Unformatted text preview: conclusions from part (c) of problem 2. 5. Calculate the energy of the following continuous-time signals. (a) x 1 ( t ) =-3[ u ( t + π )-u ( t-π )] (b) x 2 ( t ) = cos( t ) x 1 ( t ) (c) x 3 ( t ) = [ x 1 * x 2 ]( t ) 6. Calculate the energy of the signal x ( t ) = sinc( at ) with a > 0. 7. Let b > a > 0 and deﬁne x 1 ( t ) = sinc( at ) and x 2 ( t ) = sinc( bt ). Calculate [ x 1 * x 2 ]( t ). 8. Deﬁne x 1 ( t ) = sinc 2 ( t ) and x 2 ( t ) = cos(Ω t ) x 1 ( t ). Find a value W such that Z ∞-∞ x 1 ( t ) x 2 ( t ) dt = 0 for all | Ω | > W . 9. A signal has Fourier transform ˆ x ( ω ). Obtain an expression, in terms of ˆ x ( ω ) and a sinc signal, for the Fourier transform of the “truncated” signal x ( t )[ u ( t )-u ( t-T )]....
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This note was uploaded on 09/29/2008 for the course EEE 203 taught by Professor Chakrabarti during the Spring '07 term at ASU.
- Spring '07