2.1  To Learn in This Chapter
2.2  Linear Transform
2.2.1  Matrix multiplication corresponds to a linear transform
2.2.2  Basis: standard, orthogonal and orthonormal
2.3  Advanced: Inner Products to Obtain the Transform Coefficients
2.4  Block Transforms
2.4.1  Advanced: Unitary or orthonormal transforms
2.4.2  DCT transform
2.4.3  DFT transform
2.4.4  Haar transform
2.4.5  Advanced: Properties of orthogonal and unitary transforms
2.5  Fourier Transforms and Series
2.5.1  Fourier series for continuous-time signals
2.5.2  Discrete-time Fourier series (DTFS)
2.5.3  Continuous-time Fourier transform using frequency in Hertz
2.5.4  Continuous-time Fourier transform using frequency in rad/s
2.5.5  Discrete-time Fourier transform (DTFT)
2.6  Relating spectra of digital and analog frequencies
2.7  Advanced: Summary of equations for DFT / FFT Usage
2.7.1  Advanced: Three normalization options for DFT / FFT pairs
2.8  Laplace Transform
2.8.1  Motivation to the Laplace transform
2.8.2  Advanced: Laplace transform basis functions
2.8.3  Laplace transform of one-sided exponentials
2.8.4  Region of convergence for a Laplace transform
2.8.5  Inverse Laplace of rational functions via partial fractions
2.8.6  Calculating the Fourier transform from a Laplace transform
2.9  Z Transform
2.9.1  Relation between Laplace and Z transforms
2.9.2  Advanced: Z transform basis functions
2.9.3  Some pairs and properties of the Z-transform
2.9.4  Region of convergence for a Z transform
2.9.5  Inverse Z of rational functions via partial fractions
2.9.6  Calculating the DTFT from a Z transform
2.10  Applications
2.11  Comments and Further Reading
2.12  Review Exercises
2.13  Exercises