Digital signal processing (ohio state ee700)

OpenStax

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Multirate signal processing

1 Fundamentals of multirate signal processing

1.1 Downsampling

1.2 Interpolation

1.3 Application of interpolation - oversampling in cd players

1.5 Resampling with rational factor

1.6 Digital filter design for interpolation and decimation

1.7 Noble identities

1.8 Polyphase interpolation

1.9 Polyphase decimation filter

1.10 Computational savings of polyphase interpolation/decimation

1.11 A group-delay interpretation of polyphase filters

1.12 Polyphase resampling with a rational factor

1.13 Computational savings of polyphase resampling

1.14 Cd to dat conversion

1.15 Polyphase resampling with arbitrary (non-rational or time-varying) rate

1.16 Multi-stage interpolation and decimation

2 Why filterbanks?

Sub-band processing

2.1 Uniform filterbanks

3 Classical filterbanks

Uniform modulated filterbank

3.1 Uniformally modulated (dft) filterbank

3.2 Computational savings of polyphase/dft filterbanks

3.3 Drawbacks of classical filterbank designs

4 Modern filterbanks

Aliasing-cancellation conditions of filterbanks

4.1 Two-branch quadvalue mirror filterbank (qmf)

4.2 Perfect reconstruction qmf

4.3 Johnston's qmf banks

4.4 Perfect reconstruction fir filter banks

4.5 Orthogonal perfect reconstruction fir filterbank

4.6 Design of orthogonal pr-fir filterbanks via halfband spectral factorization

4.7 Bi-orthogonal perfect reconstruction fir filterbanks

4.8 Filterbanks with > 2 branches

5 Time frequency analysis and continuous wavelet transform

Why transforms?

5.1 Limitations of fourier analysis

5.2 Time-frequency uncertainty principle

5.3 Short-time fourier transform

5.4 Continuous wavelet transform

6 Hilbert space theory

Hilbert space theory

6.1 Vector space

6.2 Normed vector space

6.3 Inner product space

6.4 Hilbert spaces

7 Discrete wavelet transform

Discrete wavelet transform: main concepts

7.1 The haar system as an example of dwt

7.2 A hierarchy of detail in the haar system

7.3 Haar approximation at the kth coarseness level

7.4 The scaling equation

7.5 The wavelet scaling equation

7.6 Conditions on h[n] and g[n]

7.7 Values of g[n] and h[n] For the haar system

7.8 Wavelets: a countable orthonormal basis for the space of square-integrable

7.9 Filterbanks interpretation of the discrete wavelet transform

7.10 Initialization of the wavelet transform

7.11 Regularity conditions, compact support, and daubechies' wavelets

7.12 Computing the scaling function: the cascade algorithm

7.13 Finite-length sequences and the dwt matrix

7.14 Dwt implementation using ffts

7.15 Dwt applications - choice of phi(t)

7.16 Dwt application - de-noising

Source: OpenStax, Digital signal processing (ohio state ee700). OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10144/1.8

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