4, the resulting sample-rate is 55,125. It is an easy matter to omit them from both the data stream and the calculations. L wavelets and filter banks strang pdf faster than the original input rate.

It’s the same result as not computing them at all. An example of both these distributions is depicted in the top two graphs of Fig. When the additional samples are inserted zeros, they increase the data rate, but they have no effect on the frequency distribution until the zeros are replaced by the interpolation filter. The result is shown in the third graph of Fig. Also shown is the passband of the interpolation filter needed to make the third graph resemble the second one. Then the transform is the same Fourier series with different frequency normalization.

Upsampling requires a lowpass filter after increasing the data rate, and decimation requires a lowpass filter before downsampling. Therefore, both operations can be accomplished by a single filter with the lower of the two cutoff frequencies. Realizable low-pass filters have a “skirt”, where the response diminishes from near unity to near zero. So in practice the cutoff frequency is placed far enough below the theoretical cutoff that the filter’s skirt is contained below the theoretical cutoff.