1. Homework question 1

2. Question When designing the filter using [b,a] = ellip(7,1,80,0.95) we have a functional reconstruction filter. However if you try different values for the 4th argument to the ellip function (this argument is the normalized cut off frequency) you can get some pretty weird results. Try [b,a] = ellip(7,1,80,0.9999) 2

3. You could check How many orders do you need? [n,Wp] = ellipord(Wp,Ws,Rp,Rs) Stability ? [z,p,k] = ellip(n,Rp,Rs,Wp) It returns the zeros and poles in length n column vectors z and p and the gain in the scalar k. zplane(z,p); – Limitations For higher order filters, numerical problems due to roundoff errors may occur when forming the transfer function using the [b,a] syntax. 3

4. Limitation check example n = 7; Rp = 1; Rs = 40; Wn = 0.50; ftype = 'low'; % Transfer Function design [b,a] = ellip(n,Rp,Rs,Wn,ftype); h1=dfilt.df2(b,a); % This is an unstable filter. % Zero-Pole-Gain design [z, p, k] = ellip(n,Rp,Rs,Wn,ftype); [sos,g]=zp2sos(z,p,k); h2=dfilt.df2sos(sos,g); % Plot and compare the results hfvt=fvtool(h1,h2,'FrequencyScale','log'); legend(hfvt,'TF Design','ZPK Design') 4

5. Limitation check example n = 7; Rp = 1; Rs = 40; Wn = 0.9999; ftype = 'low'; % Transfer Function design [b,a] = ellip(n,Rp,Rs,Wn,ftype); h1=dfilt.df2(b,a); % This is an unstable filter. % Zero-Pole-Gain design [z, p, k] = ellip(n,Rp,Rs,Wn,ftype); [sos,g]=zp2sos(z,p,k); h2=dfilt.df2sos(sos,g); % Plot and compare the results hfvt=fvtool(h1,h2,'FrequencyScale','log'); legend(hfvt,'TF Design','ZPK Design') 5