Survey library.pptxThis is a test document that is used to satisfy the requirement to upload two documents.

This is a test document that is used to satisfy the requirement to upload two documents.

1. Survey library

2. Fourier transform- FT & IFT Defination ； fourier trransform is a kind of decompose the eomplex signal into multi-simply signal transform methods. Basic function ： According to ‘ Any periodic function that satisfies the Dirichlet condition can be represented by an infinite series of sine and cosine functions’; what’ more, euler formula we can tranfer the angle into exponential form. Inverse fourier transorm: f ˆ (k) = dx. Basic property: 1. The Fourier transform of an integrable function is continuous. 2. The Fourier transform of a real valued odd function is a purely imaginary valued odd function. 3. The Fourier transform of a real valued even function is real valued even function. Tips: we only investigate the basic fourier transform property.  

3. Laplace transform Laplace transform equation: Inverse equation:  

4. Wavelet Transform- DWT & IDWT Defination: The Discrete Wavelet Transform(DWT) decomposes a signal into a set of matually orthogonal wavelet basis function. Basic property: Discrete sampling the signal to decrease the computation,multi-scale anlalysis properties,inversable. DWT: ; haar filter 1.Wavelet functions are spatially localized; 2.Wavelet functions are dilated, translated and scaled verisions of a common mother wavelet; 3.Each set of wavelet function forms an orthogonal set of basis functions. IDWT: Zero padding and upsampling  

5. Appendix 1.DFT 2. CWT: We roughly investigated the CWT, equation : .