We just covered ideal (and non-ideal) (time) sampling of CT signals. This enabled DT signal processing solutions for CT applications (Figure 1):

Much of the theoretical analysis of such systems relied on
frequency domain representations. How do we carry out these
frequency domain analysis on the computer? Recall the
following relationships:

**Sampling DTFT**

Consider the DTFT of a discrete-time (DT) signal

We want to work with
*sample*

#### Example 1

Finite Duration DT Signal |
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The DTFT of the image in Figure 2 is written as follows:

Sample X(ω) |
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where again we sampled at

(This is precisely how we would plot

**Choosing M**

**Case 1**

Given

**Case 2**

Choose

In general, we require