Implementation of circular lattice model for cyclostationary process

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Implementation of circular lattice model for cyclostationary process

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to implement the circular lattice structure which comes under the area of statistical signal processing. The circular lattice structure can be used with wavelets, multi-rate signal processing systems. FPGAs perform the computation of different coefficients of the circular lattice model. Determination of coefficients for circular lattice structure can be done only from the second order statistics of the cyclostationary process. By using these coefficients, circular lattice structure can be realized.

Random process is the time evolution of a statistical phenomenon based upon probabilistic laws. The statistical phenomenon means before conducting an experiment, it is not possible to define exactly the way it evolves in time.

Keywords- Statistical Signal Processing, Circular Lattice Model, Cyclostationary Process, FPGA, Random Processes.

Abstract
Introduction
1. The partial characterization of first two moments
Stochastic model
Autoregressive model
Cyclostationary processes
The circular lattice algorithm
Implementation platforms
Design flow
Conclusion
References

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[...] The algorithm/ model that can represent the cyclostationary process is circular lattice model which is mentioned under section V. The circular lattice model can be communication channel data etc A stochastic process is not just a single function of time; rather theoretically there are infinite numbers of realizations of the process. A single particular realization of a discrete time random process is known as „time series‟. The random process is strictly stationary, if its statistical properties are invariant to time shift. [...]

[...] CONCLUSION Thus we can conclude from the above framework that, the FPGAs can be used to implement the circular lattice structure which is part of statistical signal processing. The circular lattice structure can be used with wavelets, multirate signal VIII. DESIGN FLOW processing systems. FPGAs perform the computation of different parameters of the circular lattice model. DESIGN ENTRY SIMULATION SYNTHESIS IMPLEMENTATION DEVICE PROGRAMMING REFERENCES H. Sakai, “Circular lattice filtering using pagano‟s Method”, IEEE Transactions on Acoustics, Speech and Signal processing, vol. [...]

[...] Some FPGAs have specialized sub circuits (IP Blocks) that are optimized for specific functions and can also be reconfigured in infinite number of times. FPGAs provide affordable solutions as customized, Very large system integrated chips with the ability to implement logic circuit and to provide instant manufacturing turnaround with very low cost prototypes. SPARTAN-II based VLSI Trainer Unit (MXS2FK-MB) provides easy to use development platform, useful to physically verify DSP algorithms or simple digital designs around SPARTAN -II FPGA SPARTAN-II FPGA: 200 k logic cell SPARTAN -II FPGA in PQ208 Plastic Quad Flat Package. [...]

[...] For AR cyclostationary stochastic process we say that pn In general, the time domain description of the input-output relation for the stochastic model may be described as follows present value of Model output linear combination of past values of Model output j 1 n ( j ) y j ) is zero mean, cyclostationary white sequence with periodic variance E{e 2 M E{e 2 n M n Using the minimum mean square error (MMSE) criteria, we obtain the following set of equations pn y(n l j 1 n ( j ) y(n j ) y(n 0 v pn n v,0 Which can be written as, Pn ( j j k ( j k 1 ( j k ( j j k ( j j th th ( and ( are the q coefficient of p order k k 2 k ( j 2 k ( j ( j j forward and backward predictor respectively of the n j 1 n ( j ) n j , n k th channel. [...]

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