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Professor A G Constantinides 1 Digital Filters Filtering operation Time kGiven signal OPERATION 0 14.014.0 21.12.5 3-21.6-9.3 4-3.6-20.1 5-4.7-28.8 ADD 4.0 + 1.1 - 21.6 - 3.6 =

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Professor A G Constantinides 2 Digital Filters Filtering

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Professor A G Constantinides 3 Digital Filters Filtering + -

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Professor A G Constantinides 4 Digital Filters Filtering Basic operations required (a)Delay (b)Addition (c)Multiplication (Scaling)

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Professor A G Constantinides 5 Digital Filters Filtering: More general operation INPUT OUTPUT + + + + + + +

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Professor A G Constantinides 6 Digital Filters Impulse response Most general linear form Recursive or Infinite Impulse Response (IIR) filters

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Professor A G Constantinides 7 Digital Filters A simple first order

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Professor A G Constantinides 8 Digital Filters Transfer function For FIR

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Professor A G Constantinides 9 Digital Filters-Stability For IIR Stability: Note that

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Professor A G Constantinides 10 Digital Filters Thus there is a pole at if its magnitude is more than 1 then the impulse response increases without bound if its magnitude is less than 1 decreases exponentially to zero Frequency Response: Set and

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Professor A G Constantinides 11 Digital Filters So that And hence Compare with transfer function

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Professor A G Constantinides 12 Digital Filters In the initial example or And thus

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Professor A G Constantinides 13 2-D z tranform 2-D z-transform Example:

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Professor A G Constantinides 14 2-D z tranform And hence (i)Separable transforms. (ii)Non-separable transforms.

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Professor A G Constantinides 15 2-D Digital Filters 2-D filters Thus we can have (a)FIR 2-D filters and (b)IIR 2-D filters

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Professor A G Constantinides 16 2-D Digital Filters Transfer function For convolution set

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Professor A G Constantinides 17 2-D Digital Filters Filtering a 02 a 01 a 00 a 12 a 11 a 10 a 22 a 21 a 20 b 02 b 01 b 12 b 11 b 10 b 22 b 21 b 20 Typical N 1 = N 2 = M 1 = M 2 IIR= 2 arrangement.

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Professor A G Constantinides 18 2-D Digital Filters (a) Separable filters (b) Non-separable filters is not expressible as a product of separate and independent factors

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Professor A G Constantinides 19 Ideal filters 1 1 1 1 0 0 0 0

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Professor A G Constantinides 20 Ideal filters

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Professor A G Constantinides 1 Interpolation & Decimation Sampling period T, at the output Interpolation by m: Let the OUTPUT be [i.e. Samples exist at.

Professor A G Constantinides 1 Interpolation & Decimation Sampling period T, at the output Interpolation by m: Let the OUTPUT be [i.e. Samples exist at.

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