Resampling and Interpolation

In order to synthesize music, speech, or sounds in general, accurate and flexible control of pitch is necessary. The most accurate pitch control is necessary for music synthesis. In sampling synthesis, this is accomplished by dynamic sample rate conversion (interpolation). In order to convert a sampled data signal from one sampling rate to another, three steps are required bandlimiting, interpolation, and resampling. 

The correct (ideal in a provable digital signal processing sense) way to perform interpolation is convolution with the sine function, defined as  

Resampling This is usually accomplished at the same time as interpolation, because it is not necessary to reconstruct the entire continuous waveform in order to acquire new discrete samples. The resampling ratio can be time-varying, making the problem a httle more difficult. However, viewing 

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