Orthogonal Frequency Division Multiplexing (OFDM) is a multicarrier transmission technique which is used in many digital communication systems. In this technique, Fast Fourier Transformation (FFT) and inverse FFT (IFFT) are kernel processing blocks which are used for data modulation and demodulation respectively. Another algorithm which can be used for multi-carrier transmission is the Fast Hartley Transform algorithm. The FHT is a real valued transformation and can give significantly better results than FFT algorithm in terms of energy efficiency, speed and die area. This thesis presents Application Specific Instruction Set Processors (ASIP) for the FFT and FHT algorithms. ASIPs combine the flexibility of general purpose processors and efficiency of application specific integrated circuits (ASIC). Programmability makes the processor flexible and special instructions, memory architecture and pipeline makes the processor efficient. In order to design a low power processor we have selected the recently proposed cached FFT algorithm which outperforms standard FFT. For the cached FFT algorithm we have designed two ASIPs one having a single execution unit