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# Introduction

This module will look at two signal operations affecting the time parameter of the signal, time shifting and time scaling. These operations are very common components to real-world systems and, as such, should be understood thoroughly when learning about signals and systems.

# Time Shifting

Time shifting is, as the name suggests, the shifting of a signal in time. This is done by adding or subtracting a quantity of the shift to the time variable in the function. Subtracting a fixed positive quantity from the time variable will shift the signal to the right (delay) by the subtracted quantity, while adding a fixed positive amount to the time variable will shift the signal to the left (advance) by the added quantity. Figure 1: f⁢t−T f t T moves (delays) f f to the right by T T.

# Time Scaling

Time scaling compresses or dilates a signal by multiplying the time variable by some quantity. If that quantity is greater than one, the signal becomes narrower and the operation is called compression, while if the quantity is less than one, the signal becomes wider and is called dilation. Figure 2: f⁢a⁢t f a t compresses f f by a a.
Example 1

Given $f(t)f(t)$ we woul like to plot $f(at-b)f(at-b)$. The figure below describes a method to accomplish this.