# A#07 - cases namely 2 1 ± for the pulse at the origin(a...

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Assignment #7 – p.1 Due Tue 09/26/06 1(5). Text 3.21 2(10). Text 3.40 (b), (c) 3(5). Text 3.42 (c) 4(5). Text 3.43 (a)-(ii) only. 5(20). For the periodic waveforms shown, (a) Find the equations for k a and k b . (b) Use MATLAB to plot the spectra, k vs a k . and k vs b k . , out to roughly the 10 th harmonic. (c) Study the plots and answer the following question: Which periodic signal (the wide pulse train or the narrow one) has almost all of its harmonic content at DC? 6(20). For the periodic waveforms shown, (a) Find the equations for k a and k b . (b) Compare their spectra by simply calculating their DC values ( 0 0 , b a ), and the magnitude of their first harmonics ( 29 1 1 , b a . No plot is necessary. (Find values only for 1 + = k .) What do you think is the reason for the values you obtained? Clearly, the two waveforms are different? k a t x ) ( 1 k b t y ) ( t -4 -2 2 4 8 t 0 3 1 -3 0 3 6 7 -1 1 5 k a t x ) ( 1 k b t y ) ( t t -4 -2 2 4 8 0 3 1 -3 0 3 6 7 -1 1 5 2

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Assignment #7 – p.2 Due Tue 09/26/06 7(35). Consider the following three periodic wavforms, where the pulse width is the same in all three
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Unformatted text preview: cases, namely, 2 1 ± for the pulse at the origin. (a) Using the basic pulse train equation from Example 3.5 in the text, namely, ( 29 1 1 sinc 2 T k T T a k ϖ = , ≠ k , calculate the Fourier coefficients for the three cases above. (b) Next, rewrite the three equations into the form ( 29 1 1 sinc 2 T k T Ta k = , and use MATLAB to plot k vs Ta k for all three cases. Make sure you use the same scale on each plot. Note that as T gets larger, the incremental frequency, T π 2 = , from one sample to the next gets smaller, but the variable, T k k 2 = defines the location of the current sample. See Text, Figure 4.2. (c) What can you say about the limiting values of the three plots, as ∞ → T ? Do they approach the envelope (i.e., the outer boundary) of the plots? ) ( t x a ) ( t x b ) ( t x c t 2 6 8 12 4 6 10 12 5 6 11 12 t t 1 1 1...
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A#07 - cases namely 2 1 ± for the pulse at the origin(a...

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