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# hmw2 - dt(b i 10-∞(5 cos t δ t-20 dt(c i ∞-∞ e-5 t...

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Due January 27, 2010 BME 171, Spring 2010 - HOMEWORK 2 Singularity Functions and Operations on Signals 1. Express signals shown below using singularity functions. 1 t 0 T 2T 3T 2A A t x (t) x (t) 4 2 x [n] 3 2 2 2 4 0 -3 -2 -1 1 2 3 4 5 6 n 2. Sketch signals whose mathematical descriptions are given below. Label all axes. x 1 ( t ) = e - 10 t u ( t ) x 2 ( t ) = u ( t + 5) - u ( t - 15) x 3 ( t ) = cos(10 πt ) u ( t ) u (2 - t ) x 4 ( t ) = r ( t ) - 2 r ( t - 1) + r ( t - 2) 3. Compute and sketch the first and second time derivative of the signal: x ( t ) = parenleftBig 1 - e - t parenrightBig u ( t ) 4. Evaluate the following integrals: (a) integraldisplay -∞ t 2 δ (
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Unformatted text preview: dt (b) i 10-∞ (5 + cos( t )) δ ( t-20) dt (c) i ∞-∞ e-5 t ˙ δ ( t-5) dt Note that the last integral contains ˙ δ , the time derivative of the δ function. 5. Let x [ n ] = { 1 , 4 , ⇓ 7 , 10 , 8 , 6 , 4 } . We want to determine y [ n ] = x [0 . 5 n + 1] using linear interpolation. Which operation should be performed Frst: interpolation or time shift? Justify your choice, then determine y [ n ]....
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