# Basics of Digital Filters & Sub-band Coding - PowerPoint PPT Presentation

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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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## Basics of Digital Filters & Sub-band Coding

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

• The filter is shift invariant, i.e.

• 2 & 3 ↔

• representing matrix is Toeplitz

• In finite case H = A

### Filters

or in book notation

We note that

In particular

Notation

### Filters

Z-transform

Frequency Response

Additional factor 2 will make it FT of the l1signal h

### FIR

• Impulse Response = Filter response to 0

• FIR = Finite Impulse Response

• K coefficients → length K filter (convolution is K-periodic)

• Example

### More on example

Example: Transformations of Filters

Sub-band (two-band) Filters

Need to have h0 h1 g0g1 of perfect reconstruction