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Sampling rate conversion by the rational factor I/D is accomplished by what connection of interpolator and decimator?
Explanation: A sampling rate conversion by the rational factor I/D is accomplished by cascading an interpolator with a decimator.
Which of the following has to be performed in sampling rate conversion by rational factor?
Explanation: We emphasize that the importance of performing the interpolation first and decimation second, is to preserve the desired spectral characteristics of x(n).
Which of the following operation is performed by the blocks given the figure below?
Explanation: In the diagram given, a interpolator is in cascade with a decimator which together performs the action of sampling rate conversion by a factor I/D.
Explanation: We know that the Discrete Fourier transform of a signal x(n) is given as
Thus we get Nth rot of unity W_{N}= 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
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}?
Answer: 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.
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