PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

DTFT, DFT, ZT, and FFT 465

and

g(n) → H[f(n)]

Then

gn H f k n k

K

()
()( )

 



∑ 











, from R.5.16

gn

K

()
() [( )]

 



∑ fkH n k













and

gn()
() ( )


 



fk hn k

K

∑













R.5.18 Note that the output of a linear system is given by

gn f khn k

n

()
()( )

 



∑

or in short

g(n) = h(n) ⊗ f(n)

Recall that ⊗ denotes convolution.

R.5.19 For example, let f(n) = 2 n and h(n) = (1/3)nu(n). Then g(n) = h(n) ⊗ f(n) or

gn f khn k hk f n k

kk

()

()( ) () ( )

 



 



∑∑

gn uk

k

k

()
 ()()nk


 



(^1) 
3

 2





∑ 

gn

k

k

nk n

k

k

kn

k

()

 







(^1) 
3

22 2

1

3

22

1

003























∑∑kk 

k



0

1

∑ 2









gn n

k

k

n

n

n

()

(/)









2

1

6

2

1

000 116

















∑∑∑