# hw8 - following Explain your answers a Im ω X where t t t...

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Assignment #8 Due Tue 10/04/05 1(70). Find the Fourier transform for each the signals below, using only Tables 4.2 and 4.1 in O&W ( Basic Fourier Transform Pairs and Properties of the Fourier Transform ). a. x ( t ) = 3[ u ( t ) - u ( t - 2)] b. x ( t ) = t e 2 - [ u ( t ) - u ( t - 2)] c. x ( t ) = 3 t [ u ( t ) - u ( t - 2)] d. x ( t ) = sin(4 π t )[ u ( t + 1) - u ( t - 1)] e. x ( t ) = ) 1 ( 2 - - t e u ( t -1) f. x ( t ) = t t t t cos sin 2 - (hint: what’s the derivative of a sinc?) g. x ( t ) = ( 29 ( 29 3 1 - + + t t δ h. x ( t ) = (1 - bt te - ) u ( t ), b > 0 i. x ( t ) as shown at right (hint: it’s a convolution of two pulses) j. ) ( sin 1 ) ( 2 t t t x = (hint: consider sinc functions) 2(15). Using only the symmetry properties of the Fourier Transform and Table 4.2, determine the
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Unformatted text preview: following. Explain your answers. a. )) ( Im( ω X , where t t t x cos 2 3 ) ( 2 + + = . b. )) ( Re( ω X , where 3 ) 2 ( ) 2 ( sin 3 cos ) ( t t u t u t t t x +-+ + + + = 3(15). Consider a causal LTI system with frequency response ϖ j H + = 2 1 ) ( . For a particular input ) ( t x , this system was observed to produce the output ) ( ) ( ) ( 3 2 t u e e t y t t---= . Determine ) ( t x . ) ( t x t 1 2 3 4-1 5 6 7...
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