Question 1
Marks : +2 | -2
Pass Ratio : 100%
If x(n)=xR(n)+jxI(n) is a complex sequence whose Fourier transform is given as X(ω)=XR(ω)+jXI(ω), then what is the value of xI(n)?
Explanation: We know that the inverse transform or the synthesis equation of a signal x(n) is given as
Question 2
Marks : +2 | -2
Pass Ratio : 100%
If x(n)=xR(n)+jxI(n) is a complex sequence whose Fourier transform is given as X(ω)=XR(ω)+jXI(ω), then what is the value of XR(ω)?
Explanation: We know that X(ω)=\\(\\sum_{n=-∞}^∞\\) x(n)e-jωn
Question 3
Marks : +2 | -2
Pass Ratio : 100%
What is the value of XR(ω) given X(ω)=\\(\\frac{1}{1-ae^{-jω}}\\),|a|<1?
Explanation: Given, X(ω)=\\(\\frac{1}{1-ae^{-jω}}\\), |a|<1
Question 5
Marks : +2 | -2
Pass Ratio : 100%
If x(n) is a real sequence, then what is the value of XI(ω)?
Explanation: If the signal x(n) is real, then xI(n)=0
Question 6
Marks : +2 | -2
Pass Ratio : 100%
What is the value of |X(ω)| given X(ω)=1/(1-ae-jω), |a|<1?
Explanation: For the given X(ω)=1/(1-ae-jω), |a|<1 we obtain
Question 8
Marks : +2 | -2
Pass Ratio : 100%
If x(n)=A, -M<n<M,; x(n)=0, elsewhere. Then what is the Fourier transform of the signal?
Explanation: Clearly, x(n)=x(-n). Thus the signal x(n) is real and even signal. So, we know that
Question 9
Marks : +2 | -2
Pass Ratio : 100%
What is the value of XI(ω) given \\(\\frac{1}{1-ae^{-jω}}\\), |a|<1?
Explanation: Given, X(ω)=\\(\\frac{1}{1-ae^{-jω}}\\), |a|<1
Question 10
Marks : +2 | -2
Pass Ratio : 100%
If x(n) is a real and odd sequence, then what is the expression for x(n)?
Explanation: If x(n) is real and odd then, x(n)cosωn is odd and x(n) sinωn is even. Consequently