https://github.com/youssef-ashraf71/analog-filters
A repository for signals course tasks using Matlab
https://github.com/youssef-ashraf71/analog-filters
low-pass-filters matlab transfer-function
Last synced: about 1 year ago
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A repository for signals course tasks using Matlab
- Host: GitHub
- URL: https://github.com/youssef-ashraf71/analog-filters
- Owner: Youssef-Ashraf71
- Created: 2022-06-01T15:07:38.000Z (about 4 years ago)
- Default Branch: main
- Last Pushed: 2022-06-02T00:15:22.000Z (about 4 years ago)
- Last Synced: 2025-02-11T17:16:55.191Z (over 1 year ago)
- Topics: low-pass-filters, matlab, transfer-function
- Language: MATLAB
- Homepage:
- Size: 50.8 KB
- Stars: 0
- Watchers: 1
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Bio-Signals Tasks
## Contributors
Mariam Ahmed
# Main Points :
* The magnitude and phase characteristics of the 3-pole Butterworth low-pass filter
* Low Pass to Low pass Filters
* Low Pass to Band Pass Filters
* Low Pass to Band Elimination Filters
## Task 1 Q1 :
```
Use the MATLAB bode function to plot the magnitude and phase
characteristics of the 3-pole Butterworth low-pass filter with unity gain and
normalized frequency at ω = 1 rad/sec. Print your code, results and figures.
```
## Solution :
Using the general rule at k=3 :
```
>> % it is a 3-pole Butterworth low-pass filter
>> % thus k=3 >> for the G(s)
>>
>> % Parameters : W = 1 rad/sec , b0=1 , a0=1 , a1=2 , a2=1 , a3=1
>> % let us Create 2 vectors carrying the coefficents of bn and an >> b & a Respectively
>> b = [0 0 0 1]
b =
0 0 0 1
>> a = [ 1 2 2 1 ]
a =
1 2 2 1
>> % now send them to bode to start plotting magnitude and phase where W =1 rad/sec
>> bode(b,a)
>> % to add grid lines we will use Grid Command where grid on displays the major grid lines for the current axes
>> grid
>>
```
## Task 1 Q2 :
```
Use the MATLAB buttap and lp2lp functions to find the transfer function
of a third-order Butterworth low-pass filter with cutoff frequency fc =
2KHz. Then, plot its frequency response. Print your code, results and figures.
```
## Solution :
```
% it is a 3-pole Butterworth low-pass filter with cut off freq fc=2KHz
[zeros , poles , k] = buttap(3);
% calcuate coeffecients of b(numerator) and a (denominator)
[b,a] = zp2tf ( zeros, poles , k);
% range the frequency and convert it to rad/sec(angular)
freq = 1000:30:10000;
w = 2*pi*freq;
% declare cutoff frequency and convert it to rad/sec(angular)
freqc = 2*1000 ; % we multiplied by 1000 to convert kHZ to HZ
wc = 2*pi*freqc;
% here calculate the new coefficents after low pass to low pass filter
% let their names bnew , anew
% for explaination we are converting from analog values to angular domain
[ bnew , anew ] = lp2lp(b , a, wc);
% lets calculate The transfer function of the new filtered
Gofs = freqs(bnew , anew , w);
semilogx(w, abs(Gofs)); % plot it
% add grid lines
grid;
hold on ;
title('Frequency respone plot for 3rd-order Butterworth low-pass filter with fc = 2KHz');
xlabel('Angular Frequency in :(rad/sec)');
ylabel('Magnitude of the Transfer Function in (dB) ');
```
## Task 2 Q1 :
```
Use the MATLAB functions buttap and lp2bp to find the transfer function
of a 3-pole Butterworth analog band-pass filter with the pass band
frequency centered at f0 = 4 KHz, and bandwidth BW = 2 KHz. Then, plot
its frequency response. Print your code, results and figures.
```
## Solution :
```
% it is a 3-pole Butterworth low-pass filter with pass band freq fo=4KHz , bandwidth = 2KHZ
[zeros , poles , k] = buttap(3);
% calcuate coeffecients of b(numerator) and a (denominator) of the filter
[b,a] = zp2tf ( zeros, poles , k);
% declare band pass frequency f0=4KHZ and convert it to rad/sec(angular)
freq = 100:100:100000;
freqc = 4000 ;
wc = 2*pi*freqc ;
% declare bandwidth frequency bwf= 2KHZ and convert it to rad/sec(angular)
bwf = 2000;
wband = 2*pi*bwf ;
% here calculate the new coefficents after low pass to band pass filter
% let their names bnew , anew
% for explaination we are converting from analog values to angular domain
[ bnew , anew ] = lp2bp(b , a, wc , wband );
% lets calculate the transfer function of the band-pass filter
w =2*pi*freq ;
Gofs = freqs(bnew , anew , w);
semilogx(freq, abs(Gofs)); % plot freq response in hertz
% add grid lines
grid;
hold on;
title('Frequency respone plot for 3rd-order Butterworth band-pass filter with fo=4kHZ , Bw = 2KHZ');
xlabel('Frequency in :(HZ)');
ylabel('Magnitude of the Transfer Function in (dB)');
```
## Task 2 Q2 :
```
Use the MATLAB functions buttap and lp2bs to find the transfer function of
a 3-pole Butterworth band-elimination (band-stop) filter with the stop band frequency
centered at f0 = 5 KHz, and bandwidth BW = 2 KHz. Then, plot its frequency response.
Print your code, results and figures.
```
## Solution :
```
% it is a 3-pole Butterworth with stop band frequency centered at f0 = 5 KHz , and bandwidth BW = 2 KHz
[zeros , poles , k] = buttap(3);
% calcuate coeffecients of b(numerator) and a (denominator)
[b,a] = zp2tf ( zeros, poles , k);
% declare band pass frequency f0=5KHZ and convert it to rad/sec(angular)
freq = 100:100:100000;
freqc = 5000 ;
wc = 2*pi*freqc ;
% declare bandwidth frequency bwf= 2KHZ and convert it to rad/sec(angular)
bwf = 2000;
wband = 2*pi*bwf ;
% here calculate the new coefficents after low pass to stop pass filter
% let their names bnew , anew
% for explaination we are converting from analog values to angular domain
[ bnew , anew ] = lp2bs(b , a, wc , wband );
% lets calculate the transfer function of the stop-pass filter
w =2*pi*freq ;
Gofs = freqs(bnew , anew , w);
semilogx(freq, abs(Gofs)); % plot freq response in hertz
% add grid lines
grid;
hold on;
title('Frequency respone plot for 3rd-order Butterworth band-elimination filter with fo=5kHZ , Bw = 2KHZ');
xlabel('Frequency in :(HZ)');
ylabel('Magnitude of the Transfer Function in (dB)');
```
