Test: Z Transform Properties - 2 - Electronics and Communication Engineering (ECE) MCQ

Explanation: A sampling rate conversion by the rational factor I/D is accomplished by cascading an interpolator with a decimator.

Explanation: We emphasize that the importance of performing the interpolation first and decimation second, is to preserve the desired spectral characteristics of x(n).

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

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 N-1 complex additions. So, in a total to perform N-point DFT we perform N² complex multiplications and N(N-1) complex additions.

Explanation: If XN represents the N point DFT of the sequence xN in the matrix form, then we know that

Explanation: The first step is to determine the matrix W4. By exploiting the periodicity property of W4 and the symmetry property

Explanation: The Fourier series coefficients are given by the expression

Answer: Given x(n)={0,1,2,3}
We know that the 4-point 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)=-2-2j.

Explanation: We know that according to the periodicity and symmetry property,
100/4=200/x=>x=8.