The Fast Walsh Transform: ANew Method for Analyzing EEG Data
Robert Trappl · 1972
I want to draw your attention to a new method for analyzing con tinous recordings which has not-as far as I know-been applied to EEG-data. The only medical application published up to now which came to my knowledge is the recognition of types of waveforms in the electrocardiogram by MORGAN (1971). In the commonly used Fourier analysis amplitudes and frequencies of sine- and cosine-functions are calculated the summation of which approximates a given curve. In 1923 WALSH found other ortho gonal two-valued functions (+ 1 or - 1) which can also be used to approximate (nearly) all functions in a given interval, the quality of the approximation in a least squares sense being as good as by tri gonometric functions. These functions which nowadays are called Walsh-functions can be ordered in a rather similar way like tri gonometric functions, the difference being the use of sequency (= average number of zero crossings per second divided by 2, abbr. zps; HARMUTH 1968) instead of frequency. The value of the Walsh-function wal (k, j) of order k (= number of sign changes in the interval with length N = 2P) in the j-th place of the interval may