8 Assessing Windowing

Question 1

when does leakage occur?

Answer 1

Leakage occurs when the number of oscillations of a sinusoid during the total time interval of the recordings is not an integer number.

Question 2

What is bad about leakage?

Answer 2

• Leakage degrades the efficiency of detection and coding signals
• Leakage results in a reduction of the peak amplitude of the sinusoid which corresponds to an effective energy loss at the frequency of the sinusoid.
• Leakage also results in a spreading of the energy of the sinusoid to adjacent spectral coefficients, known as sidelobes

Question 3

How can leakage be avoided?

Answer 3

Leakage can be avoided by choosing the length of the time interval such that the number of oscillations during the total time interval of the recordings is an integer number

Question 4

When can leakage not be avoided?

Answer 4

But what happens, if there are several sinusoids present and it is not possible to choose a time interval of the recordings such that all the sinusoids have an integer number of oscillations.

Question 5

What process needs to take place when leakage cannot be avoided?

Answer 5

• Mitigating
• Mitigating leakage means to limit the adverse effects of leakage as best as possible by spectrum management
• In particular, mitigating leakage aims to preserve the original amplitude of the sinusoid and to minimise the spectral sidelobes
• The meaning of ‘as best as possible’ depends on the application
• Mitigating leakage can include a range of different strategies

Question 6

Most popular technique of mitigating leakage?

Answer 6

Windowing

Question 7

What is windowing?

Answer 7

Windowing means to multiply the original time series samples x_n
with convenient weights w_n such that a new time series is formed:
y_n = w_n x_n which mitigates the effects of leakage

Question 8

The positives and negatives of windowing?

Answer 8

• Windowing can maximise the amplitude of the sinusoid
• Windowing can minimise the sidelobes of the sinusoid
• Windowing can not avoid leakage

Question 9

How to choose the best window for an application

Answer 9

The choice of the best possible window depends on the
specific application and available resources

Question 10

Windowing on a sinusoidal wave?

Answer 10

Question 11

How is the rectangular window described?

Answer 11

Question 12

The Hanning window?

Answer 12

The Hanning window chooses a finite part of the time series and smoothes (tapers) the edges compared to the rectangular window

Question 13

How is the Hanning window described mathematically?

Answer 13

Question 14

The use of the Hanning window:

Answer 14

• The Hanning window is the most popular window
• The Hanning window is often used to estimate the benefit from using more detailed windows to mitigate leakage

Question 15

Window normalization?

Answer 15

Question 16

An example use of Hanning window with no leakage?

Answer 16

Question 17

An example use of Hanning window with leakage?

Answer 17