| The traditional approach to interpolation of digital signals consists of an increase in the sampling rate followed by low-pass filtering. FIR filters are usually preferred for this application because of their linear phase characteristic and because some features of the problem can be exploited to simplify their design and implementation. In many cases, however, FIR filters are still found to be a complex and expensive solution.;The approach described above is also employed to examine four other methods for local interpolation and determine how appropriate they are for interpolation in real-time. Although some of these methods can be more advantageous when some specific aspects of the problem are considered, the cubic spline algorithm implemented as a polyphase network seems to be the best over-all choice for this application. It combines accuracy with simplicity of operation and implementation (low cost) and good cancellation of undesirable harmonics, thus resulting in a versatile and efficient system.;This work describes a different approach to the problem of real-time interpolation which utilizes local interpolative routines implemented by piecewise cubic polynomials. Such routines produce approximations to the original signal which depend only on a small number of sample points located near the interval being interpolated. Cubic spline functions, in particular, were found to be very appropriate to this type of application. These functions are here analyzed, and used as basis for the derivation of an algorithm for interpolation in real-time. A model is also developed for the implementation of the algorithm which makes use of polyphase filters, thus called the polyphase model. The performance of the cubic spline algorithm is evaluated and analyzed for different cases of end-point derivative estimation. If properly estimated, the end-points derivative can be used to control the performance criteria such that trade-offs among them can be established. The criteria are accuracy, computational complexity, and undesirable harmonic generation. |
