Pacchetto 7

Question 1

Introduction discrete fourier transform

Answer 1

• it s not possible to observe a signal for an infinite time lenght
• usually a signal is observed over finite time lenght
• if we observe a signal as a finite time record this means windowing the signal ( to see the signal in a window of time).
• ## the window has an effect on the signal

Question 2

Wich is the effect of windowing?

Answer 2

• Assumption: The window is infinite and has a value different from zero only in aceratin period T, at this stage we don’ t care about sampling.
• moltiplico segnale per window e poi applico il sampling

Question 3

Leakage

Answer 3

• Applying a window produces changes to the spectrum, because now it is discrete.
• Thus not all freq frequencies can be represented just those that are integer multiples of foundamental one.

Question 4

leakage and discontinuity

Answer 4

• Leakage is correlated to a discontinuity between the first and last point of the signal.

Question 5

How to avoid leakage?

Answer 5

• Periodic signal: 1) acquiring delta t. 2) Aurocorr to find T. 3) Cut removing the spare part of T

Question 6

How to find leakage?

Answer 6

• Periodic: Where exist discontinuity
• Non periodic: No way to reduce the impact of leakages on spectrum.