A time-distributed fast Fourier transform algorithm: Application to real-time implementation of iterative learning control-Experimental piezoactuator example

In this paper, an algorithm of time-distributed fast Fourier transform and inverse fast Fourier transform (TD-FFT/TD-IFFT) is proposed. This work is motivated by the needs to implement FFT/IFFT in real-time on general microprocessors (e.g., Intel's ×86-based microprocessors) in signal processing and control applications, for example, in real-time implementation of frequency-domain iterative learning control techniques. The proposed TD-FFT technique explores the butterfly-structure in the FFT computation, and distributes the computation needed into a sequence of stages each executing a much shorter sampled data sequence. The proposed approach is extended to real-time IFFT computation as well. For a sampled sequence of 2N length, the proposed TD-FFT/TD-IFFT algorithm maintains the total computation complexity of FFT/IFFT while distributing the computation from one sampling period to multiple sampling periods. Then, the application of the proposed TD-FFT/TD-IFFT for real-time ILC implementation is presented, and demonstrated through an online implementation of the modeling free inversion-based iterative-learning control (MIIC) of a piezoelectric actuator in experiments.