Interpolating Filter

Description

The interpolating filter is a fundamental signal processing component in 3GPP speech codecs such as AMR, AMR-WB, and EVS. It is a finite impulse response (FIR) filter designed to produce an estimate of sub-sample resolution samples from an input signal that is sampled at integer sample resolution. In the context of code-excited linear prediction (CELP) codecs, the interpolating filter is applied to the past excitation signal to generate the adaptive codebook. The filter has low-pass characteristics, which helps to smooth the interpolated signal and reduce aliasing artifacts. The adaptive codebook consists of the low-pass filtered interpolated past excitation, which is used for pitch prediction. By allowing sub-sample resolution, the codec can more accurately model the pitch period of voiced speech, leading to improved speech quality at low bit rates. The filter coefficients are typically defined in the codec specifications, such as 26.090 (AMR), 26.190 (AMR-WB), and 26.290 (EVS). The interpolating filter operates on the excitation signal, which is the residual after short-term prediction. The pitch lag is typically estimated at integer resolution and then refined to fractional resolution using the interpolating filter. This fractional pitch approach is crucial for high-quality speech coding, as it captures the fine structure of the pitch period. The filter is implemented as a polyphase filter bank in practice, allowing efficient computation of interpolated samples at different fractional delays. The design of the interpolating filter must balance stopband attenuation, passband ripple, and computational complexity. In 3GPP codecs, the filter is often a 12-tap or 20-tap FIR filter, depending on the codec mode. The interpolating filter is also used in other contexts, such as in the post-filter for enhancing speech quality. Overall, the interpolating filter is a key enabler for fractional-pitch prediction in CELP-based speech codecs, contributing significantly to the achieved speech quality and coding efficiency.

Purpose & Motivation

The interpolating filter exists to enable sub-sample resolution pitch prediction in speech codecs. In early speech codecs, pitch prediction was limited to integer sample resolution, which introduced quantization error in the pitch lag and degraded speech quality, especially for high-pitched voices. By interpolating the past excitation to fractional sample positions, the codec can more accurately match the pitch period, reducing prediction error and improving reconstructed speech quality. This is particularly important at low bit rates where every bit counts. The interpolating filter also helps to smooth the excitation signal, reducing artifacts. The concept was introduced in early CELP codecs and standardized in 3GPP as part of AMR and later codecs. It addresses the limitation of integer-resolution pitch prediction by providing a computationally efficient way to generate fractional-delay versions of the excitation signal. The low-pass characteristic of the filter ensures that the interpolated signal does not introduce high-frequency artifacts. The use of an FIR filter allows for linear phase and stable operation. The interpolating filter is a key component in achieving the high speech quality required for mobile telephony.