Compactly supported sampling functions of degree 2 for applying to reproducing DVD-Audio

In digital signal processing, a method for obtaining the output signal by convoluting sampled-values as an input signal with the sampling functions which are typical impulse responses is usually used to reconstruct multimedia signals such as audio, images, and movies. In our past research, we have researched about generalizing sampling functions including Shannon's sampling functions and their application. Especially, the sampling functions of degree 2, with only one time continuously differentiability, have been able to demonstrate their practicality for some systems such as CD-Player and DTP systems. On the other hand, signals which are dealt with in the recent multimedia communication field, tend to be high sampling rate signals such as DVD-Audio with maximum sampling rate of 192 kHz. Therefore, the conventional sampling function whose oscillation follows to infinity is not practical for reproducing these signals that require high speed processing. We derive the compactly supported sampling functions of degree 2 that are applicable to reproducing DVD-Audio with maximum sampling rate of 192 kHz.