Nuhertz

Constricted Passband Equiripple


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Chebyshev I and Elliptic filters are famous for their flat equiripple passbands.  However, many applications require a flat equiripple effect only for frequencies nearer to the cutoff frequency.  In these situations, a totally flat equiripple passband is detrimental in that it unnecessarily reduces the rate of attenuation at the band edge and possibly requires a higher order filter.

Filter Solutions removes this potential waste of quality by optionally constricting the equiripple effect to a percentage of the passband.  For example, if the quality of a low pass passband is not an issue for the lower 50%, the equiripple may be constricted to the upper 50%.  The rate of attenuation at the band edge is then increased, and the order of the filter could possibly be reduced.  Likewise, ff the stop band attenuation is fixed for an Elliptic filter, the stop band ratio could be increased slightly and possibly reduce the required order.

Filter Solutions supports constricted equiripple passbands for both odd order and even order filters and for any user-entered percent restriction.


Examples:

 The following examples are for 9th order Chebyshev and Elliptic filters with a 0.1dB equiripple pass band.  The Elliptic stop band ratio is set to 0.1.  It is easily seen that for both filters, the constriction of the equiripple in the passband produces increased attenuation in the stop band, and possible may lead to a smaller required order of filter.  Note that the Elliptic passband ripple is already pushed closer to the band edge and therefore requires a smaller percentage of constriction.

 

Chebyshev Example

Elliptic Example
Normal Chebyshev Response
Normal Chebyshev Response
Normal Elliptic Response
Normal Elliptic Response
55% Restricted Equiripple Chebyshev Response
55% Restricted Equiripple Chebyshev Response
40% Restricted Equiripple Elliptic Response
40% Restricted Equiripple Elliptic Response
55% Restricted Equiripple Chebyshev Response
55% Restricted Equiripple Chebyshev Response
40% Restricted Equiripple Elliptic Passband
40% Restricted Equiripple Elliptic Passband