Z TRANSFORM

converts a real or complex signal defined in the discrete time domain into a representation in the complex frequency domain.

transform examples

Impulse

Step

Ramp

Geometrical series

Convergence Region

The values when the transform converges

Properties

Superposition

homogeneity

additivity

Delay

Convolution

summation

multiplication by exponentials

derivation

Theorems

Initial Value

Final Value

expansion method in partial fractions

transfer function

Grafic Representation

delay unit

It is a device whose output signal is identical to the input signal
except that a unit is delayed for discrete time.

multiplier unit

The multiplier unit generates a sequence (output signal) identical to
the input sequence multiplied by some fixed scalar 'a'.

sum unit

is a device in wich two or more signals arrive that is added algebraically

cascade system

inverse system

feedback system

Discrete systems

Closed loops

Open loops

Applications

high pass filter

band pass filter

low pass filter