082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

804 Chapter 24 The Fourier transform
(a)
(b)
(c)
(d)
(e)
g[ – m]
10
6 8
4
2
– 4
g[ – m]
10
6 8
4
2
– 4
g[ 1– m]
10
6 8
4
2
– 4
g[ 2 – m]
10
6 8
4
2
– 4
g[ 3 – m]
10
6 8
4
2
– 4
1 2
1 2
1 2
1 2
1 2
m
m
m
m
m
sum of products:
(3)( – 4) = –12
sum of products:
(3)(8) + (9)( – 4) = –12
sum of products:
(3)(5) + (9)(8) + (2)( – 4) = 79
sum of products:
(9)(5) + (2)(8) + ( – 1)( – 4) = 65
(f)
(g)
g[ 4 – m]
10
6 8
4
2
– 4
g[ 5 – m]
10
6 8
4
2
– 4
1 2
1 2
m
m
sum of products:
(2)(5) + (– 1)(8) = 2
sum of products:
(– 1)(5) = –5
Figure24.25
The effect oftranslatingg[−m] bynunits,forn = 0,1, . . . ,5.