Park Mcclellan Method

• Window and freq sampling methods are simple techniques

• They posses some disadavantages

• They do not have precise control of and • This method is an optimal design criterion

• The weighted approximation error between the desired freq response and actual freq response is evenly spread across both band minimizing the maximum error

• This filter design has ripples in pasband and stopband.

• Design of lowpass with passband edge freq and stopband edge frq

• Passbad filter freq satisfies 1-1+• Stop band filter freq satisfies - • -ripple in passband• -ripple in stop band• M-filter length

Four different cases• 1)symmetric unit sample response and M odd• 2)symmetric unit sample response and M

even• 3)antisymmetric unit sample response and M

odd• 4)anti symmetric unit sample response and M

even

• Symmetric unit sample h(n)=h(M-1-n)and M-odd

• =2• Using k=(M-1)/2 –n and defining a(k) as• a(k)=• We get =

• Symmetric unit sample h(n)=h(M-1-n)and M-even

• =2• Using k=M/2 –n and defining b(k) as• b(k)=• We get =• Rearranging further we get• =• (0)=b(1)/2 and ((M/2)-1) = 2b(M/2)

• Anti Symmetric unit sample h(n)=h(M-1-n)and M-odd

• =2• Using k=M-1/2 –n and defining c(k) as• c(k)=• We get =• Rearranging further we get• =• From above two eq we get (0)+(1/2=(1)

• Anti Symmetric unit sample h(n)=h(M-1-n)and M-even

• =2• Using k=M-1/2 –n and defining d(k) as• c(k)=• We get =• Rearranging further we get• =• From above two eq we get (0)-(1/2=d(1)