Equalization of Loudspeaker and Room Responses Using Kautz Filters: Direct Least Squares Design
- PDF / 1,332,179 Bytes
- 13 Pages / 600.03 x 792 pts Page_size
- 13 Downloads / 173 Views
Research Article Equalization of Loudspeaker and Room Responses Using Kautz Filters: Direct Least Squares Design Matti Karjalainen and Tuomas Paatero Department of Electrical and Communications Engineering, Laboratory of Acoustics and Audio Signal Processing, Helsinki University of Technology, P.O. Box 3000, FI 02015, Finland Received 30 April 2006; Revised 4 July 2006; Accepted 16 July 2006 Recommended by Christof Faller DSP-based correction of loudspeaker and room responses is becoming an important part of improving sound reproduction. Such response equalization (EQ) is based on using a digital filter in cascade with the reproduction channel to counteract the response errors introduced by loudspeakers and room acoustics. Several FIR and IIR filter design techniques have been proposed for equalization purposes. In this paper we investigate Kautz filters, an interesting class of IIR filters, from the point of view of direct least squares EQ design. Kautz filters can be seen as generalizations of FIR filters and their frequency-warped counterparts. They provide a flexible means to obtain desired frequency resolution behavior, which allows low filter orders even for complex corrections. Kautz filters have also the desirable property to avoid inverting dips in transfer function to sharp and long-ringing resonances in the equalizer. Furthermore, the direct least squares design is applicable to nonminimum-phase EQ design and allows using a desired target response. The proposed method is demonstrated by case examples with measured and synthetic loudspeaker and room responses. Copyright © 2007 M. Karjalainen and T. Paatero. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1.
INTRODUCTION
Equalization of audio reproduction using digital signal processing (DSP), such as improving loudspeaker or combined loudspeaker-room responses, has been studied extensively for more than twenty years [1–8]. Availability of inexpensive DSP processing power almost in any audio system makes it desirable and practical to correct the response properties of analog and acoustic parts by DSP. The task is to improve the system response of a given reproduction channel towards the ideal one, that is, flat frequency response and constant group delay. It is now commonly understood that this equalization should be done carefully, taking into account physical, signal processing, and particularly psychoacoustic criteria. An ideal equalizer, that is, the inverse filter of a given system response, works only in offline simulations [6]. Even for a point-to-point reproduction path, minor nonstationarity of the path and limitations in response measurement accuracy make ideal equalization impossible. Furthermore, monophonic reproduction has to be usually considered as a SIMO (single-input multiple-output) system since the signal
may be received in different points, whereas multichannel reproducti
Data Loading...
