Linear Predictive analysis window

Description

The LP analysis window is a fundamental concept in the Adaptive Multi-Rate (AMR) speech codec, which is specified in 3GPP TS 26.090, TS 26.190, TS 26.290, and TS 46.060. It refers to the window of high-pass filtered speech samples used to compute the short-term filter coefficients (also known as Linear Predictive Coding, LPC, coefficients) for each frame of speech. The length of the analysis window is always 240 samples, which corresponds to 30 ms at the 8 kHz sampling rate used in AMR. The window is applied to the input speech signal to extract a segment for analysis, and the LPC coefficients are then calculated from this segment.

In the AMR codec, the LP analysis is performed differently depending on the codec mode. For the 12.2 kbit/s mode (AMR12.2), two asymmetric windows are used to generate two sets of LP coefficients per frame. This mode does not use any lookahead, meaning that no samples from future frames are used in the analysis. For all other modes, only a single asymmetric window is used to generate a single set of LP coefficients, and a 5 ms lookahead is employed. The lookahead means that the analysis window extends into the next frame, allowing for smoother transitions and better prediction, at the cost of a slight delay.

The use of asymmetric windows is a key aspect of the LP analysis in AMR. An asymmetric window weights the samples differently, typically emphasizing the most recent samples more than older ones, which is beneficial for speech signals that are non-stationary. The window shape is designed to minimize the effects of the truncation of the signal and to improve the accuracy of the LPC coefficients. The 240-sample window length is a compromise between frequency resolution and time resolution; a longer window would provide better frequency resolution but would smear rapid changes in the speech signal.

The LP analysis window is applied after high-pass filtering of the speech samples, which removes DC offset and low-frequency noise. The high-pass filtered samples within the window are then used to compute the autocorrelation coefficients, which are in turn used to solve the Levinson-Durbin recursion to obtain the LPC coefficients. These coefficients are used to build the short-term synthesis filter at the decoder, which models the spectral envelope of the speech signal.

The LP analysis window is a critical component of the AMR codec's ability to efficiently compress speech while maintaining good quality. Its design and parameters are carefully specified to ensure interoperability between different implementations and to achieve the required performance in terms of speech quality and robustness to errors. The concept is also relevant to other speech codecs, such as AMR-WB and EVS, although the specific parameters may differ.

Purpose & Motivation

The LP analysis window exists to provide a well-defined segment of the speech signal for linear predictive analysis, which is the core of many speech codecs including AMR. Linear prediction models the speech signal as the output of a filter excited by a source signal, and the filter coefficients are estimated from a window of past samples. The window is necessary because the speech signal is non-stationary, and the LPC coefficients must be computed over a short segment where the signal can be considered stationary.

The specific design of the LP analysis window in AMR, with its 240-sample length and asymmetric shape, was motivated by the need to achieve high speech quality at low bit rates while keeping the algorithmic delay low. The 12.2 kbit/s mode, which uses two windows and no lookahead, is optimized for low delay, making it suitable for applications where latency is critical. The other modes use a single window and a 5 ms lookahead to improve prediction accuracy and thus speech quality, at the expense of a small increase in delay.

Before the standardization of AMR, speech codecs used various window lengths and shapes, which led to interoperability issues and suboptimal performance. The LP analysis window in AMR was standardized to ensure consistent behavior across different implementations and to provide a reference for testing. It also allows for efficient implementation in fixed-point arithmetic, which is important for mobile devices with limited processing power. The window design has been carried forward to later codecs like AMR-WB and EVS, demonstrating its effectiveness and robustness.