Abstract
The FFT has a restriction that the number of data to be analyzed must be a power of two. If the FFT hasn't the restriction, it will be very useful. The correct formula of the universal FFT, which analyzes the arbitrary number data, is then derived by using the discrete convolution concept. The calculational procedure is also presented in this paper. The universal FFT uses 4 times as large memory as the FFT does, and analyzes the data about one-tenth times as fast as the FFT does. The FFT supplemented with zeros, which is used when the data number is smaller than the power of two, induces various calculational errors while the universal FFT gives the exact amplitudes and phases of the original data, and is much faster than the discrete Fourier transformation (DFT).
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