Implement and design filter Name Thinh Nguyen Van Lab Partner(s): Lab Date: May 24, 2011 Repetition: Introduction: What is the purpose of this lab? Implement and design:

1. Low pass filter 2. High pass filter 3. Band pass filter

Hypothesis: (Predict the outcome(s) of the experiment)

1. In low pass filter, only signals whose frequency is below the cutoff frequency can pass.

2. In high pass filter, only signals whose frequency is above the cutoff frequency can pass

3. In band pass filter, signals whose frequency is in between two frequencies can pass Procedures: (What steps did you take to accomplish this lab assignment?) I do this experiment in two ways: Simulink and *.m file. Method1: Using Simulink: Design the Simulink diagram as following figure:

Fig1: Simulink schematic filters

The parameters of low pass filter, high pass filter, band pass filter is set :

Fig2: Low pass filter parameters

Fig3: High pass filter parameters

I change the frequency value of the source (sine source) to see the result in the output. I design the low pass filter, high pass filter and band pass filter all in a Simulink window.

Method2: Using script file. We can use many algorithms to design filter such as Butterworth, Chebysev1, Chebysev2, Elliptic, Bessel. In this report, I use butterworth as an sample for designing, The other algorithms is similarity.

Butterworth algorithm to design a low pass filter, a high pass filter, a band pass filter. The *m.file in matlab is implemented as follow:

1. Low pass filter:

% For data sampled at 1000Hz, design a lowpass filter with less than 3dB of % ripple in the passband, defined from 0 to 40 Hz, and at least 60dB of % attenuation in the stopband, definde from 150Hz to Nyquist frequency % (500HZ). Plot the filter's frequency response. Wp=40/500; Ws=150/500; Rp=3; Rs=60; [n,Wn]=buttord(Wp,Ws,Rp,Rs) [b,a]=butter(n,Wn,'low') freqz(b,a,512,1000)

2. High pass filter:

% For data sampled at 1000Hz, design a heighpass filter with less than 3dB of % ripple in the passband, defined from 150 Hz, and at least 60dB of % attenuation in the stopband, definde from 0-40 Hz to Nyquist frequency % (500HZ). Plot the filter's frequency response. Wp=150/500; Ws=40/500; Rp=3; Rs=60; [n,Wn]=buttord(Wp,Ws,Rp,Rs); [b,a]=butter(n,Wn,'high') freqz(b,a,512,1000)

Fig4: Band pass filter parameters

3. Band pass filter: % Design a bandpass filter with passband of 60Hz to 200Hz with less than % 3dB of ripple in the passband, and 40dB attenuation in the stopbands % that are 50Hz wide on both sides of the passband. Wp=[60 200]/500; Rp=3; Rs=60; Ws=[10 250]/500; [n,Wn]=buttord(Wp,Ws,Rp,Rs) [b,a]=butter(n,Wn) freqz(b,a,512,1000)

Method 3: Using FDAtool In matlab command window, type the command ‘fdatool’ for opening the filter design and analysis tool. Fill the parameters in to design a filter. I design a filter with parameters as follow:

Response type

Design method

Filter order

Density factor

Fs Fpass Fstop Apass Astop

Low pass FIR Equiripple

Minimum order

20 4800 200 800 1dB 80dB

The Filter design and analysis tool window shown should be:

The high pass filter and band pass filter is total similar to low pass filter design. There for, I don’t express here.

Results: (Show your results)

1. Method1 (Simulink result): a. Low pass filter:

Source frequency

Tested Source

Comment Signal

Fig5: FDA tool in filter design

range frequency W<=1047 w= 1000 Signal

passes the filter. Magnitude is conserved totally.

1047<W <1570

w=1200 Signal is attenuated

w>1570 w=1600 Filter stops all signal.

b. High pass filter:

Source frequency

Tested source frequency

Comment signal

W<1047 w=1000 Signal is stopped.

1047<W<1570 w=1200 Signal attenuate.

w>1570 w=1600 Signal is conserved

c. Band pass filter:

Source frequency W=2*pi*f/Fs

Test source frequency

Comment signal

w < 523 w=500 Signal is stopped.

523<w<1047 W=1000 Signal attenuate partly.

1047<w<1570 w=1200 Signal passes totally.

1570<w<2355 W=2000 Signal attenuates partly.

w>2355 W=2500 Signal is stopped.

2. Method2 (Script file result):

Fig6: Low pass filter signal

Fig7: High pass filter design

Fig8: Band pass filter design.

3. Method3 (FDAtool)

The magnitude response of the filter be shown as follow:

Conclusion: (What did you learn? What conclusions can you draw form the results of this

lab assignment? Compare the results of the experiment with you hypothesis.) The result in Matlab simulation is match with the prediction in hypothesis part. The low pass filter is used to take away the signal whose frequency is greater than cutoff

frequency. In contrast, high pass filter is used to take away the frequency that smaller cutoff frequency. The band pass filter is the combination of both low pass filter and band pass filter.

By using matlab simulation, we can design the filters as be shown in previous parts.

Fig9: Filter in FDA tool