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Published byDwight Hardy Modified over 5 years ago

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Lecture #07 Z-Transform meiling chen signals & systems

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**H = The impulse response of system H eigenvalue eigenfunction**

meiling chen signals & systems

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meiling chen signals & systems MIT signals & systems

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**DTFT is a special case of Z transform**

Discrete-time Fourier transform Where z is complex if DTFT is a special case of Z transform Same as FT is a special case of Laplace transform meiling chen signals & systems

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**Let be a complex number The DTFT of a signal meiling chen**

signals & systems

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**Laplace/inverse laplace transfrom**

The z-transform of an arbitrary signal x[n] and the inverse z-transform Notation meiling chen signals & systems

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**Region of convergence (ROC)**

Critical question : Does the summation converge to a finite value In general that depends on the value of z Since Unique circle meiling chen signals & systems

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meiling chen signals & systems MIT signals & systems

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Example : Z-transform R.O.C meiling chen signals & systems

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**Properties of Z transform**

Linearity Right shift in time Left shift in time Time Multiplication Frequency Scaling Modulation meiling chen signals & systems

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Convolution meiling chen signals & systems

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Initial value theorem meiling chen signals & systems

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Final value theorem meiling chen signals & systems

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**Some common Z transforms**

meiling chen signals & systems

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**Example : Inverse Z-transform**

meiling chen signals & systems

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**Example : the Z transform can be used to solve difference equations**

Taking the Z transform meiling chen signals & systems

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