1 Crore+ students have signed up on EduRev. Have you? 
If x(n) is a finite duration sequence of length L, then the discrete Fourier transform X(k) of x(n) is given as:
Explanation: If x(n) is a finite duration sequence of length L, then the Fourier transform of x(n) is given as
If we sample X(ω) at equally spaced frequencies ω=2πk/N, k=0,1,2…N1 where N>L, the resultant samples are
If X(k) discrete Fourier transform of x(n), then the inverse discrete Fourier transform of X(k) is:
Explanation: If X(k) discrete Fourier transform of x(n), then the inverse discrete Fourier transform of X(k) is given as
A finite duration sequence of length L is given as x(n) =1 for 0≤n≤L1=0 otherwise , then what is the N point DFT of this sequence for N=L?
Explanation: The Fourier transform of this sequence is
If N=L, then X(k)= L for k=0
=0 for k=1,2….L1
Explanation: We know that the Discrete Fourier transform of a signal x(n) is given as
Thus we get Nth rot of unity WN= e^{j2π/N}
Which of the following is true regarding the number of computations requires to compute an Npoint DFT?
Explanation: The formula for calculating N point DFT is given as
From the formula given at every step of computing we are performing N complex multiplications and N1 complex additions. So, in a total to perform Npoint DFT we perform N^{2} complex multiplications and N(N1) complex additions.
Explanation: If XN represents the N point DFT of the sequence xN in the matrix form, then we know that
What is the DFT of the four point sequence x(n)={0,1,2,3}?
Explanation: The first step is to determine the matrix W4. By exploiting the periodicity property of W4 and the symmetry property
W_{N}^{k+N/2}= W_{N}^{k}
The matrix W_{4} may be expressed as
If X(k) is the N point DFT of a sequence whose Fourier series coefficients is given by c_{k}, then which of the following is true?
Explanation: The Fourier series coefficients are given by the expression
What is the DFT of the four point sequence x(n)={0,1,2,3}?
Given x(n)={0,1,2,3}
We know that the 4point DFT of the above given sequence is given by the expression
In this case N=4
=>X(0)=6,X(1)=2+2j,X(2)=2,X(3)=22j.
If W_{4}^{100}=W_{x}^{200}, then what is the value of x?
Explanation: We know that according to the periodicity and symmetry property,
100/4=200/x=>x=8.
32 videos76 docs64 tests

Use Code STAYHOME200 and get INR 200 additional OFF

Use Coupon Code 
32 videos76 docs64 tests








