下面的介绍摘自PLP and RASTA (and MFCC, and inversion) in Matlab
RASTA is a separate technique from RASTA-PLP(Relative Spectral Transform - Perceptual Linear Prediction, a popular speech feature representation). RASTA applies a band-pass filter to the energy in each frequency subband in order to smooth over short-term noise variation and to remove any constant offset resulting from static spectral coloration in the speech channel
RASTA的提出者Hermansky在论文中写道
It suppresses the spectral components that change more slowly or quickly that the typical range of change speech
计算过程[^hermansky1994]
-
Compute the critical-band power spectrum
-
Transform spectral amplitude through compressing statistic nonlinear tranformation
取对数
-
Filter the time trajectory of each transformed spectral component
使用IIR滤波器，其传递函数为
$$H(z)=0.1z^4*\frac{2+z^{-1}-z^{-3}-2z^{-4}}{1-0.98z^{-1}}$$ 但是在实验中，最终分母中的0.98改成了0.94，滤波器的time constant从原来的500ms减至160ms。论文中给出的滤波器的幅频响应
自己用Matlab画出的幅频、相频响应曲线
非因果
在实现过程中，可以分步实现该滤波器。首先$z^{4}$即是将输入信号提前4个采样点，剩下的部分即是因果系统了。但设置延时的目的动机是什么？
-
Transform the filtered speech representation through expanding static nonlinear transformation
与步骤2相反，取指数 上述计算结果即为RASTA，如果在此基础上再计算PLP即可得到RASTA-PLP，即
-
Multiply by the equal loudness curve and raise to the power 0.33 to simulate the power low of hearing
-
Compute an all-pole model of the resulting spectrum, following the conventional PLP techinique