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17DigitalFilter

# 17DigitalFilter - MAE 591 RANDOM DATA Digital Filter Analog...

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MAE 591 RANDOM DATA Digital Filter Analog linear filter can be expressed as: y t h x t d ( ) ( ) ( ) = −∞ τ τ τ where x ( t ) and y ( t ) are the filter input and output, and h ( τ ) is the weighting function of filter. And the frequency response of the filter becomes H f h e d i f ( ) ( ) = −∞ τ τ π τ 2 The digital filter structure is the general tapped delay-line filter described by the difference equation: y n b k x n k a m y n m k n m n b a ( ) ( ) ( ) ( ) ( ) = + + = + = + 1 1 1 1 2 1 or equivalently, the z-transform: H z Y z X z b b z b z b n z a z a z a n z b n a n b a ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = = + + + ⋅⋅⋅⋅⋅ + + + + + ⋅⋅⋅⋅⋅ + + 1 2 3 1 1 2 3 1 1 2 1 2 and the Fourier transform: + = = + = = 1 2 ) 1 ( 2 1 2 ) ( 1 ) ( ) ( ) ( ) ( a b n m t m f i n k t fk i e m a e k b f X f Y f H π π Filter structure: y n x n b 1 b 2 b 3 -a 2 -a 3 z -1 z -1 Digital filters may be used for a range of applications such as rejecting unwanted signals, data smoothing, sample rate conversion (upward and downward decimation), zoom analysis and inverse filtering.

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MAE 591 RANDOM DATA Design methodologies for digital filter are categorized by: (rf. The Student Edition of MATLAB , 1992) 1. Infinite impulse response(IIR) filter design using analog prototypes. Analog filters are designed first, when only the magnitude response performance specifications are given, and then transformed into discrete equivalents.
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