Filtering and Analysis Functions

Filtering

Filter Analysis

1.zero,pole-->transfer function form

[b,a] = zp2tf(zer,pol,1);
fvtool(b,a)

2.transform function-->zero/polo

fvtool(b,a,‘Analysis‘,‘polezero‘)

zplane(b,a)

3.Z-transform frequency response of a digital filter.

[h,w] = freqz(b,a,p)

returns the p-point complex frequency response, H(ejω), of the digital filter.

For example, a ninth-order Butterworth lowpass filter with a cutoff frequency of 400 Hz, based on a 2000 Hz sampling frequency, is

[b,a] = butter(9,400/1000);

To calculate the 256-point complex frequency response for this filter, and plot the magnitude and phase with freqz, use

freqz(b,a,256,2000)

4.filter

Use filter in the form y = filter(d,x) to filter an input signal, x, with a digitalFilter, d, and obtain output data, y.

5.designfilt(https://ww2.mathworks.cn/help/signal/ref/designfilt.html)

Use designfilt in the form d = designfilt(resp,Name,Value) to design a digital filter, d, with response type resp. Specify the filter further using a set of Name,Value pairs.

Type d.Coefficients to obtain the coefficients of a digitalFilter, d. For IIR filters, the coefficients are expressed as second-order sections.

Lowpass IIR Filter

Design a lowpass IIR filter with order 8, passband frequency 35 kHz, and passband ripple 0.2 dB. Specify a sample rate of 200 kHz. Visualize the magnitude response of the filter. Use it to filter a 1000-sample random signal.

lpFilt = designfilt(‘lowpassiir‘,‘FilterOrder‘,8, ...
         ‘PassbandFrequency‘,35e3,‘PassbandRipple‘,0.2, ...
         ‘SampleRate‘,200e3);
fvtool(lpFilt)

dataIn = randn(1000,1);
dataOut = filter(lpFilt,dataIn);

Output the filter coefficients, expressed as second-order sections.

sos = lpFilt.Coefficients

sos = 4×6

    0.2666    0.5333    0.2666    1.0000   -0.8346    0.9073
    0.1943    0.3886    0.1943    1.0000   -0.9586    0.7403
    0.1012    0.2023    0.1012    1.0000   -1.1912    0.5983
    0.0318    0.0636    0.0318    1.0000   -1.3810    0.5090

Bandpass FIR Filter

Design a 20th-order bandpass FIR filter with lower cutoff frequency 500 Hz and higher cutoff frequency 560 Hz. The sample rate is 1500 Hz. Visualize the magnitude response of the filter. Use it to filter a random signal containing 1000 samples.

bpFilt = designfilt(‘bandpassfir‘,‘FilterOrder‘,20, ...
         ‘CutoffFrequency1‘,500,‘CutoffFrequency2‘,560, ...
         ‘SampleRate‘,1500);
fvtool(bpFilt)

dataIn = randn(1000,1);
dataOut = filter(bpFilt,dataIn);

Output the filter coefficients.

b = bpFilt.Coefficients

b = 1×21

   -0.0113    0.0067    0.0125   -0.0445    0.0504    0.0101   -0.1070    0.1407   -0.0464   -0.1127    0.1913   -0.1127   -0.0464    0.1407   -0.1070    0.0101    0.0504   -0.0445    0.0125    0.0067   -0.0113 ?

6.fvtool

fvtool(b,a)
fvtool(sos)
fvtool(d)
fvtool(b1,a1,b2,a2,...,bN,aN)
fvtool(sos1,sos2,...,sosN)
fvtool(Hd)
fvtool(Hd1,Hd2,...,HdN)
h = fvtool(...)

Use fvtool to visualize a digitalFilter, d.

Matlab filter常用函數