Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev

Signal and System

Electrical Engineering (EE) : Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev

The document Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev is a part of the Electrical Engineering (EE) Course Signal and System.
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Z-Transform

  • Computation of the Z-transform for discrete-time signals.
  • Enables analysis of the signal in the frequency domain.
  • Z-Transform takes the form of a polynomial.
  • Enables interpretation of the signal in terms of the roots of the polynomial.
  • z−1 corresponds to a delay of one unit in the signal.

The Z - Transform of a discrete time signal x[n] is defined as
Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev

  • The discrete-time Fourier Transform (DTFT) is obtained by evaluating Z-Transform at z = ejω.
  • The z-transform defined above has both sided summation. It is called bilateral or both sided Z-transform.

Unilateral (one-sided) z-transform

  • The unilateral z-transform of a sequence x[n] is defined as
    Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev

Region of Convergence (ROC):
ROC is the region where z-transform converges. It is clear that z-transform is an infinite power series. The series is not convergent for all values of z.

Significance of ROC

  • ROC gives an idea about values of z for which z-transform can be calculated.
  • ROC can be used to determine causality of the system.
  • ROC can be used to determine stability of the system.

Summary of ROC of Discrete Time Signals for the sequences

Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev

Characteristic Families of Signals and Corresponding ROC
Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev
Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev

Note: X(z) = z{x(n)} ; X1 (z) = Z {xl (n)} ; X2(z) = z{x2 (n)}; Y(z) = z (y (n))
Summary of Properties of z- Transform:
Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev
Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev
Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev

Impulse Response and Location of Poles
Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev
Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev
Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev
Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev
Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev
Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev
Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev
Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev
Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev
Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev
Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev
Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev
Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev
Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev
Study Notes For Z-Transform Electrical Engineering (EE) Notes | EduRev

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