文档介绍：Comb b Filters
• In its most general form, b filter has a
• The simple filters discussed so far are frequency response that is a periodic
characterized either by a single passband function of w with a period 2p/L, where L is
and/or a single stopband a positive integer
• There are applications where filters with • If H(z) is a filter with a single passband
multiple passbands and stopbands are and/or a single stopband, b filter can
required be easily generated from it by replacing
• b filter is an example of such each delay in its realization with L delays
filters resulting in a structure with a transfer
G(z) = H( zL)
1 2 function given by
Copyright © 2001, S. K. Mitra Copyright © 2001, S. K. Mitra
Comb b Filters
• For example, b filter generated from
jw jw the prototype lowpass FIR filter H ( z ) =
• If | H ( e ) | exhibits a peak at w p , then |G(e )| 0
1(1+ z ­ 1 ) has a transfer function
will exhibit L peaks at wpk / L ,0 £ k £ L ­1 2
in the frequency range 0 £ w < 2p G (z) = H (zL ) = 1(1+ z­L )
0 0 2
jw jw
• Likewise, if | H ( e ) | has a notch at w , •| G 0 ( e ) | has L b filter from lowpass prototype
o 1
then | G ( e j w ) | will have L notches at w k / L , at w = (2k+1)p/L and L
o
0 £ k £ L ­ 1 in the frequency range0 £ w < 2p peaks at w = 2p k/L,
0 £ k £ L ­1 , in the
• b filter can be generated from either Magnitude
frequency range
an FIR or an IIR prototype filter
0 £ w< 2p
0
3 4 0 1 2
Copyright © 2001, S. K. Mitra Copyrightw/ p © 2001, S. K. Mitra
Comb b Filters
• For example, b filter generated from
the prototype highpass FIR filterH1(z) = • Depending on applications, comb filters
1(1­ z­1) has a transfer function
2 with other types of periodic magnitude
G (z) = H (zL ) = 1 (1­ z­L ) responses can be easily generated by
1 1 2
jw appropriately choosing the prototype filter
•| G 1 ( e ) | has L b filter from highpass prototype
1 • For example,