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Thesis - Leigh Moody.pdf - Bad Request - Cranfield University

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Appendix I / Utilities / Digital Filters<br />

_ _<br />

22.8.5 Digital Notch Filters<br />

D_NOTCH propagates up to 50 digital notches over time interval (∆t), with<br />

time varying characteristics.<br />

y<br />

: = D_NOTCH<br />

ϕ<br />

DN<br />

( X , ∆t<br />

, t , t , t , t , N , I )<br />

( X , t , t , t , t )<br />

I<br />

I<br />

22.8-4<br />

N1<br />

≡<br />

N2<br />

N1<br />

D1<br />

N2<br />

D2<br />

D1<br />

D2<br />

Equation 22.8-21<br />

These filters are the discrete equivalent to the continuous transfer function:<br />

ξ<br />

4<br />

ξ<br />

ξ<br />

ξ<br />

ξ<br />

⋅ χ<br />

⎛<br />

2<br />

1 + t ⋅ s + t ⋅ s ⎞<br />

y<br />

⎜<br />

⋅ 2<br />

1 t D1<br />

s t D2<br />

s ⎟<br />

⎝ + ⋅ + ⋅ ⎠<br />

k<br />

N1 N2<br />

( s ) : = ⎜<br />

⎟ XI<br />

( k −1<br />

) ⋅ ξ3<br />

− ξ5<br />

⋅ χk<br />

1 − ξ6<br />

⋅ χk<br />

2<br />

: = XI<br />

−<br />

−<br />

( ξ ⋅ χ + ξ ⋅ χ )<br />

−1<br />

yk : = χk<br />

− 2 + ξ3<br />

⋅ 1 k 2 k −1<br />

1<br />

3<br />

4<br />

6<br />

2<br />

( 2 ⋅ t ∆t<br />

) + ( 4 ⋅ t t )<br />

: = 1 +<br />

∆<br />

ξ<br />

2<br />

N1<br />

N2<br />

2<br />

( 1 − ( 4 ⋅ t t ) )<br />

: = 2 ⋅<br />

∆<br />

N2<br />

2<br />

( 2 ⋅ t ∆t<br />

) + ( 4 ⋅ t t )<br />

: = 1 −<br />

∆<br />

N1<br />

N2<br />

2<br />

( 2 ⋅ t ∆t<br />

) + ( 4 ⋅ t t )<br />

: = 1 +<br />

∆<br />

ξ<br />

5<br />

D1<br />

D2<br />

2<br />

( 1 − ( 4 ⋅ t t ) )<br />

: = 2 ⋅<br />

∆<br />

D2<br />

2<br />

( 2 ⋅ t ∆t<br />

) + ( 4 ⋅ t t )<br />

: = 1 −<br />

∆<br />

D1<br />

D2<br />

Equation 22.8-22<br />

Equation 22.8-23<br />

Equation 22.8-24<br />

Equation 22.8-25<br />

Equation 22.8-26<br />

Equation 22.8-27<br />

Equation 22.8-28<br />

Equation 22.8-29<br />

Equation 22.8-30

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