A novel extension of the SB-FFT: Sub-segment inverse fast Fourier transform (SS-IFFT) with different applications

In this paper we present a new fast approximate inverse FFT for short-time signal applications. This approach is derived from the sub-band FFT (SB-FFT) and it is called Sub-Segment IFFT (SS-IFFT). SS-IFFT uses the idea of decomposing the input signal into two segments (early and late) according to their order of occurence in time. An approximation can be done by implementing the IFFT of one of the two-segments according to a pre-known information about the time-domain characteristics of the signal. Such an approximation leads to fast computation at the cost of less accuracy. Both the reduction in complexity and the approximation errors of the new algorithm are investigated in this paper. The SS-IFFT has an adaptive capability like the forward SB-FFT. The idea of SS-IFFT is extended also to the two dimensional case. The algorithm is also tested by using different filters other than the Hadamard filters used in the SB-FFT. Different applications of the new technique are included in speech analysis, echo detection, FIR filter design, and ECG compression.