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We propose an alternative approach to the Balanced Model Truncation method (standard method). This approach reduces substantially the order of minimum-phase inverse filters for equalizing room acoustics. This method is based on a property of the filter

Although partial equalization in room acoustics allows shorter length FIR digital inverse filters than that required in case of complete equalization (perfect dereverberation) [

Let be an

Now applying the

if the matrix

the rank of

the singular values of

The primary principle used for a system order reduction lies in the elimination of a subsystem associated with the smallest Hankel singular values [

The truncated Hankel matrix with a rank

Now having

The original system whose transfer function is

The standard algorithm can be implemented as follows [

Given

create the Hankel matrix

decompose the matrix

display the Hankel singular values, (

calculate the matrices

convert the system state-space representation (

In this method, we use a well-known property of the

The transfer function

Alternatively, the standard algorithm stated in Section

The transfer function of the corresponding implementable IIR filter is now given by

Both techniques were applied to a partial equalization FIR digital filter for an acoustic impulse response, representing the context of an audio-conferencing room (Figure

Acoustic impulse response measured in an audio-conferencing room.

Hankel singular values plot of both methods for the FIR sequence corresponding to Figure

IIR filter spectral reproduction obtained by different methods for

Both methods were also compared to the direct average of the delayed original FIR sequence (

To overcome the complexity implementation problem when using the alternative method, (

Hankel singular values plot of the standard method for the transformed IIR (delivered by the alternative method for

IIR filter spectral reproduction obtained by the standard method for

The corresponding magnitude and phase error are both less than −70 dB in the entire frequency band (Figures

An alternative approach to the Balanced Model Truncation algorithm (standard method) to substantially reduce minimum-phase inverse filters order for room acoustics equalization is proposed. This method is based on a property of the FIR filter

The authors would like to thank the reviewers for their constructive comments.