7 Assessing Leakage

Question 1

The definition of spectral resolution?

Answer 1

This is defined as the difference between two consecutive harmonic frequencies in the spectrum

Question 2

The equation for spectral resolution?

Answer 2

Question 3

DFT signal frequency?

Answer 3

Question 4

Answer 4

Question 5

Parseval’s theorem and leakage?

Answer 5

Parseval’s theorem for all spectral coefficients still holds, but the

• signal energy ‘leaks’ over all (but mainly adjacent) c_k
• spectrum is blurred
• coding of the signal is corrupted

Question 6

Signal example with no leakage?

Answer 6

Question 7

Signal example with leakage?

Answer 7

Question 8

How is leakage described?

Answer 8

(The arguments of the sinus can become zero such that the Dirichlet function may be undefined. These cases need to be considered separately.)

Question 9

The Dirichlet Formula when

q-k = m = number

Answer 9

Question 10

The Dirichlet formula when:

q-k = m = 0

Answer 10

Question 11

In summery when does leakage happen?

Answer 11

In summary, leakage happens when the sinusoid, which is subject to the DFT, does not have an integer number of oscillations in the total time interval of the recordings