Question 2
Marks : +2 | -2
Pass Ratio : 100%
If x(n) is real and even, then what is the DFT of x(n)?
Explanation: Given x(n) is real and even, that is x(n)=x(N-n)
Question 3
Marks : +2 | -2
Pass Ratio : 100%
If X1(n), x2(n) and x3(m) are three sequences each of length N whose DFTs are given as X1(k), X2(k) and X3(k) respectively and X3(k)=X1(k).X2(k), then what is the expression for x3(m)?
Explanation: If X1(n), x2(n) and x3(m) are three sequences each of length N whose DFTs are given as X1(k), x2(k) and X3(k) respectively and X3(k)=X1(k).X2(k), then according to the multiplication property of DFT we have x3(m) is the circular convolution of X1(n) and x2(n).
Question 4
Marks : +2 | -2
Pass Ratio : 100%
What is the circular convolution of the sequences X1(n)={2,1,2,1} and x2(n)={1,2,3,4}?
Explanation: We know that the circular convolution of two sequences is given by the expression
Question 5
Marks : +2 | -2
Pass Ratio : 100%
What is the circular convolution of the sequences X1(n)={2,1,2,1} and x2(n)={1,2,3,4}, find using the DFT and IDFT concepts?
Explanation: Given X1(n)={2,1,2,1}=>X1(k)=[6,0,2,0]
Question 6
Marks : +2 | -2
Pass Ratio : 100%
If x(n) is real and odd, then what is the IDFT of the given sequence?
Explanation: If x(n) is real and odd, that is x(n)=-x(N-n), then XR(k)=0. Hence X(k) is purely imaginary and odd. Since XR(k) reduces to zero, the IDFT reduces to
Question 8
Marks : +2 | -2
Pass Ratio : 100%
If x(n) is a complex valued sequence given by x(n)=xR(n)+jxI(n), then what is the DFT of xR(n)?
Explanation: Given x(n)=xR(n)+jxI(n)=>xR(n)=1/2(x(n)+x*(n))