Lesson 18

**Properties of the DTFT**
We cover a few here and you can read about the rest in the textbook.

**LINEARITY**

**TIME SHIFT**

**MODULATION - Frequency Shift**

**CONVOLUTION IN TIME**

As usual,

Ex. Given . Find its inverse system .

. Find its DTFT.

**MULTIPLICATION OF SIGNALS**

where denotes CIRCULAR CONVOLUTION:

Now,

is just the DTFT of

that is,

So,