Research Of (0,1) Coding Spectral Transform Methods

In the field of DSP, Fourier transform is a useful research tool. Similarly, in the field of logic design, spectral transform is also a useful research tool. Its use in logic design has a history of more than 40 years. As a means of abstract harmonic analysis, spectral transform takes the research of logic design from the area of logic to the area of spectral. For this reason, many hard and tough problems are now easy to be solved.There are two coding of spectral transform, (1,-1) and (0, 1). For the meaning of the spectral coefficients, traditional research focused more on (1,-1) coding than on (0, 1) coding. We will research the (0, 1) coding spectral transform.Traditional research also concluded that spectral transform matrix should be orthogonal as in the field of DSP. We believe, from the point of information integrity, this restriction can be relaxed to reversible matrix. Based on that, we believe spectral coefficients also can be customized.The primary drawback of the application oriented spectral coefficients is the complexity of its calculation. The state-of-art spectral coefficients calculation method is the Decision Diagram. It turns the calculation complexity from the order of exponential to the order of polynomial by the use of shared diagram and so on. Decision Diagram is an effective method of calculating the whole spectral but not the separate coefficients. We propose a method that is effective in the calculating of separate coefficients based on the character of (0, 1) coding. It is attractive for the simple principle.As application is concerned, Spectral transform have been applied in many areas of logic design. These include analysis, synthesis, testing and so on. We will research these three areas systematically based on the properties of (0,1) coding spectral coefficients.The spectral transform methods we research hear are Walsh transform, Haar transform, Reed-Muller transform and Arithmetic transform. We mainly research the Walsh transform.