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Improving the Magnitude Responses of Digital Filters for Loudspeaker Equalization

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There are numerous techniques that can approximate the frequency and phase response of an analog filter when converted into its digital counterpart. A new transform technique was shown to be comparable or superior to traditional transform techniques. The resulting filters were closer to the ideal analog version over the full frequency range. The approach was applied successfully to the kind of filters that would be used for loudspeaker equalization.

JAES Volume 58 Issue 12 pp. 1064-1082; December 2010
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Itai Neoran

Comment posted January 31, 2012 @ 14:35:56 UTC (Comment permalink)

After checking the Matlab code supplemented in this article, I found an error in the implementation of the MZTi, which is used as a reference in the article.

After fixing the error, I found, in the Matlab code example, that the MZTi method worked better then the article method

Comparing to the simple MZT method (Matched Z Transform), I found that the
article method, gave the same result as the MZT method

I checked it for the bell filter given in the Matlab example code, I can send the corrected Matlab code, for further investigation

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Mohamad Al-alaoui

Comment posted March 5, 2012 @ 14:34:59 UTC (Comment permalink)

I am grateful for these comments that are basically correct. The comments concern the manuscript that was published in December 2011 in JAES [1]. In [1] the method introduced in [2] was applied to the bell filters examples that appeared in [3] together with a comparison with the MTZi method that was introduced in [3].
There was indeed an error in the MTZi code. However, after correcting the code the MTZi method worked better than the article method for cases 1 and 3. The article method is clearly better, after correction,   for cases 4, 7, and 9 and rather similar for the other cases. In all the cases the article method gave lower order filters, order 2, the same as the analog filters for all the 10 cases while the MTZi filters are of order 4 for cases 1, 3, 9, and 10 and of order 3 for the remaining cases.
The second comment is also correct. Indeed the MZT for the bell filter give the same results as the article method.  This was observed in two of the 6 examples presented in the original paper that presented the article method while in all the other examples the article method performed clearly better than the MZT [2]. In that paper all the examples were also compared with MZT method. Thus for some filters, and this obviously include the bell filter, the article method and the MZT method coincide. Due to the error in the MTZi code, indicated in the first comment, the article method yielded better results than the MTZi method and since the MTZi method was shown to be better than the MZT method this seemed to obviate the need for comparison with the MZT method.
It should be noted that the MTZi paper dealt with cases 1 and 2 and [1] added the other cases which show now after the correction that MTZi give better results than the MZT only in some cases, and with higher order filter, and this is indeed a contribution of the new article.
It should be noted that comments started as a private correspondence and I proposed that the discussion should be public. I am grateful indeed for the valuable comments that gave the opportunity to improve the results in [2]. With these improvements better results than MTZi in all cases will be obtained and the improved method does not coincide with the MZT Method. I will be submitting the manuscript which addresses also the error in [1] to JAES in the near future.
 [1]M. A. Al-Alaoui, “Improving the Magnitude Response of Digital Filters for Loudspeaker Equalization ”, Journal Audio Engineering Society, Volume 58, Number 12, pp. 1064-1082, December 2010.
[2] M. A. Al-Alaoui, “ Novel Approach to Analog to Digital Transforms,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, . Vol. 54, No. 2, pp.338-350 , February, 2007.
[3] D. W. Gunness, O. S. Chauhan, “Optimizing the Magnitude Response of Matched z-Transform Filters (“MZTi”) for Loudspeaker Equalization”, AES 32nd International Conference Proceedings, pp. 1-10, Hillerod, Denmark, September 2007.

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