Black Box methodology for the characterization of Sample Rate Conversion systems
Digital systems dedicated to audio and speech processing usually require sample rate conversion units in order to adapt the sample rate from different signal flows: for instance 8 and 16 kHz for speech, 32 kHz for the broadcast rate, 44.1 kHz for CDs and 48 kHz for studio work. The designer chooses the sample rate conversion (SRC) technology based on objective criteria, such as figures of complexity, development or integration cycle and of course performance characterization. For linear time-invariant (LTI) systems, the transfer function contains most information necessary for the system characterization. However, being not LTI, the SRC characterization also requires aliasing characterization. When the system under study is available only through input excitations and output observations (i.e. in black box conditions), aliasing characterization obtained for instance through distortion measurements is difficult to evaluate properly. Furthermore, aliasing measurements can be messed up with weakly nonlinear artifacts, such as those due to internal rounding errors. Consider now the fractional SRC system as a linear periodically time-varying (LPTV) system whose characteristics describe simultaneously the aliasing and the in-band (so-called linear) behaviour from the SRC. An interesting and new compound system made of multiple instances of the same SRC system builds a LTI system. The linear features from this compound system fully characterizes the SRC (i.e. its linear and aliasing rejection behaviour) whereas weakly nonlinear features obtained from distortion measurements are only due to internal rounding errors. The SRC system can be analyzed in a black box condition, either in batch processing or real-time processing. Examples illustrate the capability of the method to fully recover characteristics from a multistage SRC system and to separate quantization effect and rounding noise in actual SRC implementations.