Hadamard transformed carbon-13 nuclear magnetic resonance spectra. Pattern recognition analysis

Pattern recognition analysis of carbon-13 free induction decay data

Automation in the laboratory is becoming increasingly common as the scale and complexity of instrumentation and experimentation increase. Computers and electronic logic can provide data manipulation and control to match most laboratory situations, but few potential users appreciate the scope and limitations of the techniques available. A perspective is given of the range of applications of digital techniques in laboratory automation and instrumentation and some indication of current trends and the impact of recent developments in electronics.

https://iopscience.iop.org/article/10.1088/0022-3735/9/10/001/pdf

Digital techniques in laboratory automation.

In this paper we show that every matrix in the class of Sylvester Hadamard matrices of order 2 k under H-equivalence can have full row and column sign spectrum, meaning that tabulating the numbers of sign interchanges along any row (or column) gives all integers 0,1,...,2 k ???1 in some order. The construction and properties of Yates Hadamard matrices are presented and is established their equivalence with the Sylvester Hadamard matrices of the same order. Finally, is proved that every normalized Hadamard matrix has full column or row sign spectrum if and only if is H-equivalent to a Sylvester Hadamard matrix. This provides us with an efficient criterion identifying the equivalence of Sylvester Hadamard matrices.

A sign test for detecting the equivalence of Sylvester Hadamard matrices

1 – a survey of infrared spectral data processing techniques

Concise algorithm for conversion between normal and sequency ordered Hadamard matrices

A discussion of sampling theory, aliasing, and an experiment designed to establish the relationship between the analog-to-digital conversion rate and the frequency of a sine wave voltage input.

Ray M. Swanson

Papers

Concise algorithm for conversion between normal and sequency ordered Hadamard matrices

Determination of the Nyquist frequency. A computer-interfacing experiment