5.3. Exercises

EXERCISE 5.14.

Consider the following digital signals:

images

Demonstrate analytically that the real parts of the DFT1D 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:

images

for the following digital signal:

images

EXERCISE 5.16.

The function ρi mod N, images i images [1, N −1] performs the permutation of the sequence {1,2,3,..., N −1} into the sequence {ρ1, ρ2, ρ3,..., ρN−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.

images

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 ...

Get Digital Signal Processing Using Matlab now with the O’Reilly learning platform.

O’Reilly members experience live online training, plus books, videos, and digital content from nearly 200 publishers.