Digital Signal Processing Experiment (v) Design of--IIR filter

I. Using the self-coding function to design IIR filter 1, impulse response method

(1) The digital filter indicator given in the note is first modeled as a simulation indicator

(2) Design the analog filter:

(3) Convert to digital filter using impulse response method

(4) a demo

Clear All;wp=0.2*pi; %Digital Indicator WS=0.3*Pi; Rp=1; as= the; T=1; fs=1/T;%Impulse response method [Cs,ds]=afd_butt (wp/t,ws/t,rp,as); [B,a]=IMP_INVR (cs,ds,t); [C,b,a]=Dir2par (B,a) [Db,mag,pha,grd,w]=freqz_m (b,a); figure (1) Subplot (2,2,1), Plot (W/pi,mag), title ('amplitude'); Grid;axis ([0,1,0,1.1]); subplot (2,2,2), Plot (w/pi,db), title ('amplitude in db'); Grid;axis ([0,1,- -,5]); subplot (2,2,3), Plot (W/PI,PHA/PI), title ('Phase'); Grid;axis ([0,1,-1,1]); subplot (2,2,4), Plot (W/PI,GRD), title ('Group Delay'); Grid;axis ([0,1,0,Ten]);

2. Design IIR with bilinear method

(1) Pre-distortion:

(2) Design of low-pass filter

(3) Convert to digital filter

(4) a demo

%= (2/t) *tan (wp/2= (2/t) *tan (ws/2);             %= Afd_butt (omegap,omegas,rp,as); %== Dir2cas (b,a) [db,mag,pha,grd,w]=freqz_m (b,a);

Second, Matlab self-function design 1, analog low-pass filter to digital filter design

(1) Design the order n and cutoff frequency of the analog filter according to the digital index

(2) to find a low-pass analog prototype filter

(3) As the resulting result is a 0-pole type, it must also be converted to b/a type, usable function ZP2TF

[Bap,aap]=zp2tf (Z,p,k)

(4) Convert analog filter to digital filter

(Low-pass, high-pass, band-pass, Band-stop) available functions LP2LP, Lp2hp,lp2bs, lp2bp.

(5) Calculating the amplitude frequency, phase frequency and impulse response of the filter

(6) a demo

wp=0.2*pi; rp=1; Ws=0.3*pi; as= the; [N,wn]=buttord (Wp,ws,rp,as,'s') [Z,p,k]=Buttap (n); [Bap,aap]=ZP2TF (z,p,k) [B,a]=LP2LP (BAP,AAP,WN); [Db,mag,pha,w]=freqs_m (B,a,0.5*pi); [Ha,x,t]=Impulse (b,a); figure (1) Subplot (2,2,1), Plot (W/pi,mag), title ('amplitude'); Subplot (2,2,2), Plot (w/pi,db), title ('amplitude in db'); subplot (2,2,3), Plot (W/PI,PHA/PI), title ('Phase'); Subplot (2,2,4), Plot (T,ha), title ('Impulse Response'); figure (2) Freqs (b,a);

2, direct digital filter design

(1) According to the given indicators, the low-pass analog prototype filter order and cutoff frequency:

[N,wn]=Buttord (Wp,ws,rp,as) [N,wn]=cheb1ord (wp,ws,rp,as)

(2) The digital filter is obtained directly, and the function butter,cheby1,cheby2 is used.

[b,a]=butter (n,wn, ' ftype ') [B,a]=cheby1 (n, rp,wn, ' ftype ')  ; ' ftype ' means: ' low ', ' bandpass ', ' High ', ' Stop

(3) Calculating the amplitude frequency, phase frequency and group delay of the filter

[Db,mag,pha,grd,w]=freqz_m (b,a);(P 258) directly draw the amplitude and phase frequency characteristics: FREQZ (b,a) (Matlab comes with)

(4) a demo

wp=0.2; rp=1; ws=0.3; as= the; [N,wn]=Buttord (Wp,ws,rp,as) [B,a]=butter (N,WN); [Db,mag,pha,grd,w]=freqz_m (b,a); figure (3) Subplot (2,2,1), Plot (W/pi,mag), title ('amplitude'); grid; Subplot (2,2,2), Plot (w/pi,db), title ('amplitude in db'); grid; Subplot (2,2,3), Plot (W/PI,PHA/PI), title ('Phase'); Grid;subplot (2,2,4), Plot (W/PI,GRD), title ('Group Delay'); Grid;figure (4); Freqz (B,a)

Ps:

MATLAB, the digital angular frequency is normalized, that is, 0-1 means 0-pi

Frequency is given in Hz, which means analog frequency, so the direct design of the filter using MATLAB, the first to be converted into a digital frequency.

Example: wp=[100 200]*2/fs

Digital Signal Processing Experiment (v) Design of--IIR filter