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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu HST.582J / 6.555J / 16.456J Biomedical Signal and Image Processing Spring 2007 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . HST-582J/6.555J/16.456J-Biomedical Signal and Image Processing-Spring 2007 Problem Set 3 DUE: 3/1/07 Problem 1 Consider the continuous-time function, ( t ), given by 1 t /T if T < t < T ( t ) = | | s s s o t h e r w i s e (a) Show that ( t ) can be thought of as resulting from the convolution of a rectangular window with itself, that is, ( t ) = c T ( t ) T ( t ) , where 1 if T < t < T T ( t ) = 0 otherwise Specify the values of c and T in terms of T s . (b) Determine ( F ), the CTFT of ( t ). Now consider the continuous-time function, ( t ), given by sin F s t ( t ) = . F s t (c) Sketch ( t ) and ( t ) on the same coordinates. (d) Determine ( F ), the CTFT of ( t ), and then sketch ( F ) and ( F ) on the same coordinates. As we saw in Chapter 1, the sampling theorem states that any bandlimited continuous- time signal can, in principle, be exactly reconstructed from its samples by means of the interpolation formula, x ( t ) = x [ n ] ( t n = nT s ) . (1) In many cases this formula is not practical because it requires a summation over the entire duration of the sampled signal. Here we will consider the effect of replacing the interpolationduration of the sampled signal....
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ps3 - MIT OpenCourseWare http://ocw.mit.edu HST.582J /...

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