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.

中文翻译：

---

非均匀采样率转换：一种有效的方法


我们提出了一种用于非均匀采样率转换的离散时间算法，该算法具有较低的计算复杂度和内存需求。它通过适应时变转换比率来概括任意采样率转换，即它可以有效地适应输入和输出采样率的瞬时变化。该方法基于对用于转换的时变离散时间滤波器进行适当因式分解。满足此分解属性的常见滤波器是那些基础连续时间滤波器由指数的线性组合组成的滤波器，例如由线性常系数微分方程描述的滤波器。这种因式分解将计算分为两部分：一个部分由仅取决于输出采样时刻的因子组成，另一个部分由可递归计算的求和组成，其项仅取决于输入采样时刻，其项数为由输入和输出采样时刻之间的关系给出。因此，可以通过更新所涉及的因素并调整添加的项数来适应不均匀的采样率。当脉冲响应由指数组成时，可以以有效的方式递归地计算因子。