1. DERET FOURIER WAKTU KONTINU (DFWK) TEAM DOSEN
EE2423 SINYAL & SISTEM
DERET FOURIER WAKTU KONTINU (DFWK)
TEAM DOSEN
Signal&System
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2. Deret Fourier Waktu Kontinu (DFWK)
a0, ak, bk : Fourier coefficients.
k: harmonic number,
T: period,  = 2/T
For all t but discontinuities
synthesis
analysis
(signal average over a period, i.e. DC term & zero-frequency component.)
Signal&System
Jurusan Elektro STT Telkom

3. Deret Fourier Waktu Kontinu (DFWK)
Deret Fourier Bentuk Eksponensial Kompleks
DFS defined as:
analysis
Bentuk ini lebih memberikan
banyak informasi, karena
koefisien Fourier dinyatakan
secara eksplisit
synthesis
Link to FS real coeffs.
Signal&System
Jurusan Elektro STT Telkom

4. Jurusan Elektro STT Telkom
Spektral Fourier
amplitude
phase
Signal&System
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5. Jurusan Elektro STT Telkom
DFWD
Diskret square wave.
amplitude
phase
Signal&System
Jurusan Elektro STT Telkom

6. Fourier analysis - tools
Periodic (period T)
Discrete
Continuous FT
Aperiodic FS
Note: j =-1,  = 2/T, s[n]=s(tn), N = No. of samples
Input Time Signal Frequency spectrum **
Calculated via FFT
Discrete
DFS
Periodic (period T)
Continuous
DTFT
Aperiodic
DFT
Signal&System
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7. Jurusan Elektro STT Telkom
FS convergence
s(t) piecewise-continuous;
s(t) piecewise-monotonic;
s(t) absolutely integrable ,
(a)
(b)
(c)
Dirichlet conditions
In any period:
if s(t) discontinuous then |ak|<M/k for large k (M>0)
Rate of convergence
Example: square wave
(a)
(b)
(c)
Signal&System
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8. Sifat-sifat Deret Fourier
Diberikan dua sinyal periodik dengan period T dan fundamental frequency 0=2/T sama:
Linearity:
Time-Shifting:
Time-Reversal (Flip):
Time-Scaling:
Signal&System
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9. Sifat-sifat Deret Fourier (cont’d)
Differentiation:
Integration:
Dekomposisi Genap-Ganjil dari Sinyal Real:
Multiplication:
Signal&System
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10. Jurusan Elektro STT Telkom
Tabel FS properties
Time Frequency
Homogeneity a·s(t) a·S(k)
Additivity s(t) + u(t) S(k)+U(k)
Linearity a·s(t) + b·u(t) a·S(k)+b·U(k)
Time reversal s(-t) S(-k)
Multiplication * s(t)·u(t)
Convolution * S(k)·U(k)
Time shifting
Frequency shifting S(k - m)
Signal&System
Jurusan Elektro STT Telkom