PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

348 Practical MATLAB® Applications for Engineers

e. Differentiation in freq(s)

tft

dF s

ds

⋅↔()

()

or a more general relation is given by

() () 1 nn [()]

n

tft n

d

ds

↔ Fs

f. Differentiation in t

df t

dt

sF s f

()

↔ () ( ) 0 

The second derivative is given by

d

dt

df t

dt

d

dt

ft ssFs f f

sFs s

()

[ ( )] [ ( ) ( )] ( )

()









↔

2

2

2



00





fff() ()00

The preceding process can be repeated for higher-order derivatives.

g. Integration in s

ft

t

Fsds

()

↔ ()

∞

∫

(^0)
h. Periodic functions f(t), with period T > 0
ft
e ftdt
e
T st
() sT

()

()

↔

∫



 

0

(^1)
i. Integration in t
fd sFs
f
() () s

()



0

1 0

∫ ↔ 

j. Convolution in t or product in s

ft 12 ()⊗↔ft() f 12 ( ) (ft )d [ () ()]FsFs 12

∞

∞


∫





k. Product in t or convolution in s

ftft

j

12 Fs 1 Fs 2

1

2

() ()↔⊗[ () ()]