TABLE OF CONTENTS The down-sampling operation is easy enough to envision: only the even indexed values are kept. It squeezes the signal to half of its size. The inverse operation, up-sampling, stretches the signal back out, usually by inserting a 0 between each two successive samples. The effect of a down-sampler followed by an up-sampler is that every other value will be 0.
In this text, we show the down-sampler as the arrow followed by the number 2, as in the top left corner of Figure 9.7, and the up-sampler as in the top right corner of the same figure. Alternatively, some texts use the two symbols along the bottom of this figure [35], as in two inputs enter but only one leaves for the down-sampler, and one input enters but two exit the up-sampler.
Intuitively, using up- and down-samplers may seem like it cannot work. How can we throw out half of our calculations after filtering without losing information? This section gives a brief example of how this process works.
Figure 9.8 shows an example of a two-channel filter bank with down-samplers followed by up-samplers. The filters are very simple, in fact, these filters would be implemented as in Figure 8.2, which reduces down to Figure 8.3.
Since the filter with coefficients {1, 0} allows the input to pass through to the output, we...
