A detailed information about Filters i.e Band Pass , High Pass and Low pass Filters as well as methods of Echelon and Reduced Echelon Form in Matlab.

1. Echelon And Reduced Echelon
Forms &
Filters

2. Zahid
ALi
Presented By:
Zahid ALi

3. Contents
 Matrix And Row Operations
 Echelon Form
 Reduced Echelon Form
 Low pass Filter
 High Pass Filter
 Band pass Filter
 References

4. Matrix And Row Operations
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mnmmm
n
n
n
aaaa
a
a
a
aaa
aaa
aaa
A
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321
3
2
1
333231
232221
131211row
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mnmmm
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a
a
a
aaa
aaa
aaa
A
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321
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333231
232221
131211
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mnmmm
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321
3
2
1
333231
232221
131211

5. Matrix And Row Operations(Cont.)
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44434241
34333231
24232221
14131211
aaaa
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A

6. Matrix And Row Operations(Cont.)
 Interchange any two rows.
 Multiply every element in a row by a non zero constant.
 Add element of one row to corresponding elements of the another row.

8. Echelon Form
 We use Row Operations to make the matrix look like above.
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#100
##10
###1

9. x +2y +z = 1
3x +5y+z = 3
2x +6y +7z = 1
Just Pick off the coefficient and put them in Matrix
And that Matrix will be called Augmented Matrix
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1762
3153
1121

10. -3r1+r2
-3r1
-r2
-3 -6 -3 -3
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1762
3153
1121
-3 -5 -1 -3
0 -1 -2 0
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
1762
0210
1121
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1762
0210
1121
-2r1+r3
-2r1
r3
-2 -4 -2 -2
0 2 5 -1
2 6 7 1

11. 
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1520
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1121
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#100
##10
###1
-r2
-2r2
+r3
0 -2 -4 0
0 2 5 -1
0 0 1 -1
-2r2+r3
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1100
0210
1121
SAME
Echelon Form

12. 
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#100
##10
###1
Third column also satisfises Echelon Form
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1100
0210
1121
Substitute −1 in for z in second
equation to find y
1
02
12



z
zy
zyx
xcolumn
ycolumn
zcolumn
equal signs   012 y
2y
Substitute −1 in for z and 2 for y in first
equation to find x.
    1122 x
2x
Solution is: (−2 , 2 , −1)

14. Reduced Echelon Form
 We use Row Operations to make the matrix look like above.
 There is no need for any substitution of variables back in equation.
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#100
#010
#001

15. Let’s try this method on the problem we just
did. We take the matrix we ended up with
when doing row echelon form:
1762
353
12

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
zyx
zyx
zyx
Let’s get the 0 we need in the
second column by using the
second row as a tool.
−2r2+r1
Now we’ll use row 3 as a tool to work on the
third column to get zeros above the 1.
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#100
#010
#001
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1100
0210
1121
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1100
0210
1301
−2r3+r2
3r3+r1
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1100
0210
2001
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1100
2010
2001
Notice when we put the variables and = signs
back in we have the solution
1,2,2  zyx

16. Code For Echelon And Reduced Echelon
Form

18. Low Pass Filter
 Only allows low frequency signals from 0Hz to its cut-off frequency.
Ideal low pass filter

19. Low Pass Filter(cont.)
Practical case

20. High Pass Filter
 Only allows high frequency signals from its cut-off frequency.
Ideal Case

21. High Pass Filter (Cont.)
Practical Case

22. Band Pass Filter
 Allows signals falling within a certain frequency band setup between two points to
pass through while blocking both the lower and higher frequencies either side of
this frequency band.
Ideal Case

23. Band Pass Filter(cont.)
Practical Example

24. References
 Basic Electronics Tutorials. (2018). Low Pass Filter - Passive RC Filter Tutorial.
[online] Available at: http://www.electronics-tutorials.ws/filter/filter_2.html
[Accessed 1 Jan. 2018].
 Stattrek.com. (2018). Echelon Form.
[online] Available at: http://stattrek.com/matrix-algebra/echelon- form.aspx
[Accessed 1 Jan. 2018].