Interpolation in Digital Signal Processing and Numerical Analysis

In many practical applications of digital signal processing, one is faced with the problem of changing the sampling rate of a signal, either increasing it or decreasing it by some amount. An increase in the sampling rate by an integer factor L can be accomplished by interpolating L-1 new samples between successive values of the signal. The interpolation process can be accomplished in a variety of ways in both fields of digital signal processing or numerical analysis. There is one very simple and straightforward approach to changing the sampling rate of a digital signal. This approach, called the analog approach, merely reconstructs the continuous-time signal from the original set of samples and then resamples the signal at the new rate. In practice this approach suffers from one major problem, namely, that the ideal operations required reconstructing the continuous-time signal from the original samples and to resample the signal at the new rate cannot be implemented exactly [1]. An alternative is the so-called direct digital approach that does the job without going through D/A or A/D conversion.