In this paper, a general class of split-radix fast Fourier transform (FFT) algorithms for computing the length-2(m) DFT is proposed by introducing a new recursive approach coupled with an efficient method for combining the twiddle factors. This enables the development of higher split-radix FFT algorithms from lower split-radix FFT algorithms without any increase in the arithmetic complexity. Specifically, an arbitrary radix-2/2(s) FFT algorithm for any value of s, 4 <= s <= m, is proposed and its arithmetic complexity analyzed. It is shown that the number of arithmetic operations (multiplications plus additions) required by the proposed radix-2/2(s) FFT algorithm is independent of s and is (2m-3)2(m+1) + 8 regardless of whether a complex multiplication is carried out using four multiplications and two additions or three multiplications and three additions. This paper thus provides a variety of choices and ways for computing the length-2(m) DFT with the same arithmetic complexity.