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Because the coefficients of digital filters are definite, they can be used to achieve much more complex and selective designs – specifically with digital filters, one can achieve a lower passband ripple, faster transition, and higher stopband attenuation than is practical with analog filters.
Even if the design could be achieved using analog filters, the engineering cost of designing an equivalent digital filter would likely be much lower.
Furthermore, one can readily modify the coefficients of a digital filter to make an adaptive filter or a user-controllable parametric filter.
While these techniques are possible in an analog filter, they are again considerably more difficult.

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