Tuomas Paatero

About room response equalization and dereverberation

Improvement of sound reproduction in rooms by signal processing techniques has been studied seriously for more than twenty years. Such methods are called for example dereverberation, room (response) equalization, and room (response) correction. Understanding the limitations and quality criteria for such methods is gradually achieved through studies of this highly multidimensional problem. In the present paper we discuss the terminology and goals, compare some recent approaches of these techniques in practical cases, and finally point out future challenges

Equalization of loudspeaker and room responses using Kautz filters: direct least squares design

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.

Frequency-dependent signal windowing

Signal windowing is a temporal weighting operation whereby a signal is multiplied by a function that pays more emphasis on desired parts of the signal and typically attenuates it outside this span, normally to zero, in order to result in a finite support (nonzero part). In audio and acoustics applications it is quite common that better frequency resolution is desirable at low frequencies, while at high frequencies better time resolution calls for a shorter analysis or processing window. In this paper methods to realize and utilize frequency-dependent signal windowing are presented that exhibit this desirable frequency-dependent property. Particularly methods based on time-frequency warping and rewarping of signals are discussed. Audio examples are presented where this technique is found useful.

Modeling and equalization of audio systems using Kautz filters

Frequency warping using all pass structures or Laguerre filters has increasingly found applications in audio signal processing due to having a good match with auditory frequency resolution. Kautz filters are an extension where the frequency warping and related resolution can have more freedom. We discuss the properties of Kautz filters and how they meet typical requirements found in modeling and equalization of audio systems. Case studies include transfer function modeling of the guitar body and loudspeaker response equalization.

A time-domain interpretation for the LSP decomposition

The line spectrum pair (LSP) decomposition is a widely used method in speech coding. In this article, we will show that the LSP polynomials, whose trivial zeros have been removed, are equivalent to two optimal (in the mean square sense) predictors in which a sample is predicted from linear combinations of its previous averaged and differentiated values.

Efficient pole-zero modeling of resonant systems using complex warping and Kautz filter techniques

The paper describes new methods for designing pole-zero filters that utilize a particular filter structure called Kautz filters and an efficient procedure for the optimization of filter parameters. In the design phase, complex warping is used to emphasize a chosen frequency region in the modeling. The motivation, from an audio signal processing perspective, is as follows. Many audio related target responses can be well-modelled by a combination of distributed decaying exponential components, which is by definition what a Kautz filter does, but in an orthonormalized form, providing many favorable properties. The most essential part is then how to choose the Kautz filter poles, for which we propose a new effective and well-behaving iterative method. Utilizing an intermediate warping procedure, the desired frequency resolution allocation is incorporated into the choosing of poles

Kautz Filters and Generalized Frequency Resolution: Theory and Audio Applications *

the target signal is warped prior to the pole optimization and then the produced poles are mapped back to the original frequency domain using inverse warping.