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EE511 Day 4 Class Notes Discussion of Fourier Transform Laurence Hassebrook Updated 9-5-03 Friday 9-5-03 Wednesday 8-31-05 Covered written notes for Fourier Transforms up to convolution theory (8-27-01). GET VALUES TO BE USED IN DSSS VISUALIZATION Projection Integral and the Fourier Transform Recall the projection integral but let’s remove the normalization such that the projection has units of energy rather than power s.t. y ab at bt dt a projected onto b t2 t1 where we dropped the 1/T multiplier. Consider the case where bt e j 2ft so y ab a t e j 2ft dt t2 t1 The Fourier Transform (FT) is the limit of the above such that lim t2 Fa t t1 at e j 2ft dt at e j 2ft dt A f t1 t2 The FT is invertible s.t. a t F1 A f A f e j 2ft df PROPERTIES OF A FT 1. Duality 1 2. Time Shift 3. Frequency Shift 4. Convolution 5. Correlation 6. Multiplication 2