Hardware security has emerged as an important topic in the wake of increasing threats on integrated circuits which include reverse engineering, intellectual property (IP) piracy and overbuilding. This paper explores obfuscation of circuits as a hardware security measure and specifically targets digital signal processing (DSP) circuits which are part of most modern systems. The idea of using desired and undesired modes to design obfuscated DSP functions is illustrated using the fast Fourier transform (FFT) as an example. The selection of a mode is dependent on a key input to the circuit. The system is said to work in its desired mode of operation only if the correct key is applied. Other undesired modes are built into the design to confuse an adversary. The approach to obfuscating the design involves control-flow modifications which alter the computations from the desired mode. We present simulation and synthesis results on a reconfigurable, 2-parallel FFT and discuss the security of this approach. It is shown that the proposed approach results in a reconfigurable and flexible design at an area overhead of 8% and a power overhead of 10%.