Lecture 7

Question 1

Power spectrum

Answer 1

can describe signal f(t) using Fourier series

Question 2

Fourier transform F(f(t)) decomposes f(t) into

Answer 2

these sines + cosines

Question 3

Power spectrum or Power spectral density (PSD) =

Answer 3

|F(f(t))|^2

peaks at frequencies of the identified periodic basis functions

Question 4

If signal random

Answer 4

“white-noise”

PSD ≈ constant or flat

one part of the signal is entirely uncorrelated with any other

Question 5

PSD(v)^2 =

Answer 5

C(v)^2 + S(v)^2

Question 6

Filter out low and high frequency noise (graph)

Answer 6

see notes

Question 7

inverse Fourier transform of PSD gives

Answer 7

“clean” signal

Question 8

Phase folding

Answer 8

for repeating signal, not clear sinusoid + badly sampled

Question 9

To get signal period

Answer 9

1) Guess period Ti
2) Divide data into Ti chunks
3) Fold/Stack data together on this trial Ti
4) Take average of same element in all chunks
5) Plot average vs element (bin) number

Question 10

Why do we use Wavelets

Answer 10

Fourier transform not always best approach if aperiodic
=> burst or ‘quasi periodic’ with changing frequency or amplitude
=> how is the signal changing with time

Question 11

Wavelets

Answer 11

Decomposes into basis functions called mother wavelets Ψa,b(t) many to choose from

Question 12

W(a,b) =

Answer 12

(-∞ ∫ ∞) h(t) 1/√a Ψ (t-b/a)dt

a = scaling (period)
b = time shift

Question 13

Wavelet superposition

Answer 13

signal will be linear sum of the wavelets scaled + shifted.

if had W(a,b) for various a,b could reconstruct signal