# HW3 - BIM 281 Homework 03 1. Due date: Friday, 05/23/08 (A)...

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1 1. The above figures show a real, discrete signal ( ) A j g (top left), as well as a signal ( ) B j g (top right) that consists of two repeats of ( ) A j g . The shifted, normalized DFT magnitude spectra of the two signals are also shown (including negative frequencies). We are seeking a rigorous ma- thematical explanation for the appearance of spectrum B. a. First, prepare a table that gives for both cases the number of originally sampled points N , the sample spacing Δ x , the frequency spacing Δ f , the sampling frequency f S , the Nyquist frequency f Ny , and the width of the truncation window L . b. Next, translate the remaining given information into proper mathematical notation by filling in the blanks: Considering only the range 03 1 j , we have ( ) ( ) BB jj gg + == …… .. Further, if we denote by ( ) , A B k G the coefficients of the two unnormalized, shifted DFT, what is actually shown in the above two magnitude spectra? (Hint: The plots are consis- BIM 281 Homework 03 Due date: Friday, 05/23/08

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2 tent with the convention used in the lecture notes.)
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## HW3 - BIM 281 Homework 03 1. Due date: Friday, 05/23/08 (A)...

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