An data processing apparatus for performing signal processing on an input signal having a finite length. The apparatus performs a wavelet transform to divide the input signal into sub-bands for signal processing. An extrapolation process is performed to limit transform artifacts at the leading and trailing ends of each sub-band of the finite length signal. An extrapolation processing discriminator is used to determine whether the extrapolation process satisfies a complete reconstruction condition, whereby an output signal will be a substantial reconstruction of the input signal. The extrapolation process is chosen from among four different loopback methods.