Elliptical Filter

Figure 17 shows the effective density using the elliptic filter with a characteristic length of 2.9 mm. The optimal length must be determined for each consumable set and process conditions since the planarization length is dependent not only on the polish pad type but also on the polish process conditions, notably the down force. 

The presented approach has been successfully tested on some high-level synthesis benchmarks. Although the fifth order elliptic filter benchmark is not representative for the investigated application domain, it was submitted to the synthesis system, mainly for testing the synthesis fiow. The example could be mapped successfully onto the emulator board, and the scheduling results are comparable to the best reported in literature. 

Sharp cutoff filters should be avoided in biopotential measurements where the bioelectric waveform shape is of interest Filtering can greatly distort waveforms where waveform frequencies are near the filter breakpoints. Phase and amplitude distoitions are more severe with higher-order sharp-cutoff filters. Filters such as the Elliptic and the Tchebyscheff exhibit drastic phase distortion that can seriously distort bioelectric waveforms. Worse still for biopotential measurements, these filters have a tendency to ring or overshoot in an oscillatory way with transient events. The result can be addition of features in the bioelectric waveform that are not really present in the raw signal, time delays of parts of the waveforms, and inversion of phase of the waveform peaks. Figure 17.34 shows that the sharp cutoff of a fifth-order elliptical filter applied to an ECG waveform produces a dramatically distorted waveform shape. 

In comparison, the Butterworth filter requires a higher order than both types of Chebyshev filters to satisfy the same specification. There is another type of filters called elliptic filters (Cauer filters) that have equiripples in the pass band as well as in the stop band. Because of the lengthy expressions, this type of filters is not given here (see the references). The Butterworth filter and the inverse Chebyshev filter have better (closer to linear) phase characteristics in the pass band than Chebyshev and elliptic filters. Elliptic filters require a smaller order than Chebyshev filters to satisfy the same specification. 

Algorithmic level behavioral and structural transformations, adding concurrent processes to an elliptical filter, pipelining theMCS6502. 

A large DSP example from a computer image generation application, a Chel chev preprocessor, a pipelined 16-point FIR filter example, a pipelined fifth-order digital elliptic filter example, and various smaller examples. 

The Intel 8251, the MCS6502, the FRISC microprocessor, a Kalman filter example, a fifth-order digital elliptic filter... 

A differential equation example, a digital filter example, and a fifth-order digital elliptic filter example. 

The Elliptical Filter presented in Chapter 3 and for which partitioning results are presented in Chapter 4 is an interesting candidate for resource constraint information because there are many possible schedules for the data-flow. Table 5-1 shows the results of using various resource options to make schedules for the filter example. 

As the scheduler for the Workbench, it is appropriate for CSTEP to use a fixed hardware approach to scheduling rather than a fixed schedule length because it can use the high level structural information provided by the partitioner to help determine an appropriate number of functional units. Chapter 8 describes the synthesis of the Elliptical Filter. The partitioner suggests a 2 partition design which implies a minimum of 2 adders and 2 multipliers, producing a 19 control step schedule, as listed in Table 5-1. This schedule will be used by EMUCS and is used in Chapter 8 to determine a data path for the elliptical filter. 

Workshop on High-Level Synthesis [BorrielloSS], The VT for the Elliptical Filter is shown in Figure 8-1. 

Table 8-2. Summary of Synthesis Options for Elliptical Filter Designs...

Behavioral transformations were run on 4 of the Elliptical Filter designs to create multiple process designs. Ultimately, the RT designs... 

Vertical Two-Process Filter. Alternately the Elliptical Filter s VT can be split vertically to form another two-process design. In Figure 8-1, the dark gray oval becomes the second process. The design that is the result of this process division is referred to as design C in Table 8-2. 

Some other scheduling results for the Elliptical Filter are listed in Table 5-1. 

Figure 8-4. Data Path for Partitioned Elliptical Filter Design...

Since the Elliptical Filter is a small design, a number of design alternatives could be presented here for comparison, and a number of conclusions can be drawn. 

Overall, the Elliptical Filter shows how the first two tools in the general synthesis path can be used to explore the system level design space. The utility of behavioral transformations in exploring various... 

MOS Technology s MCS6502 is a small microprocessor. Like the Elliptical Filter, this architecture was one of the examples from the ACM / IEEE 1988 Workshop on High-Level Synthesis. This section... 

Great care was also taken to implement a system that is fast enough to allow the synthesis of large designs in a reasonable time HIS is two orders of magnitude faster than the YSC. A M6502 like microprocessor can be synthesized in a few minutes smaller examples like the well-known 5th order elliptical filter [22] run in seconds. 

In [4], we have proposed an Integer Linear Programming(ILP) formulation for the time-constrained scheduling problem. Since we use the As-Soon-As-Possible(ASAP) and As-Late-As-Possible(ALAP) scheduling techniques to reduce the solution space, the ILP formulation is very efficient and able to optimally solve practical problems, such as the fifth order elliptic filter[10], in a few seconds. 

We have tested THEDA using a number of well-known benchmarks. Here, we show the results of the fifth order elliptic filter[10]. It contains 26 additions and 8 multiplications. A multiplication takes 2 cycles while an addition takes 1 cycle to complete. The critical path length is 17 cycles and it can be reduced to 16 cycles by loop folding. TABLE II shows the results obtained by this system. Fig. 5(a) shows the schedule of 17 control steps by Pipeline List Scheduling[7] and Fig. 5(b) shows the allocation result. 

Table 11.13 Comparison of schedule latency for the Elliptic filter example.

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