficient conditions, because necessary and sufficient conditions are difficult to find or to test. In this study, we make a detailed comparison of the various approaches available for testing the stability of 2-D recursive digital filters. Though researchers had done a lot on the stability testing methods, a comparative study by listing the computational complexities of various methods had not been done so far. This study would help the researchers to choose proper stability testing methods based on the computational complexities.

Due to the monotonically decaying nature of its magnitude response, an all-pole recursive digital filter, with its group delay approximating a prescribed constant value, does not exhibit a sharp transition band. Using transformation as the mathematical means, this correspondence describes a design technique for a recursive digital filter with a maximally flat group delay and a Chebyshev attenuation stopband.

Stability guarantee is the most important issue in designing variable recursive digital filters since unstable variable filters are not useful in signal processing applications. This paper proposes a technique for designing separable-denominator variable two-dimensional (2-D) digital filters having variable magnitude characteristics, and the stability of the designed variable recursive 2-D filters is always guaranteed. The method assumes each coefficient of the variable recursive filter as a polynomial of the spectral parameters that specify different variable magnitude responses. Since the filter coefficients are represented by different polynomials, substituting different values of the spectral parameters into the polynomials obtains different filter coefficients and thus different magnitude responses. To guarantee the stability, first coefficient transformations are performed on the denominator coefficients of the recursive transfer function such that the stability conditions of the recursive 2-D filter are always satisfied for arbitrary values of the new coefficients. Then both the denominator and the numerator coefficients are determined as the polynomials of the spectral parameters. The proposed technique is effective for designing separable-denominator variable 2-D digital filters with guaranteed stability.

We present a new transform which, when applied to the denominator polynomial of the transfer function of an unstable multidimensional recursive digital filter (of a special class) will yield a stable polynomial with good preservation of the magnitude spectrum. In fact, the discrete Hilbert transform (DHT), used to stabilize 2-D and 1-D recursive digital filters, is a special case of the general multidimensional transform we present here. We also address the problem of stability testing of a multidimensional recursive digital filter and show that the new transform may be used to implement a straightforward test for stability of any causal multidimensional recursive digital filter, having no nonessential singularities of the second kind.

This paper considers designing in the minimax sense complementary low-pass/high-pass recursive digital filters with variable magnitude characteristics. A filter structure based on the parallel connection of two variable fractional delay all-pass filters is proposed for implementing these filters. The filter optimization is performed in two basic steps. First, an initial filter is generated using a simple design scheme. Second, this filter is used as a start-up solution for further optimization being carried out by an efficient constrained nonlinear optimization algorithm. Examples are included for illustrating the efficiency of the proposed design scheme. In addition, the performance and the complexity of the proposed variable recursive digital filters are compared with those of the other variable recursive digital filters proposed in the literature. This comparison shows that the number of multipliers for the proposed filters is less than 15 percent compared with other existing structures.