Digital sampling rate conversion (SRC) systems receive sampled input signals at a given sampling rate and output the signal with a different sampling rate. The SRC system may increase (upsample) or decrease (downsample) the sampling rate of the signal.
The sampling rate conversion systems are widely used in audio or video systems for performing conversion of audio or video files from a given codec to another. SRC systems may have other applications.
Before integrating a sampling rate conversion system in a multimedia (e.g. audio and/or video) architecture, there may be the need of characterizing the SRC system for studying its behaviour.
Different approaches to characterization and performance measurements for multirate systems exist in the prior art.
SRC may be dealt with as a specific case of a multirate system (MRS). In some prior art approaches, fractional rate sampling rate convertors (SRC) are not considered as Linear Periodically Time Varying (LPTV) systems. For an SRC, input and output periods are constrained to be different. In other approaches, assuming an explicit definition of LPTV with potentially different input and output periods, SRC is clearly considered as LPTV. LPTV systems form a wider class than SRC since filter banks belong to LPTV.
LPTV systems may be entirely described in a polyphase context with tools including: analysis network (PPAN), synthesis network (PPSN) and polyphase matrix.
Typically, the following approach may be used in order to describe a LPTV system: Find a representation that embeds a Linear Time Invariant (LTI) system and characterize the LTI system with some suitable method.
Various different approaches are possible. For example, the LTI system may include a MIMO LTI system characterized by a bi-spectrum. Other approaches include a linear switched time varying (LSTV) system.
The characterizing bi-spectrum may be obtained through different means. For example via formal analysis by serial or parallel concatenation of basic building blocks (MIMO LTI system, decimator, expander, modulator), or via black box analysis with excitation of the system with a set of orthogonal test vectors.
Several techniques may be used for characterizing sampling rate conversion systems (SRC) from the outside (the SRC system being considered as a black box or a near black box (or grey) component).
The parameters characterizing the SRC system may be:                the in-band linear characteristics of the system,        the out-of-band characteristics of the system that generates spectrum aliases, and        the additional background noise due to rounding errors.        
The characterizing methods may be based on a distortion measurement either on a sine wave or on a sine sweep wave. The characterization methods may also be based on the reconstruction of the impulse response of the SRC system.
However, SRC systems are not shift-invariant (or time-invariant) systems. For an SRC system, the output of a delayed sequence is not necessarily the delayed version of the resulting output of the non-delayed sequence. This lack of shift-invariance generates aliasing, which penalizes the characterization methods.
Therefore, whereas the aliasing behaviour is not due to a non-linear behaviour, aliasing of SRC systems is usually studied as if it was a non-linear distortion with methods and criterion such as total distortion methods.
In fact, for an SRC system, a source of non-linearity may be the rounding errors. Total distortion methods are thus unable to discriminate between aliasing and real non-linearity.
Hence, there is a need for facilitating the characterization of the SRC systems.