5.3.2 LP analysis and interpolation
26.2903GPPAudio codec processing functionsExtended Adaptive Multi-Rate - Wideband (AMR-WB+) codecRelease 17Transcoding functionsTS
The principles are similar to 3GPP TS 26.190 (Section 5.2) except for the window shape and position, and the interpolation factors.
LPC analysis is performed every 256 samples in the superframe. The analysis window has 448 samples in duration, and has the shape of a half-sine cycle. It is symmetrical, and centred, for each LP analysis, at the middle of the first 64-sample sub-frame following each 256-sample frame. Hence, the lookahead required for LP analysis is half the analysis window length plus 32 samples, for a total of 256 samples.
The autocorrelations of windowed speech are converted to the LP coefficients using the Levinson-Durbin algorithm. Then the LP coefficients are transformed to the ISP domain for quantization and interpolation purposes. The interpolated quantized and unquantized filters are converted back to the LP filter coefficients (to construct the synthesis and weighting filters at each subframe).
The LP coefficients are quantized in the ISF domain, and interpolated every 64 samples. Depending on the coding mode selected (ACELP or TCX), the LP coefficients are transmitted at different update rates. For ACELP, which is based on the AMR-WB encoder, the LP coefficients are transmitted every 256 samples. For TCX, the LPC coefficients are transmitted every 256, 512 or 1024 samples, depending on the TCX frame length.
The LPC analysis is identical for ACELP or TCX.
5.3.2.1 Windowing and auto‑correlation computation
A 448-sample symmetrical sine window is used. The window is given by
where L=488 is the window length.
Autocorrelation computation and lag windowing are similar to 3GPP TS 26.190 (Section 5.2.1) with the exception that the window length is 488 samples and centred at the middle of the first subframe of the next 256-sample frame.
5.3.2.2 Levinson‑Durbin algorithm
Same as 3GPP TS 26.190.
5.3.2.3 LP to ISP conversion
Same as 3GPP TS 26.190.
5.3.2.4 ISP to LP conversion
Same as 3GPP TS 26.190.
5.3.2.5 Quantization of the ISP coefficient
Same as 3GPP TS 26.190. The difference is that the in case of TCX, the LP parameters are quantized and transmitted once per TCX frame (256, 512, or 1024 samples).
5.3.2.6 Interpolation of the ISPs
Since the LP analysis window shape and position is changed compared to AMR-WB, the interpolation factors have changed.
The interpolation is performed on the ISPs in the 
domain (cosine domaine). Let
be the ISP vector from LP analysis at frame n (centred at the 1st subframe of the frame n+1), and 
the ISP vector from LP analysis at frame n-1 (centred at the 1st subframe of the frame n). The interpolated ISP vectors in each subframe are given by
.
The interpolated ISP vectors are used to compute a different LP filter at each subframe using the ISP to LP conversion method.
The interpolation is performed for both unquantized and quantized parameters. In case TCX frames, the LP parameters are quantized once per 256-sample, 512-sample, or 1024-sample TCX frame, depending on the selected TCX mode. Thus the interpolation of quantized ISPs is performed as follows. In case of ACELP or 256-sample TCX frames, the interpolated quantized parameters are given by
.
In case of 512-sample TCX frames, comprised of 256-sample frames n and n+1, the interpolated quantized parameters are given by
.
In case of 1024-sample TCX frames, comprised of 256-sample frames n, n+1, n+2, and n+3, the interpolated quantized parameters are given by
.