Area-Efficient Scaling-Free DFT/FFT Design Using Stochastic Computing

Discrete Fourier transform (DFT) is an important transformation technique in signal processing tasks. Due to its ultrahigh computing complexity asO(N-2), N-pointDFTis usually implemented in the format of fast Fourier transformation (FFT) with the complexity of O(N logN). Despite this significant reduction in complexity, the hardware cost of the multiplicationintensive N-point FFT is still very prohibitive, particularly for many large-scale applications that require large N. This brief, for the first time, proposes high-accuracy low-complexity scalingfree stochastic DFT/FFT designs. With the use of the stochastic computing technique, the hardware complexity of the DFT/FFT designs is significantly reduced. More importantly, this brief presents the scaling-free stochastic adder and the random number generator sharing scheme, which enable a significant reduction in accuracy loss and hardware cost. Analysis results show that the proposed stochastic DFT/FFT designs achieve much better hardware performance and accuracy performance than state-of-the-art stochastic design.