numerical analysis – digital signal processing
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Numerical Analysis – Digital Signal Processing. Hanyang University Jong-Il Park. Digital Signal Processing. Discrete Fourier Transform Fast Fourier Transform(FFT) Multi-dimensional FFT Convolution. Sampling and aliasing. Discrete Fourier Transform. Fourier Transform - PowerPoint PPT PresentationTRANSCRIPT
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Numerical Analysis – Numerical Analysis – Digital Signal ProcessingDigital Signal Processing
Hanyang University
Jong-Il Park
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Division of Electrical and Computer Engineering, Hanyang University
Digital Signal Processing Discrete Fourier Transform
Fast Fourier Transform(FFT)
Multi-dimensional FFT
Convolution
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Division of Electrical and Computer Engineering, Hanyang University
Sampling and aliasing
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Division of Electrical and Computer Engineering, Hanyang University
Discrete Fourier Transform Fourier Transform
Discrete Fourier Transform
DFT:
IDFT:
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Division of Electrical and Computer Engineering, Hanyang University
Fast Fourier Transform(FFT)
[Danielson&Lanczos][Cooley&Tukey]
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Division of Electrical and Computer Engineering, Hanyang University
Decimation-in-time FFTDecimation-in-time FFT
Cooley-Tukey Algorithm
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Division of Electrical and Computer Engineering, Hanyang University
Sande-Tukey AlgorithmSande-Tukey Algorithm
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Division of Electrical and Computer Engineering, Hanyang University
Decimation-in-frequency FFT(I)Sande-Tukey Algorithm
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Division of Electrical and Computer Engineering, Hanyang University
Decimation-in-frequency FFT (II)
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Division of Electrical and Computer Engineering, Hanyang University
Why FFT?Why FFT?
Further reading: http://en.wikipedia.org/wiki/Cooley-Tukey_FFT_algorithm
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Division of Electrical and Computer Engineering, Hanyang University
Computation of FFT(I)
input and output of four1() in NR in C
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Division of Electrical and Computer Engineering, Hanyang University
Computation of FFT(II) Eg. FFT
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Division of Electrical and Computer Engineering, Hanyang University
2D FFT(I)
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Division of Electrical and Computer Engineering, Hanyang University
2D FFT(II)
* Generalization to L-dimension
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Division of Electrical and Computer Engineering, Hanyang University
2D FFT(III) Eg. 2D FFT
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Division of Electrical and Computer Engineering, Hanyang University
Convolution(I) Def.
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Division of Electrical and Computer Engineering, Hanyang University
Convolution(II) Convolution theorem
o direct convolution complex computation
o FFT and multiplication less computation
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Division of Electrical and Computer Engineering, Hanyang University
Convolution(III) Convolution of discrete sampled function
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Division of Electrical and Computer Engineering, Hanyang University
Convolution(IV) Trouble in using DFT of finite duration
End effects Treated by zero padding
End effect
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Division of Electrical and Computer Engineering, Hanyang University
Convolution(V) Zero padding
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Division of Electrical and Computer Engineering, Hanyang University
Convolution(VI) Convolving very large data sets
<Overlap-add method>