COMPUTATIONALLY ATTRACTIVE REAL GABOR TRANSFORMS

In this paper, we present a Gabor transform for real, discrete signals and present a computationally attractive method for computing the transform. For the critically sampled case, we derive a biorthogonal function which is very Localized in the time domain. Therefore, truncation of this biorthogonal function allows us to compute approximate-expansion coefficients with significantly reduced computational requirements. Further, truncation does not degrade the numerical stability of the transform. We present a tight upper bound on the reconstruction error incurred due to use of a truncated biorthogonal function and summarize computational savings. For example, the expense of transforming a length 2048 signal using length 16 blocks is reduced by a factor of 26 over similar FFT-based methods with at most 0.04% squared error in the reconstruction.