This paper has demonstrated the benefits of using frequency-domain blocking with minimum weighted norm extrapolation. The proposed algorithm greatly reduces computational time and memory, and enables large data segments that exceed the application limits to be processed through the extrapolation algorithm. The tradeoff is shown to be an increase in error.
Problems were revealed when dealing with non-tonal music. This problem is inherent in the extrapolation method. Since the overall algorithm is independent of the extrapolation method, a different extrapolation method could be set in its place and the rest of the algorithm would perform in a similar fashion.
The optimal known data length, block size, and overlap percentage should be determined based on the application of this algorithm. Best results are obtained when the overlap percentage is small and the block size is minimized but still greater than the number of blocks. In some applications the automatic gain control (RMS factor) may be optional to the user depending on the input and listener preference.
Future study regarding this algorithm could be made with the extrapolation system and the automatic gain. The extrapolation method was shown to perform poorly on percussive, noise-like signals and to produce mirror-like images with some input vectors. An improved extrapolation method could be put in place of the minimum weighted norm extrapolation method. Although simple linear extrapolation was tested for the envelope estimation and was deemed inferior to the RMS factor, there may be other methods of improving the extrapolated envelope, which do not add too much computation. Another improvement that could be made to the proposed system is to reduce the raised spectrum noise floor produced when frequency-domain blocking extrapolation is used on pure sinusoids. A time/frequency decomposition of the signal could also improve the extrapolation. This decomposition could improve extrapolation of non-tonal signals and estimation of extrapolation envelope. Other transforms such as Cosine, Sine, or Karhunen-Loéve transforms [4] could be used to block the signal instead of using the Fourier transform.
A new algorithm has been presented that reduces the computational requirements of the extrapolation system. While there is an increase in error, the reduction in computational requirements may be more desirable for particular applications, especially in digital audio where small time intervals are data intensive.