Power Spectra for Analytic and Numerical Data

function

raw signal

time series

power spectrum

simple function parameters

A

1

1

A

2

2

ω

1

1

ω

2

3

Consider a function defined by

f(t)=

A

1

sin(

w

1

t)+

A

2

cos(

w

2

t)

, in which you can vary the parameters

A

1

,

A

2

,

w

1

, and

w

2

. This Demonstration calculates the power spectrum of

f(t)

based on the method described in [1]. In addition, the power spectrum of raw data is obtained. Power spectra represent a generalization of Fourier analysis, applicable even when the Fourier transform is not well defined.