There are several easily derived identities that can simplify the computation of many transforms and play significant roles both in applications and in further development of our theory. Some of these, such as those identities associated with the linearity of the transforms and the principle of near-equivalence, have already been discussed. In this chapter, we will discuss those identities involving translation, “modulation”, scaling and complex conjugation. We will also discuss a few topics relating to these identities (such as the intelligent use of tables).
For convenience, many of the formulas for transforms we have already computed are listed in table 21.1.