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Spectral Logic and Its Applications for the Design of Digital Devices by Jaakko T. Astola, Radomir S. Stankovic, Mark G. Karpovsky

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APPENDIX A

This appendix presents 21 classes of switching functions (Table A.0.1) that often appear in engineering practice. For these functions, Walsh and the autocorrelation can be expressed analytically.

Table A.0.2, shows their Walsh spectra in Paley ordering (see Section 2.3.2.1).

The corresponding autocorrelation functions are shown in Tables A.0.3.

In Table A.0.4, we present complexities of functions (numbers of nonzero spectral coefficients) in terms of Walsh spectra.

Spectral complexities in terms of Haar series for the same functions are given in Table A.0.5.

TABLE A.0.1 Switching Functions and Their Analytical Expressions.

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TABLE A.0.2 Functions and Their Walsh Spectra.

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TABLE A.0.3 Functions and Their Autocorrelation Functions.

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TABLE A.0.4 Functions and Their Walsh Complexities. ...

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