Instructional report by Yogesh Sawant (ID: 104605545) in partial fulfillment of course requirements of ESE 558

Submitted to

Professor Murali Subbarao

Aliasing

Aliasing is a potential problem whenever an analog signal is point sampled to convert it into a digital signal Aliasing is what happens when analog data is represented on a digital system. It happens whenever an analog signal is not sampled at a high enough frequency. A curved line drawn on a grid, where the curved line represents the analog data and the grid represents the digital system, is a good example of analog data on a digital system (see figure 1.1)

Figure 1.1 Figure 1.2 Digital version of the line

Line on grid representing analog

data on digital system

When the analog data is converted to digital some problems arise. The digital system in this example is the grid. To convert the analog line to a digital line each point in the grid may either represent a point in the line, by being filled in, or represent an area where the line does not exist, by remaining white. There can't be a square that is only partly filled. Each square must be either filled in or not. In other words, to draw the line in digital format we need to completely fill in any square that a portion of the line passes through. That's all part of it being digital.

Okay no problem, right? The line goes through the different squares so we'll fill in each square that the line goes through. Figure 1.2 shows what the line looks like when we do this. Not very smooth, is it? We no longer have curves; all we have is a choppy line made up of squares and rectangles. Now let us describe the same thing discussed above in slightly technical terms.

A signal x(t), periodically sampling at time...