Details

The function is defined by for , with . The sinc interpolation formula is defined as , where is the sampling period used to determine from the original signal, and is the reconstructed signal. The above formula represents a linear convolution between the sequence and scaled and shifted samples of the function. In this Demonstration, a limited number of samples are generated, and the above sum is carried out for samples, labeled from to . Due to the shifting of the function by integer multiples of , this results in having the exact value of a sample located at a multiple of . This can be seen by observing that the absolute error is always zero at times which are integer multiples of , in other words at the sample locations. In this implementation, the function is sampled at a much higher rate than the sampling frequency used for the original function, in order to produce a smoother plotted result.

A. V. Oppenheim and R. W. Schafer, Digital Signal Processing, Englewood Cliffs, NJ: Prentice Hall, 1975.