Class Code:  

            BIO 442           

Total Grade:     100 points       

            (Final Exam: 75 - Mid-Term Exam: 12.5 - Computer Projects/Homework Assignments: 12.5)

Class Meeting Place and Time : 

            Auditorium 3002 - Mondays from 3:30p - 6:30p        

Recommended Textbooks:

B.P. Lathi, Modern Sigital and Analog Communication Systems, 2^nd ed., Oxford University Press, Oxford, 1995.

John R. Buck, Alan V. V. Oppenheim, Alan V. Oppenheim, and Ronald W. Schafer, Discrete-Time Signal Processing, 2^nd ed., Prentice Hall, 1998.

R.N. Bracewell, The Fourier Transform and Its Applications, 3^rd ed., McGraw Hill, New York, 2000.

J.W. Goodman, Introduction to Fourier Optics, 2nd ed., McGraw Hill, New York, 1996.

(in addition to several research papers to be handed out to students in class)

Topics to be Covered

1. 1D Continuous Fourier transformation                                               
   1. General introduction                                                 Covered
   2. Linearity and orthogonality of transformations                            Covered
   3. Definition of forward/inverse 1D continuous Fourier transform            Covered
   4. Properties                            Covered
   5. Examples: sampled signals and sampling criterion to avoid aliasing        Covered
   6. Special cases: DTFT, DFS, and DFT                Covered
   7. Fast Implementations                Covered

    

2. Sampling
   1. Uniform vs. nonuniform sampling        Covered
   2. Sampling theorems            Covered
   3. Sampling rate change            Covered
   4. Design of a sampling in real applications            Covered
   5. Recovery of original analog signal            Covered

    

3. Digital Filter design techniques (IIR and FIR methods)            Covered

    

4. Power Spectrum Estimation (periodogram based methods)        Covered

    

5. Special Topics
   1. Linear and circular convolution using DFT                    Covered
   2. Hilbert transform       
   3. Interleaved and nonuniform Fourier transformation
   4. Short-time Fourier transformation (applied to spectrogram estimation)        Covered

    

6. Multi-dimensional Fourier Transformation    (2D Fourier transformation)    Covered

    7. Projection-slice theorem and its application in CT reconstruction            Covered

    8. Applications to Image/volume reconstruction

1. Image/volume reconstruction in ultrasound imaging
2. Image/volume reconstruction in CT
3. Image/volume reconstruction in MRI

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Last modified: February 14, 2012