One of the difficulties of VLSI design is the magnitude of the task. It is not easy to lay out one hundred thousand transistors, let alone ten million of them. Yet there is a sense in which the scale of VLSI is advantageous. The complexity of a VLSI chip is so great that asymptotic approximation can give insight into performance evaluation and design. This paper shows how asymptotic analysis can aid in the design of Fourier transform circuits in VLSI.