This paper presents a new method for the design of Walsh to Fourier Transform (WFT), and discusses its application to vibration diagnosis of rotating machinery.
W-FT is faster than the Cooley-Tukey FFT when the number 2
n of sampled data is small or when the number of Fourier components is relativery small compared with 2
n. However as the number 2
n increases, the W-FT program size expands rapidly, because the program requires 2
n×2
n matrix
Ci, k to convert Walsh components to Fourier components. Thus the implementation of the program into a micro computer is impractical when 2
n is large.
To solve the above problem, a simplified algorithm of W-FT is derived. Namely, its linear conversion matrix
Ci, k is expressed by Walsh matrix and Fourier matrix. First, WFT algorithm is improved, by using orthogonal relations between sinusoids and Walsh functions. And 2
n×2
n matrix is reduced by dividing the matrix into 2
p-2×2
p-2 submatrices
C(p)s(i), s(k) which are independent each others, and by deleting zero submatrices among them. Next, when
p is large, the elements whose values are small are deleted. As the result, the number of elements of
C(p)s(i), s(k) are reduced by 2/3 and the time to calculate is shortened so as to meet for practical use.
From the simulation results of vibration diagnosis for turbine and generator, it was shown that the improved W-FT, presented in this paper, was faster than FFT by 3/4.
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