  We present a discrete-time algorithm for nonuniform sampling rate conversion
that presents low computational complexity and memory requirements. It
generalizes arbitrary sampling rate conversion by accommodating time-varying
conversion ratios, i.e., it can efficiently adapt to instantaneous changes of
the input and output sampling rates. This approach is based on appropriately
factorizing the time-varying discrete-time filter used for the conversion.
Common filters that satisfy this factorization property are those where the
underlying continuous-time filter consists of linear combinations of
exponentials, e.g., those described by linear constant-coefficient differential
equations. This factorization separates the computation into two parts: one
consisting of a factor solely depending on the output sampling instants and the
other consists of a summation -- that can be computed recursively -- whose
terms depend solely on the input sampling instants and its number of terms is
given by a relationship between input and output sampling instants. Thus,
nonuniform sampling rates can be accommodated by updating the factors involved
and adjusting the number of terms added. When the impulse response consists of
exponentials, computing the factors can be done recursively in an efficient
manner.
