DERET FOURIER WAKTU KONTINU (DFWK) TEAM DOSEN EE2423 SINYAL & SISTEM DERET FOURIER WAKTU KONTINU (DFWK) TEAM DOSEN Signal&System Jurusan Elektro STT Telkom

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

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

Jurusan Elektro STT Telkom Spektral Fourier amplitude phase Signal&System Jurusan Elektro STT Telkom

Jurusan Elektro STT Telkom DFWD Diskret square wave. amplitude phase Signal&System Jurusan Elektro STT Telkom

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 Jurusan Elektro STT Telkom

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 Jurusan Elektro STT Telkom

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 Jurusan Elektro STT Telkom

Sifat-sifat Deret Fourier (cont’d) Differentiation: Integration: Dekomposisi Genap-Ganjil dari Sinyal Real: Multiplication: Signal&System Jurusan Elektro STT Telkom

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