For the signal 2a g(t) (t + to) +a determine the essential bandwidth B Hz of...

  

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For the signal 2a g(t) (t + to)² +a² determine the essential bandwidth B Hz of g(t) such that the energy contained in the spectral components of g(t) of frequencies below B Hz is 99% of the signal energy Eg. Hint: Determine G(f) by applying the duality property and time/frequency shift properties to pair 3 of Table 3.1. TABLE 3.1 SOME COMMON z-TRANSFORM PAIRS Sequence Transform ROC 1. S[n] 1 All z 1 2. и[n] Iz| > 1 1- z- 1 3. —и[—п — 1] |z| < 1 1 4. S[n – m] All z except 0 (if m > 0) or oo (if m < 0) 1 5. a"u[n] z| > la| az-i 1 1 6. —а"и[—п — 1] |z| < la| 1- az-! az-! 7. na" u[n] |z| > la| (1 – az-1)2 az-1 8. —па"и[-п — 1] |z| < la| (1 – az-1)2 For the signal 2a g(t) (t + to)² +a² determine the essential bandwidth B Hz of g(t) such that the energy contained in the spectral components of g(t) of frequencies below B Hz is 99% of the signal energy Eg. Hint: Determine G(f) by applying the duality property and time/frequency shift properties to pair 3 of Table 3.1. TABLE 3.1 SOME COMMON z-TRANSFORM PAIRS Sequence Transform ROC 1. S[n] 1 All z 1 2. и[n] Iz| > 1 1- z- 1 3. —и[—п — 1] |z| < 1 1 4. S[n – m] All z except 0 (if m > 0) or oo (if m < 0) 1 5. a"u[n] z| > la| az-i 1 1 6. —а"и[—п — 1] |z| < la| 1- az-! az-! 7. na" u[n] |z| > la| (1 – az-1)2 az-1 8. —па"и[-п — 1] |z| < la| (1 – az-1)2