Embodiments of the present invention exploit redundancy of succeeding FFT spectra and use this redundancy for computing interpolated temporal supporting points. An analysis filter bank converts overlapped sequences of an audio (ex. loudspeaker) signal from a time domain to a frequency domain to obtain a time series of short-time loudspeaker spectra. An interpolator temporally interpolates this time series. The interpolation is fed to an echo canceller, which computes an estimated echo spectrum. A microphone analysis filter bank converts overlapped sequences of an audio microphone signal from the time domain to the frequency domain to obtain a time series of short-time microphone spectra. The estimated echo spectrum is subtracted from the microphone spectrum. Further signal enhancement (filtration) may be applied. A synthesis filter bank converts the filtered microphone spectra to the time domain to generate an echo compensated audio microphone signal. Computational complexity of signal processing systems can, therefore, be reduced.