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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
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Example : Inverse Z-transform
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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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