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17 Dec 2013: Analogue ModulationFrequency Modulation. Bandwidth of FM SignalsUsing cos(A B) = cos A cos B sin A sin B we can write. ... Analogue ModulationFrequency Modulation. Bandwidth of FM Signals. Using the relationships sin A sin B = 12 [cos(A B) cos(A B)]

11 Sep 2013: T(t) = A exp{kt} B exp{. kt}, k > 0. T(t) = A cos(|k|t) B sin(. ... Thus k = ω2. Furthermore, we need A = 0 to get ridof the cos term.

17 Dec 2013: a) Convolution: f(t) g(t) F(ω)G(ω)(b) Modulation: f(t) cos(ω0t) 12 [F(ω ω0) F(ω ω0)](c) Parseval’s Theorem:. ... where a1(t) = b cos(2πfxt) is a sinusoidal modulating signal and a2(t) = cos(2πfct)is a unit amplitude carrier signal.

11 Feb 2016: a) g(t) = a0 sin(πt/Tb)b) g(t) = a0[1 cos(2πt/Tb)]. You may assume that g(t) is zero outside the above interval.For each PSD determine ... 2 3F4 Digital Modulation - Examples Paper 1. s(t) r-. 62 cos(ωCt φref ). -i′(t) i(t). LowpassFilter r. 0v.

16 Dec 2013: Analogue ModulationFrequency Modulation. Bandwidth of FM SignalsUsing cos(A B) = cos A cos B sin A sin B we can write. ... Analogue ModulationFrequency Modulation. Bandwidth of FM Signals. Using the relationships sin A sin B = 12 [cos(A B) cos(A B)]

15 Aug 2013: b) xn = A cos(n0) B sin(n0) where A and B are uncorrelated random vari-ables with zero mean and identical variances. ... rXX[k] = 0.5A2 cos(k0). ]. 5. A stationary random process has autocorrelation function:.

16 Dec 2013: b) -1, 2, -1. (c) -1, 0, 2, 0, -1. (d) 1, 2, 2, 1. ... b) Explain how you would use the Hamming window. w (n) = 0.54 0.46 cos. (.

4 Feb 2015: b) Explain how you would use the Hamming window. wn = 0.54 0.46 cos. ... pass. 7. 8. (a) 1πn (sin (0.5πn) sin (0.4πn))(b). (c). 9.

16 Dec 2013: sinAsinB=0.5[cos(A-B)-cos(AB)]. fixed constants. cos(AB)=cosAcosB-sinAsinB, where B = 2φ and A fixed constant simplify and show as before. ... E[cos(2φ)] = E[sin(2φ)]. = 0. Condition 2 Ok. Example: random phase sine-wave.

15 Aug 2013: b) Explain how you would use the Hamming window. wn = 0.54 0.46 cos. ... 10. A digital filter has the transfer function (1bz1)/(1az1), where a > 0,b > 0, b < a.