Transformasi Fourier. dan invers tranformasi Fourier adalah;

Presentasi berjudul: "Transformasi Fourier. dan invers tranformasi Fourier adalah;"— Transcript presentasi:

1 Transformasi Fourier

2 dan invers tranformasi Fourier adalah;

3 dimana:

4 t Boxcar function

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8 t General boxcar function

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11 adalah Transient function

12 dimana:

13 Delta Dirac function

14 Cossinus function

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16 Sinus function

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18 Constan function

19 Gaussian function

20 n Note: Fourier transforms Gaussian function

21 Note: Fourier transforms Gaussian function

22 Note: Fourier transforms Gaussian function

23 Note: Fourier transforms Gaussian function

24 Note: Fourier transforms Gaussian function

25 Note: Fourier transforms Gaussian function

26 Note: Fourier transforms Gaussian function

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33 t t-1/2T T+1/2T

34 Time frequency window of the windowing Fourier transforms.

35 Non Stationary signals GaussianWindow Robi Polikar, The Wavelet Tutorial, http://users.rowan.edu/~polikar/WAVELETS/WTpart1.htmlhttp://users.rowan.edu/~polikar/WAVELETS/WTpart1.html

36 STFT with a = 0.01 (narrowest window) Well separated in timeWell separated in time Peaks correspond to a band of frequenciesPeaks correspond to a band of frequencies Robi Polikar, The Wavelet Tutorial, http://users.rowan.edu/~polikar/WAVELETS/WTpart1.htmlhttp://users.rowan.edu/~polikar/WAVELETS/WTpart1.html

37 STFT with a = 0.0001 (3rd widest window) Time resolution is becoming poorerTime resolution is becoming poorer Frequency resolution is improvingFrequency resolution is improving Robi Polikar, The Wavelet Tutorial, http://users.rowan.edu/~polikar/WAVELETS/WTpart1.htmlhttp://users.rowan.edu/~polikar/WAVELETS/WTpart1.html

38 STFT with a = 0.00001 (widest window) Terrible time resolutionTerrible time resolution Excellent frequency resolutionExcellent frequency resolution Robi Polikar, The Wavelet Tutorial, http://users.rowan.edu/~polikar/WAVELETS/WTpart1.htmlhttp://users.rowan.edu/~polikar/WAVELETS/WTpart1.html

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76 A B

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81 TIME·CONVOLUTION THEOREM

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87 CORRELATION THEOREM

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106 window

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111 Blackman–Nuttall window

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