Introduction to Signals and Systems
Types of Signals
Properties of the Unit Impulse
Signal transformations
Signals can be transformed by modifying the variable.
: Shift a signal right by steps.
: Rotate a signal about the
: Stretch a signal by a factor of
These operations can be combined to give more complex transformations. For example, flips and shifts it right by timesteps. This is equivalent to shifting left by timesteps and then flipping it.
Convolution
While written in discrete time, these properties apply in continuous time as well.
Systems and their properties
Notice: The above conditions on linearity require that because if , then we need for scaling to be satisfied
Exponential Signals
Exponential signals are important because they can succinctly represent complicated signals using complex numbers. This makes analyzing them much easier.
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