Decorrelation

The decorrelation algorithm may be used to reduce distortions present in multiple recordings of the same signal made in different communication channels. If only one version of the recording is available, decorrelation is possible after time transposition is applied.

If the signal is recorded simultaneously in different communication channels, each recording is a sum of the same speech signal and different noise and distortions:

y_k(n) = s(n) + x_k(n), k=1, 2, ... K

s(n) - speech signal, x_k(n) - noise and distortions in k-th channel, K - number of available channels. The noise and distortions in different channels are not correlated, but they have identical statistic parameters. If the speech and noise are independent stochastic processes, then:

W(y_k) = W(s) + W(x_k)

where W is the variance of the process and W(x_k) = W(x) for each channel k. The variance of the sum of distorted signals from all channels (Y = y₁ + y₂ + ... +y_K) is:

W(Y) = K² W(s) + K W(x)

It can be seen that the signal-to-noise level is improved by 10 log₁₀ K. If K=4 versions of the recording are available, SNR is improved by ca. 6 dB.

If only one version of the recording is available, it is possible to process this recording using the time transposition algorithm and treat the processed signals as multiple channel recordings. With this approach, besides the reduction of the noise and distortions, some kind of filtration is performed, similar to notch filtering. In this case, further signal processing may be needed.

The user may set two parameters in the decorrelation module window: decorrelation order 1 and decorrelation order 2. These parameters determine the time shift as a multiple of sampling period. The user needs to find the values that reduce the non-correlated noise and distortions without affecting speech intelligibility.