A Quadrature Signals Tutorial: Complex, But Not Complicated

Understanding the 'Phasing Method' of Single Sideband Demodulation

Complex Digital Signal Processing in Telecommunications

Introduction to Sound Processing

Introduction of C Programming for DSP Applications

**Search Introduction to Digital Filters**

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An important representation for discrete-time linear systems is the
*state-space* formulation

where is the length

The state-space representation is especially powerful for
*multi-input, multi-output* (MIMO) linear systems, and also for
*time-varying* linear systems (in which case any or all of the matrices
in Eq.(G.1) may have time subscripts ) [37].
State-space models are also used extensively in the field of
*control systems* [28].

An example of a Single-Input, Single-Ouput (SISO) state-space model appears in §F.6.

- Markov Parameters
- Response from Initial Conditions
- Complete Response
- Transfer Function of a State Space Filter

- Transposition of a State Space Filter
- Poles of a State Space Filter
- Difference Equations to State Space
- Converting to State-Space Form by Hand
- Signal Flow Graph to State Space Filter
- Controllability and Observability
- A Short-Cut to Controller Canonical Form
- Matlab Direct-Form to State-Space Conversion
- State Space Simulation in Matlab
- Other Relevant Matlab Functions
- Matlab State-Space Filter Conversion Example

- Similarity Transformations
- Modal Representation
- Diagonalizing a State-Space Model
- Finding the Eigenvalues of A in Practice
- Example of State-Space Diagonalization
- Properties of the Modal Representation

- Repeated Poles

- Digital Waveguide Oscillator Example

- References
- State Space Problems

Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.

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