Perceptual Weighting Filter

Description

The Perceptual Weighting Filter is a core component of analysis-by-synthesis (AbS) speech codecs standardized by 3GPP, including the Adaptive Multi-Rate (AMR), AMR-WB, and EVS codecs specified in TS 26.090, 26.190, and 26.290. In AbS coding, the encoder searches a codebook for the excitation vector that minimizes a weighted error between the original speech and the synthesized speech. The weighting is performed by the perceptual weighting filter, which exploits the noise masking properties of the human auditory system. Specifically, the filter weights the error less in spectral regions near the formants (vocal tract resonances) and more in regions away from them, because quantization noise near strong formants is masked by the speech energy itself and is less audible.

Mathematically, the perceptual weighting filter is typically derived from the short-term linear prediction (LP) synthesis filter A(z). A common form is W(z) = A(z/γ1) / A(z/γ2), where γ1 and γ2 are weighting factors with 0 < γ2 < γ1 < 1. The numerator A(z/γ1) places zeros that partially cancel the formant peaks, while the denominator A(z/γ2) places poles that broaden the spectral valleys. The net effect is a filter whose magnitude response is inversely related to the formant envelope, attenuating the error spectrum where speech energy is high and amplifying it where speech energy is low. This shaping makes the quantization noise perceptually less noticeable.

In the encoder, the weighted error is computed by filtering the difference between the original and synthesized speech through W(z). The codebook search then minimizes the energy of this weighted error. Because W(z) is a linear filter, the search can be performed efficiently using impulse responses and correlation matrices, as described in the respective codec specifications. The decoder does not need the perceptual weighting filter; it only reconstructs speech using the quantized LP parameters and excitation. Thus, the filter is an encoder-side tool that improves the selection of excitation vectors without adding bit rate.

The perceptual weighting filter is closely related to the concept of noise shaping in speech and audio coding. It is also related to the weighting filter used in Code-Excited Linear Prediction (CELP) and its variants. In 3GPP codecs, the filter parameters γ1 and γ2 are fixed or adapted depending on the bit rate and mode. For example, in AMR, different modes may use slightly different weighting to optimize quality across rates. In EVS, additional perceptual considerations such as formant enhancement and bandwidth extension are combined with the weighting filter to achieve high quality at very low bit rates.

Understanding the perceptual weighting filter is essential for codec designers and speech quality researchers. It exemplifies how psychoacoustic principles are embedded in standardized algorithms to deliver efficient compression. The filter's design directly affects the trade-off between speech quality and computational complexity, and it is a key reason why 3GPP codecs can maintain natural-sounding speech even at rates as low as 4.75 kbps.

Purpose & Motivation

The Perceptual Weighting Filter exists to improve the subjective quality of synthesized speech in analysis-by-synthesis codecs by shaping quantization noise according to human auditory masking. Without it, the codebook search would minimize unweighted error, treating all spectral regions equally. This would allocate quantization accuracy uniformly, wasting bits on spectral regions where noise is inaudible due to masking and under-allocating bits where noise is audible. The filter solves this by making the error criterion perceptually relevant.

The motivation comes from the physiology of hearing: the ear's sensitivity is non-uniform across frequency and is influenced by the presence of masking sounds. Formants are high-energy regions that mask nearby noise, so errors there are less perceptible. The perceptual weighting filter capitalizes on this by attenuating the error spectrum near formants and amplifying it in valleys. This allows the encoder to focus its limited bit budget on perceptually important details.

Historically, the concept was introduced in early CELP codecs and adopted in 3GPP standards starting with the AMR codec in Rel-8 (though AMR itself was specified earlier, the glossary entry was introduced in Rel-8). It has remained a stable component across releases because the underlying psychoacoustic principles are timeless. The filter's parameters have been refined over time, but its fundamental role in AbS search has not changed, ensuring backward compatibility and consistent quality.