Filter synthesis

Design of a filter with specified characteristics based on following definition

 

 

Different ways of approximating the ideal "brick wall" filter:

 

• Butterworth

o Defined by

             N ... filter order

                                                         W ... normalized frequency

                                                         W_c ... cutoff frequency

o Maximally flat filter magnitude responses with no consideration of phase linearity or group delay considerations

o DC gain is 1

o Magnitude response is a monotonically decreasing function of frequency

o No ripples

• Bessel

o The most linear phase response of all IIR filters with no consideration of the frequency magnitude response

o Maximally constant group delay

• Chebyshev

o Passband, or stopband, ripples constrained within fixed bounds

o Two families

• Type I
  Ripples in the passband and flat stopband

• Type II
  Flat passband and ripples in the stopband

o Cannot have ripples in both the passband and the stopband

o Have steeper transition region roll-off
but more nonlinear phase response characteristics than Butterworth filters

• Cauer (Elliptic)

o Sharpest roll-off for a given number of filter coefficients

o Poorest phase linearity of the most common IIR filter design functions

o Ripple in passband and stopband are equal

 

Two categories of analogue filters

• Continuous time filters
• Discrete time filters (switch-capacitor filters)