Fouriess Series w nus
Only for periodic signals 5 B J Fourier F s in 1827
Aim one period many frequencies Albert Micheal son
signals should be orthogonal Cspectrum analyser
Fourier series
Approximation process where non sinusoidal waveform converted
to sinusoidal such that all periodic signals can be represented
in unique form
Fourier series i Trigonometric fourier series
ii Exponential fourier series
Advantages of Fourier series
i
Easy to find spectral width
ii steady state response due to periodic input can be find
easily
of Fs
Target
i verification of symmetry
i spectral analysis
iii Properties of fourier series
spectrum Variation with frequency
KE
I
i e
It sinwot
cosmeot
6 4 2 2 4 6
I
, sin
sin 20 2 Sino coso
t sin30 35in0 4sin 0
since
t
i sint cost dt o
sinst
t
94
sine
1
ᵗ
x̅ 2A
I
C see t t ct
get e
Error etc get crest
dE Failed ect
felt at glt dt fc.se gel
, t2
at Ct c set dt
Ee
t
G241 dt cfsektl.dt zcfgltl.se J.dt
t t
To minimize Eeg 4ft o
tz
0 2Cfxt J.dt 2 It sect de
t t
c
jgctl.xctl.at
t
sectl at
a in sinct sine at
sinned
c cost I cos I
1H sm2
I I I I
RA o
c
Only for periodic signals 5 B J Fourier F s in 1827
Aim one period many frequencies Albert Micheal son
signals should be orthogonal Cspectrum analyser
Fourier series
Approximation process where non sinusoidal waveform converted
to sinusoidal such that all periodic signals can be represented
in unique form
Fourier series i Trigonometric fourier series
ii Exponential fourier series
Advantages of Fourier series
i
Easy to find spectral width
ii steady state response due to periodic input can be find
easily
of Fs
Target
i verification of symmetry
i spectral analysis
iii Properties of fourier series
spectrum Variation with frequency
KE
I
i e
It sinwot
cosmeot
6 4 2 2 4 6
I
, sin
sin 20 2 Sino coso
t sin30 35in0 4sin 0
since
t
i sint cost dt o
sinst
t
94
sine
1
ᵗ
x̅ 2A
I
C see t t ct
get e
Error etc get crest
dE Failed ect
felt at glt dt fc.se gel
, t2
at Ct c set dt
Ee
t
G241 dt cfsektl.dt zcfgltl.se J.dt
t t
To minimize Eeg 4ft o
tz
0 2Cfxt J.dt 2 It sect de
t t
c
jgctl.xctl.at
t
sectl at
a in sinct sine at
sinned
c cost I cos I
1H sm2
I I I I
RA o
c