B. Edward McDonald
Gregory J. Orris
Naval Res. Lab., Washington, DC 20375-5000
It has been shown elsewhere that information about the shape of the noise spectrum with no phase knowledge can be used to construct a noise rejection algorithm which we call the matched-phase filter. Here, it is demonstrated that to first order in the signal-to-noise ratio (SNR), the matched-phase filter is capable of improving an arbitrarily low SNR (<<1) to order unity when the spectrum of the noise is known exactly. This analysis accounts for properties of numerical results with computer-generated signal and noise, with SNR values below -100 dB. Since computers have dynamic ranges far in excess of audio equipment, these results in an actual experiment would be limited by the dynamic ranges of the equipment used. Also shown are examples illustrating the performance of the algorithm when the noise spectrum is known only approximately.