Transformée de Fourier discrète : série de Fourier

u(t)T
u(t) =
∞
X
n=−∞
cnexp j2πn
Tt
n∈Z
cn=1
TZT
0
u(t) exp −j2πn
Ttdt
u(t)N0≤k≤
N−1
tk=kT
N
uk=u(tk)
cn'1
T
N−1
X
k=0
ukexp −j2πn k
NT N
N0≤
n≤N−1
Sn=1
N
N−1
X
k=0
ukexp −j2πn k
N
N ukN Sn
Sncn
fn=n
T
1/N

T

c0 = 1 c1 = 2/2
c2 = 0.5/2c3 = −j/2c10 = 0.2/2
|Sn|=|SN−n|
u(t)
SN−n=S∗
n
c−n'SN−n
Sn
Sn=SN+n

fe=N
T

n= 5
10