A-7 HILBERT TRANSFORM PAIRS+ Definition of Hilbert Transform: x(t) = x(t) * Function 1. x(at +...

Transcribed Image Text:

A-7 HILBERT TRANSFORM PAIRS+ Definition of Hilbert Transform: x(t) = x(t) * Function 1. x(at + b) 2. x(t) + y(t) dnx(t) 3. dtn 4. A constant 5. 1 t 6. sin (wot + 0) 7. sin at at 8. ejwot 9. 8 (t) = Sa(at) 10. 11. a (t + a) A 1, t T/2 (4) = {b t elsewhere t = 1 x() T t- Hilbert Transform (at + b) (t) + (t) dn x(t) dtn 0 -(t) -cos (wot + 0) 1 at Sa(at) 2T Fjejwot t t (1 + a) 2t+T In T 2t - T 5-17 An SSB-AM transmitter is modulated by a rectangular pulse such that m(t) = (t/T) and A = 1. (a) Prove that as given in Table A-7. 1 m(t) == 2t + T In T 2t (b) Find an expression for the SSB-AM signal s(t), and sketch s(t). (c) Find the peak value of s(t). A-7 HILBERT TRANSFORM PAIRS+ Definition of Hilbert Transform: x(t) = x(t) * Function 1. x(at + b) 2. x(t) + y(t) dnx(t) 3. dtn 4. A constant 5. 1 t 6. sin (wot + 0) 7. sin at at 8. ejwot 9. 8 (t) = Sa(at) 10. 11. a (t + a) A 1, t T/2 (4) = {b t elsewhere t = 1 x() T t- Hilbert Transform (at + b) (t) + (t) dn x(t) dtn 0 -(t) -cos (wot + 0) 1 at Sa(at) 2T Fjejwot t t (1 + a) 2t+T In T 2t - T 5-17 An SSB-AM transmitter is modulated by a rectangular pulse such that m(t) = (t/T) and A = 1. (a) Prove that as given in Table A-7. 1 m(t) == 2t + T In T 2t (b) Find an expression for the SSB-AM signal s(t), and sketch s(t). (c) Find the peak value of s(t).

Answer rating: 100% (QA)

Here is a list of some common Hilbert transform pairs 1 Hilbert Transform of xat b The Hilbert transform of xat b is given by xHilbertt Hxat b 1 PV to xat b t d where PV denotes the Cauchy principal v... View the full answer