Warped linear prediction (WLP) in speech and audio processing

Laine, Unto K.; Karjalainen, Matti; Altosaar, Toomas

doi:10.1109/icassp.1994.390018

Cited by 38 publications

(14 citation statements)

References 13 publications

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“…Compared with other spline or polynomial approximations, the arctangent form (23) was found to provide a more parsimonious expression at a given accuracy level. 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.…”

Section: E Arctangent Approximations Formentioning

confidence: 96%

“…Allpass transformations of order greater than one appear not to have been used in frequency warping applications, since allpass transformations of order map the unit circle to traversals of the unit circle, and a one-to-one mapping of the unit circle to itself is desired. 2 More recently, in 1994 [23], an allpass coefficient of 0.62 was used to generate a frequency warping closely approximating the Bark scale for a sampling rate of 22 kHz. Experiments comparing the performance of warped LPC and "normal" LPC for speech coding and speech recognition applications showed that warped LPC required less than half the predictor model order for comparable performance.…”

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: 96%

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

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“…The first block is a pre-whitening filter that is used to remove short-time correlation of the signal. The whitening filter is implemented using warped linear prediction (WLP) as described in [28]. The WLP technique works as ordinary linear prediction except that it implements critical-band auditory resolution of spectral modeling instead of uniform frequency resolution, and can be used to reduce the To a certain extent, the whitening filter may be interpreted as functionally similar to the normalization of the hair cell activity level toward spectral flattening due to the adaptation and saturation effects [29], [30].…”

Section: B Two-channel Pitch Analysismentioning

confidence: 99%

A computationally efficient multipitch analysis model

Tolonen¹,

Karjalainen²

2000

IEEE Trans. Speech Audio Process.

Self Cite

255

159

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Abstract-A computationally efficient model for multipitch and periodicity analysis of complex audio signals is presented. The model essentially divides the signal into two channels, below and above 1000 Hz, computes a "generalized" autocorrelation of the low-channel signal and of the envelope of the high-channel signal, and sums the autocorrelation functions. The summary autocorrelation function (SACF) is further processed to obtain an enhanced SACF (ESACF). The SACF and ESACF representations are used in observing the periodicities of the signal.The model performance is demonstrated to be comparable to those of recent time-domain models that apply a multichannel analysis. In contrast to the multichannel models, the proposed pitch analysis model can be run in real time using typical personal computers. The parameters of the model are experimentally tuned for best multipitch discrimination with typical mixtures of complex tones.The proposed pitch analysis model may be used in complex audio signal processing applications, such as sound source separation, computational auditory scene analysis, and structural representation of audio signals. The performance of the model is demonstrated by pitch analysis examples using sound mixtures which are available for download at http://www.acoustics.hut.fi/~ttolonen/pitchAnalysis/.

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“…We propose to postprocess the output signal of the mesh using a warped finite impulse response (FIR) filter [8], [9], which effectively introduces frequency shifting to reduce the dispersion error. The structure is an FIR filter where every unit delay element has been replaced with a first-order allpass transfer function…”

Section: Frequency Warpingmentioning

confidence: 99%

Reduction of the dispersion error in the triangular digital waveguide mesh using frequency warping

Savioja¹,

Välimäki²

1999

IEEE Signal Process. Lett.

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The digital waveguide mesh has been successfully used for simulation of two-dimensional (2-D) and threedimensional (3-D) wave propagation in musical instruments and acoustic spaces. Nevertheless, digital waveguide mesh algorithms suffer from dispersion which increases with frequency. In this letter, we show how the dispersion error of the triangular digital waveguide mesh can be reduced by frequency warping. By using this technique, the worst-case dispersion error of 0.6% is obtained, whereas in the original triangular mesh it is about 6.5%.

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Warped linear prediction (WLP) in speech and audio processing

Cited by 38 publications

References 13 publications

Bark and ERB bilinear transforms

Bark and ERB bilinear transforms

A computationally efficient multipitch analysis model

Reduction of the dispersion error in the triangular digital waveguide mesh using frequency warping

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