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Basics of Digital Filters & Sub-band Coding

Basics of Digital Filters & Sub-band Coding. Gilad Lerman Math 5467 (stealing slides from Gonzalez & Woods). Digital Filters. The basic setting Assumptions: Input and output signals in or ( n -periodic) The filter is linear → matrix representation

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Basics of Digital Filters & Sub-band Coding

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  1. Basics of Digital Filters & Sub-band Coding Gilad Lerman Math 5467 (stealing slides from Gonzalez & Woods)

  2. Digital Filters • The basic setting • Assumptions: • Input and output signals in or (n-periodic) • The filter is linear → matrix representation • The filter is shift invariant, i.e. • 2 & 3 ↔ • representing matrix is Toeplitz • In finite case H = A

  3. Filters or in book notation We note that In particular

  4. Notation

  5. Filters Z-transform Frequency Response Additional factor 2 will make it FT of the l1signal h

  6. FIR • Impulse Response = Filter response to 0 • FIR = Finite Impulse Response • K coefficients → length K filter (convolution is K-periodic) • Example

  7. More on example

  8. Example: Transformations of Filters

  9. Sub-band (two-band) Filters Need to have h0 h1 g0g1 of perfect reconstruction

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