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# hw7 - EE210 Signal Systems Home Work Set 7 1 Let h(n be the...

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EE210 Signal Systems (March 31, 2009) Home Work Set 7 1. Let h ( n ) be the impulse response of a linear shift-invariant filter. Prove that the filter is BIBO stable iff n = -∞ | h ( n ) | < . 2. Derive the inverse DTFT expression using the orthogonality property of the complex exponential sequence { e jωn } n = -∞ 3. Show that [ Sinc ( t - nT T )] * [ Sinc ( t - mT T )] = TSinc ( t - ( n + m ) T T ) Sinc ( t/T ) Sinc πt/T πt/T 4. Show that, in general, a frequency function having the following form H ( e ) = N k =0 a k e - jkω N k =0 a N - k e - jkω will be ’all pass’, i.e. | H ( e ) | = 1 , ω 5. Let p ( t ) is periodic signal with period

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