Digital Signal Processing Using Matlab

5.3. Exercises

EXERCISE 5.14.

Consider the following digital signals:

Demonstrate analytically that the real parts of the DFT_1D of the signals x[n] and y[n] are equal. Verify this property using a MATLAB code.

EXERCISE 5.15.

Using a MATLAB code, verify the Parseval theorem:

for the following digital signal:

EXERCISE 5.16.

The function ρⁱ mod N, i [1, N −1] performs the permutation of the sequence {1,2,3,..., N −1} into the sequence {ρ¹, ρ², ρ³,..., ρ^N−1} if N is a prime number and ρ is a primitive root of N. For example, the permutation of the sequence {1, 2, 3, 4} into the sequence {2, 4, 3, 1} is obtained for N = 5, as it is illustrated in the table below.

The sequence {1,2,3,. N −1} can be also permutated into the sequence {ρⁱ mod N with i = 0..N −2}. Thus, in the case N = 5 and ρ = 2, the following permutation is obtained:

In the Galois field GF(5), the element ρ = 2 is a primitive ...