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Matlab: Discrete Linear Systems
 

Matlab: Discrete Linear Systems

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Matlab: Discrete Linear Systems

Matlab: Discrete Linear Systems

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    Matlab: Discrete Linear Systems Matlab: Discrete Linear Systems Presentation Transcript

    • Discrete Linear Systems
    • Discrete Linear Systems
      A discrete linear system is a digital implementation of a linear time-invariant system. A linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that are much simpler than the general, nonlinear case.
    • Discrete Linear Systems
      >> A=[8 -7 6 -5 6 -5 2 -3 2 -1];
      x=[0 1 0 0 0 0 0 0 0 0 ];
      B=conv(A,x);
      subplot(2,3,1); plot(A);
      subplot(2,3,2); plot(x);
      subplot(2,3,3); plot(B);
      x=[0 1 0 0 0 0 0 1 0 0 ];
      B=conv(A,x);
      subplot(2,3,4); plot(A);
      subplot(2,3,5); plot(x);
      subplot(2,3,6); plot(B);
    • Discrete Linear Systems
    • Discrete-Time System Models
      Transfer Function
      Zero-Pole-Gain
      State-Space
      Partial Fraction Expansion (Residue Form)
      Second-Order Sections (SOS)
      Lattice Structure
      Convolution Matrix
    • Discrete-Time System Models
      The transfer functionis a basic z-domain representation of a digital filter, expressing the filter as a ratio of two polynomials.
    • Discrete-Time System Models
      The factored or zero-pole-gain form of a transfer function is
    • Discrete-Time System Models
      It is always possible to represent a digital filter, or a system of difference equations, as a set of first-order difference equations. In matrix or state-space form, we can write the equations as
    • Discrete-Time System Models
      Each transfer function also has a corresponding partial fraction expansion or residue form representation, given by
    • Discrete-Time System Models
      Any transfer function H(z) has a second-order sections representation
    • Discrete-Time System Models
      The function latc2tf calculates the polynomial coefficients for a filter from its lattice (reflection) coefficients. Given the reflection coefficient vector k(above), the corresponding polynomial form is
      b = latc2tf(k)
      b = 1.0000 0.6149 0.9899 -0.0000 0.0031 -0.0082
      The lattice or lattice/ladder coefficients can be used to implement the filter using the function latcfilt.
    • Discrete-Time System Models
      Given any vector, the toolbox function convmtx generates a matrix whose inner product with another vector is equivalent to the convolution of the two vectors. The generated matrix represents a digital filter that you can apply to any vector of appropriate length; the inner dimension of the operands must agree to compute the inner product.
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