Ooops, the example I gave the other day was incorrect. This is what it should have been: Let N(z) = (1 + z^-1)^p = b(z^2) + c(z^2)/z (for p >= 2) Then H(z) = N(z)/b(z^2) is linear phase IIR. example: take p=3 N(z) = 1 + 3*z^-1 + 3*z^-2 + z^-3 = (1 + 3*z^-2) + (3 + z^-2)/z b(z^2) = 1 + 3*z^-2 Butterworth wavelets (Martin Viterli, et al) fall into this group. -chatonda --- Tirthankar De <> wrote: > Dear ALL, > > This is the first time am writing something to this group........ > > Coming straight to the point of linear phase IIR Filter design. > > Yes, it is possible to design linear phase IIR Filter. > > To prove above point......lets start with the very basic thing which is > pretty clear to all.....The Linear Phase FIR Filter. > > Here let say A0, A1, A2, A3, A4,.....Ap (0 <= p < N) are the coefficients. > Then......... > > N-1 > _ > Yn = \ (Ap * Xn-p) > /_ > p=0 > > Taking Z Transform on both sides we have......... > N-1 > _ -p > Y(z) = \ [ Ap * X(z) * z ] > /_ > p=0 > N-1 > _ -p > H(z) = Y(z) = \ [ Ap * z ] > X(z) /_ > p=0 > > -jkw/N > H(w) = M(w) * e .....................Here M(w) is Magnitude response > and other is Linear Phase > response > also k = 0......N-1 > > Now lets invert the above equation..... > > -jkw/N > Hi(w) = Y(w) = 1 / [ M(w) * e ] > X(z) > > N-1 > _ -p > Hi(z) = Y(z) = 1 / { \ [ Ap * z ] } > X(z) /_ > p=0 > > N-1 > _ -p > \ [ Ap * Y(z) * z ] = X(z) > /_ > p=0 > N-1 > _ > \ (Ap * Yn-p) = Xn > /_ > p=0 > > N-1 > _ > A0*Yn + \ (Ap * Yn-p) = Xn > /_ > p=1 > N-1 > _ > Yn = B0*Xn - \ (Bp * Yn-p) ..........Here Bp = Ap/A0 > /_ where 0 <= p < > N > p=1 > > Above equation is a linear Phase IIR. > > Hence, > a LPF in FIR can be represented as a HPF in IIR > a BPF in FIR can be represented as a BSF in IIR > > and vice versa........(As frequency domain response is reversed) > > Hope this explanation suffice your requirement. > > Well thats it!.......this is tirthankar signin off.......till then take care.....BYE > > --------------------------------- > Want to chat instantly with your online friends?Get the FREE Yahoo!Messenger ===== __________________________________ |