Warped filters and their audio applications

Karjalainen, Matti; Härmä, Aki; Laine, Unto K.; Huopaniemi, Jyri

doi:10.1109/aspaa.1997.625615

Cited by 21 publications

(12 citation statements)

References 11 publications

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“…The idea was that the arctangent function provided a mapping from the interval the domain of to the interval [0, 1), the range of The additive component allowed to be zero at smaller sampling rates, where the Bark scale is linear with frequency. As an additional benefit, the arctangent expression was easily inverted to give sampling rate in terms of the allpass coefficient (24) To obtain the optimal arctangent form the expression for in (23) was optimized with respect to its free parameters to match the optimal Chebyshev allpass coefficient as a function of sampling rate: (25) For a Bark warping, the optimized arctangent formula was found to be (26) where is expressed in units of kHz. This formula is plotted along with the various optimal curves in Fig.…”

Section: E Arctangent Approximations Formentioning

confidence: 99%

“…Very recently, the first-order allpass transformation was used to implement audio-warped filters directly in the warped domain [24], [25]. In this application, a digital filter is designed over the warped frequency axis, and in its implementation, each delay element is replaced by a first-order allpass filter, which implements the unwarping "on the fly."…”

Section: B Prior Use Of First-order Conformal Maps As Frequency Warpmentioning

confidence: 99%

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Bark and ERB bilinear transforms

Smith¹,

Abel

1999

IEEE Trans. Speech Audio Process.

258

133

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Use of a bilinear conformal map to achieve a frequency warping nearly identical to that of the Bark frequency scale is described. Because the map takes the unit circle to itself, its form is that of the transfer function of a first-order allpass filter. Since it is a first-order map, it preserves the model order of rational systems, making it a valuable frequency warping technique for use in audio filter design. A closed-form weighted-equation-error method is derived that computes the optimal mapping coefficient as a function of sampling rate, and the solution is shown to be generally indistinguishable from the optimal least-squares solution. The optimal Chebyshev mapping is also found to be essentially identical to the optimal least-squares solution. The expression 0:8517 [arctan(0:06583fs)] 1=2 00:916 is shown to accurately approximate the optimal allpass coefficient as a function of sampling rate fs in kHz for sampling rates greater than 1 kHz. A filter design example is included that illustrates improvements due to carrying out the design over a Bark scale. Corresponding results are also given and compared for approximating the related "equivalent rectangular bandwidth (ERB) scale" of Moore and Glasberg using a first-order allpass transformation. Due to the higher frequency resolution called for by the ERB scale, particularly at low frequencies, the first-order conformal map is less able to follow the desired mapping, and the error is two to three times greater than the Bark-scale case, depending on the sampling rate.

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Section: E Arctangent Approximations Formentioning

confidence: 99%

Section: B Prior Use Of First-order Conformal Maps As Frequency Warpmentioning

confidence: 99%

Bark and ERB bilinear transforms

Smith¹,

Abel

1999

IEEE Trans. Speech Audio Process.

258

133

View full text Add to dashboard Cite

show abstract

“…In the following section, only the phase differences between individual components are investigated as the magnitude responses can be accurately equalized using digital filters to obtain magnitude matched components at lower frequencies (e.g. by using frequency warped filters [32], [33]), but the phase mismatches are harder to correct.…”

Section: ) Magnitude Errormentioning

confidence: 99%

Theoretical Analysis of Open Spherical Microphone Arrays for Acoustic Intensity Measurements

Hacıhabiboğlu

2014

IEEE/ACM Trans. Audio Speech Lang. Process.

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Acoustic intensity is a vectorial measure of acoustic energy flow through a given region of interest. Three-dimensional measurement of acoustic intensity requires special microphone array configurations. This paper provides a theoretical analysis of open spherical microphone arrays for the 3-D measurement of acoustic intensity. The calculations of the pressure and the particle velocity components of the sound field inside a closed volume are expressed using the Kirchhoff-Helmholtz integral equation. The conditions which simplify the calculation are identified. This calculation is then constrained to a finite set of microphones positioned at prescribed points on an open sphere. Several open spherical array topologies are proposed. Their magnitude and directional errors and measurement bandwidths are investigated via numerical simulations. A comparison with conventional open-sphere 3-D intensity probes is presented.

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“…Response modeling is especially challenging at low frequencies where standing waves cause significant variations in the frequency response at the listening position. Typical approaches for realizable equalization filter design include IIR filters or warped FIR filters (.e.g, [1], [2]). …”

Section: Introductionmentioning

confidence: 99%

Room Acoustic Response Modeling and Equalization with Linear Predictive Coding and Parametric Filters for Speech and Audio Enhancement

Bharitkar

Zhang

Kyriakakis

2006

2006 Fortieth Asilomar Conference on Signals, Systems and Computers

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Room acoustic response modeling is a challenging problem. Typical applications include speech dereverberation and loudspeaker correction. Traditionally, infinite-duration impulse response (IIR) or finite-duration impulse response (FIR) filters have been used for acoustic response modeling and equalization. The IIR filter, also called a parametric filter, has a bell-shaped magnitude response and is characterized by its center frequency, the gain at the center frequency, and a Q factor (which is inversely related to the bandwidth of the filter) and is easily implemented as a cascade for purposes of room response modeling and equalization. In this paper we present a technique for determining the coefficients of a second order IIR using a Linear Predictive Coding (LPC) model, where the poles or roots of a high-order LPC dictate the parameters of the parametric filter. Due to the band interactions between the IIR filters, forming the cascade to model the room response, we also present a technique to optimize the Q values so as to better characterize the room response. An accurate model allows for better equalization, for correcting the loudspeaker and room acoustics for speech/audio enhancement, particularly at low frequencies. Alternatively, this technique can be utilized for speech dereverberation applications where the room responses have been estimated a priori. The advantages of the proposed method is the fast computation of the IIR filter parameters, from to the LPC model, since (i) the LPC model is efficient to compute since it uses the Levinson-Durbin recursion to solve the normal equations that arise from the least squares formulation, and (ii) a reasonably high-order LPC model is able to accurately model the low-frequency room response modes.

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Warped filters and their audio applications

Cited by 21 publications

References 11 publications

Bark and ERB bilinear transforms

Bark and ERB bilinear transforms

Theoretical Analysis of Open Spherical Microphone Arrays for Acoustic Intensity Measurements

Room Acoustic Response Modeling and Equalization with Linear Predictive Coding and Parametric Filters for Speech and Audio Enhancement

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