We discuss the advantages of using the approximate quantum Fourier tra
nsform (AQFT) in algorithms which involve periodicity estimations. We
analyze quantum networks performing AQFT in the presence of decoherenc
e and show that extensive approximations can be made before the accura
cy of AQFT (as compared with regular quantum Fourier transform) is com
promised. We show that for some computations an approximation may impl
y a better performance.