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Time dependent changes-

1. Time delay- In simple terms you are shifting the original signal by a factor. For eg.

Time shift example

In this example as you can see, a simple way of understanding time shift/delay is by looking at how the graph changes when you want a shift in the signal.

2. Time scaling- amplitude scaling graph example

In simple terms you are shifting the height/width of the graph of a signal. The change in graph depends on the value of a. If |a|>0, then the height increases, else it decreases.

3. Time reversal- time reversal When you negate the independent variable, the graph of the dependent variable changes to a mirror image of the original graph.

Even/Odd Signals- Graph1.4.PNG As can be seen in the above function, the graphs do not change when you substitute x as -x. Similarly in signals, when a signal remains unchanged under time negation, it is termed as an "even" signal.

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Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett