Computationally attractive real Gabor transforms

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