This paper presents a method for computing the fourier coefficients of a complex valued periodic function resulting from tracing the contour of a closed shape using the arithmetic fourier transform (AFT). It rewires only simple addition operations, thus saving computational time and load. Moreover, the algorithm is much suitable for parallel computation and has a good match w i t h VLSI implemetation. Thus, i t s usage in pattern recognition i s valuable. Results obtained from simulatian studies show that the method is both accurate and efficient.