Question 1
Marks : +2 | -2
Pass Ratio : 100%
What is the equivalent time domain relation of xl(t) i.e., lowpass signal?
Explanation: \\(x_l (t)=x_+ (t) e^{-j2Ï€F_c t}\\)
Question 2
Marks : +2 | -2
Pass Ratio : 100%
If the signal ẋ(t) can be viewed as the output of the filter with impulse response h(t) = 1/πt, -∞ < t < ∞ when excited by the input signal x(t) then such a filter is called as __________
Explanation: The signal ẋ(t) can be viewed as the output of the filter with impulse response h(t) = 1/πt,
Question 5
Marks : +2 | -2
Pass Ratio : 100%
In time-domain expression, \\(x_+ (t)=F^{-1} [2V(F)]*F^{-1} [X(F)]\\). The signal x+(t) is known as
Explanation: From the given expression, \\(x_+ (t)=F^{-1} [2V(F)] * F^{-1}[X(F)]\\).
Question 6
Marks : +2 | -2
Pass Ratio : 100%
In equation \\(x_+ (t)=F^{-1} [2V(F)]*F^{-1} [X(F)]\\), if \\(F^{-1} [2V(F)]=δ(t)+j/πt\\) and \\(F^{-1} [X(F)]\\) = x(t). Then the value of ẋ(t) is?
Explanation: \\(x_+ (t)=[δ(t)+j/πt]*x(t)\\)
Question 7
Marks : +2 | -2
Pass Ratio : 100%
If we substitute the equation \\(x_l (t)= u_c (t)+j u_s (t)\\) in equation x (t) + j ẋ (t) = xl(t) ej2πFct and equate real and imaginary parts on side, then what are the relations that we obtain?
x(t)=\\(u_c (t) \\,cosâ¡2Ï€ \\,F_c \\,t+u_s (t) \\,sinâ¡2Ï€ \\,F_c \\,t\\); ẋ(t)=\\(u_s (t) \\,cosâ¡2Ï€ \\,F_c \\,t-u_c \\,(t) \\,sinâ¡2Ï€ \\,F_c \\,t\\)
x(t)=\\(u_c (t) \\,cosâ¡2Ï€ \\,F_c \\,t-u_s (t) \\,sinâ¡2Ï€ \\,F_c \\,t\\); ẋ(t)=\\(u_s (t) \\,cosâ¡2Ï€ \\,F_c t+u_c (t) \\,sinâ¡2Ï€ \\,F_c \\,t\\)
x(t)=\\(u_c (t) \\,cosâ¡2Ï€ \\,F_c t+u_s (t) \\,sinâ¡2Ï€ \\,F_c \\,t\\); ẋ(t)=\\(u_s (t) \\,cosâ¡2Ï€ \\,F_c t+u_c (t) \\,sinâ¡2Ï€ \\,F_c \\,t\\)
x(t)=\\(u_c (t) \\,cosâ¡2Ï€ \\,F_c \\,t-u_s (t) \\,sinâ¡2Ï€ \\,F_c \\,t\\); ẋ(t)=\\(u_s (t) \\,cosâ¡2Ï€ \\,F_c \\,t-u_c (t) \\,sinâ¡2Ï€ \\,F_c \\,t\\)
Explanation: If we substitute the given equation in other, then we get the required result
Question 8
Marks : +2 | -2
Pass Ratio : 100%
What is the frequency response of a Hilbert transform H(F)=?
Explanation: H(F) =\\(\\int_{-∞}^∞ h(t)e^{-j2πFt} dt\\)
Question 9
Marks : +2 | -2
Pass Ratio : 100%
In the relation, x(t) = \\(u_c (t) cosâ¡2Ï€ \\,F_c \\,t-u_s (t) sinâ¡2Ï€ \\,F_c \\,t\\) the low frequency components uc and us are called _____________ of the bandpass signal x(t).
Explanation: The low frequency signal components uc(t) and us(t) can be viewed as amplitude modulations impressed on the carrier components cos2Ï€Fct and sin2Ï€Fct, respectively. Since these carrier components are in phase quadrature, uc(t) and us(t) are called the Quadrature components of the bandpass signal x (t).