电子科技大学：《生物医学信号处理 Biomedical Signal Processing》课程教学资源（课件讲稿）Lecture 2 Classical Power Spectral Estimation Methods and Biomedical Applications

Lecture 2 Classical Power Spectral Estimation Methods and Biomedical Applications Prof.N.Rao

Lecture 2 Classical Power Spectral Estimation Methods and Biomedical Applications Prof. N. Rao

Discrete Fourier Transform (DFT) 。DFT definition: Forx(n)with length N, N-1 X)=∑xaw k=0,1,,W-11 WN=e-2m时jlN -0 1-1 树=之w 2=0,1,,W-1

Discrete Fourier Transform (DFT) • DFT definition: For x ( n) with length N

·DFT Properties: (1)Linearity (2)Orthogonality (3)Displacement(移位性) (4)Symmetry

• DFT Properties: (1) Linearity (2) Orthogonality (3) Displacement (移位性) (4) Symmetry

Fast Fourier Transform (FFT) FFT is a fast algorithm for computing DFT. Cooley and Tukey proposed FFT DFT:multiplying number:N2 Adding number:N (N-1) FFT multiplying number:(N/2)log2M

Fast Fourier Transform (FFT) FFT is a fast algorithm for computing DFT. Cooley and Tukey proposed FFT DFT: multiplying number: N2 Adding number: N （ N-1 ） FFT : multiplying number: （ N/2 ）log 2 N

FFT computing cost For instance,if N=1024 DFT multiplying number is 1048576 FFT multiplying number is 5120,taking up 4.88%of DFT multiplication

FFT computing cost • For instance ，if N=1024 • DFT multiplying number is 1048576 • FFT multiplying number is 5120, taking up 4.88% of DFT multiplication