O.E. Herrmann

Range-chart-guided iterative data-flow graph scheduling

An alternative method for the scheduling of iterative data-flow graphs is described. The method is based on the scheduling-range chart, which contains the information on the range within which each operation in the graph can be scheduled. The scheduling range is determined by considering the intraiteration and interiteration precedence relations. The goal is to find an optimal position within the scheduling range of each operation in such a way that some quality criteria (number of hardware resources, iteration period, latency, register lifetime) are optimized. A formal proof of the NP-completeness of the problem is given and two polynomial-time heuristics are introduced: fixed-rate (rate-optimal as a special case) scheduling where the number of hardware resources is optimized at the same time that a specific iteration period is guaranteed, and maximum-throughput scheduling with limited resources where the iteration period is optimized for a fixed number of processors. The algorithms are able to find optimal solutions for well-known benchmark examples. >

A polynomial time algorithm for the computation of the iteration-period bound in recursive data flow graphs

Rate-optimal scheduling of iterative data-flow graphs requires the computation of the iteration period bound. According to the formal definition, the total computational delay in each directed loop in the graph has to be calculated in order to determine that bound. As the number of loops cannot be expressed as a polynomial function of the number of modes in the graph, this definition cannot be the basis of an efficient algorithm. A polynomial-time algorithm for the computation of the iteration period bound based on longest path matrices and their multiplications is presented. >

Switchbox routing by stepwise reshaping

An algorithm for switchbox routing called PACKER is presented. In an initial phase, the connectivity of each net is established in a fast way without taking the other nets into account. In general, this gives rise to conflicts (short circuits). In the second stage the conflicts are removed iteratively using connectivity-preserving local transformations. They reshape a net by displacing one of its segments without disconnecting it from the net. The transformations are applied in a systematic way using a scan-line technique. During this process, a subset of the segments at the position of the scan line is densely packed in the (two) layers available for routing. The remaining segments are pushed to the next scan-line position. Scanning in the four available directions (left to right, right to left, top to bottom, and bottom to top) is performed until all conflicts have disappeared or no solution is found within a maximum number of iterations. It turns out that the new approach to routing, as implemented in PACKER, also has practical merits: most of the well-known benchmark examples are solved. >

Second order Volterra inverses for compensation of loudspeaker nonlinearity

High quality sound reproduction by loudspeakers is increasingly problematic if the dimensions of the loudspeaker decrease. To produce enough power, large diaphragm excursions are needed which give rise to significant distortions especially at very low frequencies. Instead of improving the mechanical construction of the transducer we apply a feedforward nonlinear digital inverse circuit. Results of two 2nd order Volterra compensators show a significant reduction of the second order harmonics, leaving higher order distortions unchanged. The structure of the realization influences the performance considerably. Two realization structures are considered, and the error caused by the differentiators in the output of the compensators are compared. Both algorithms are implemented in real-time on a digital signal processor (DSP) for on-line testing with the transducer.

Digital compensation of nonlinear distortion in loudspeakers

Loudspeakers produce nonlinear distortion. The authors present a method to compensate for this distortion in real time by nonlinear digital signal processing implemented on a digital signal processor (i.e., the TMS320C30 DSP). Based on the literature, an electrical equivalent circuit of an electrodynamic loudspeaker is developed, resulting in a linear lumped parameter model. The parameters in this model are matched with the measurements of a selected test loudspeaker. The linear model is extended to include nonlinear effects by developing the parameters as a function of the voice coil excursion of the loudspeaker in a Taylor series expansion. The resulting nonlinear system is described by a Volterra series. On the basis of this description, an inverse circuit is designed for the second-order nonlinear distortion. This circuit was implemented in real time on the DSP, using a high-level design and code generation system. Simulations and experiments are presented.<<ETX>>

Rate-optimal scheduling of recursive DSP algorithms based on the scheduling-range chart

A method for rate-optimal scheduling of recursive DSP algorithms is presented. The approach is based on the determination of the scheduling window of each operation and the construction of a scheduling-range chart. The information in the chart is used during scheduling to optimize some quality criteria (number of hardware resources, latency, register life time) at the same time that a rate-optimal solution is guaranteed. An algorithm based on this approach is introduced. It can schedule cyclic as well as acyclic data-flow graphs. The algorithm is powerful enough to solve optimally some problems for which other proposed methods fail.<<ETX>>

Efficient two-dimensional ARX modeling

In this paper a fast spatial adaptive algorithm is presented for the efficient least squares (LS), autoregressive exogenous (ARX), two-dimensional (2-D) modeling. Filter masks of general boundaries are allowed. Efficient space updating recursions are developed by exploiting the spatial shift invariance property of the 2-D data set.<<ETX>>

PACKER: a switchbox router based on conflict elimination by local transformations

PACKER is an algorithm for switchbox routing, based on a novel approach. In an initial phase, the connectivity of each net is established without taking the other nets into account. In general, this gives rise to conflicts (short circuits). In the second stage, the conflicts are removed iteratively using connectivity-preserving local transformations. They reshape a net by displacing one of its segments without disconnecting it from the net. The transformations are applied in a asystematic way using a scan line technique. The results obtained by PACKER are very positive: it solves all well-known benchmark examples.<<ETX>>

CRACKER: a general area router based on stepwise reshaping

CRACKER is an algorithm able to handle a large class of routing problems. Operating on a grid and using two wiring layers, it can deal with floating and fixed terminals, arbitrarily located in the routing area, and with obstacles in either of the two layers. The routing process consists of two stages. In the first stage, all nets are interconnected quickly, without avoiding conflicts with previously routed nets or obstacles. In the iterative second stage, connectivity-preserving local transformations are applied in a systematic way, such that, eventually, a solution without conflict is reached. There is no rip-up and reroute. The same algorithm is able to solve well-known examples of switchbox routing, routing with irregular boundaries, L-shaped channels, three-sided channels, etc.<<ETX>>

Identification and compensation of the electrodynamic transducer nonlinearities

Based on a simplified nonlinear lumped element model of the electrodynamic loudspeaker in either a closed or a vented cabinet, a new nonlinear controller is derived, simulated and implemented on a DSP. The Volterra series expansion, a well known functional expansion to model nonlinear systems, is used to estimate the nonlinear parameters from distortion measurements. The controller is directly based on the nonlinear differential equation, and is tested for the case of a low frequency electrodynamic loudspeaker in a closed cabinet. Digital implementation is realized on a general purpose TMS320C30 DSP development board, using the automatic code generation from schematic entry of the Alta-Group SPW software.