Orthogonal frequency division multiplexing (OFDM) is a data transmission technique which is used in wired and wireless digital communication systems. In this technique, fast Fourier transformation (FFT) and inverse FFT (IFFT) are kernel processing blocks in an OFDM system, and are used for data (de)modulation. OFDM systems are increasingly required to be flexible to accommodate different standards and operation modes, in addition to being energy-efficient. A trade-off between these two conflicting requirements can be achieved by employing application-specific instruction-set processors (ASIPs). In this paper, two ASIP design concepts for the cached FFT algorithm (CFFT) are presented. A reduction in energy dissipation of up to 25% is achieved compared to an ASIP for the widely used Cooley-Tukey FFT algorithm, which was designed by using the same design methodology and technology. Further, a modified CFFT algorithm which enables a better cache utilization is presented. This modification reduces the energy dissipation by up to 10% compared to the original CFFT implementation.