Applying Analytics

110 Applying Analytics: A Practical Introduction

5.8.1.2 Power Spectrum

As an alternative to directly plotting the outputs of the DFT, a plot o f the

power spectrum, P

k

, can be used to examine the strength of the signal at

different frequencies. When I use a Fourier transform, I usually don’t need to

view the positive and negative frequency components separately, so I prefer

to a nalyze the power spectrum. The power spectrum’s definition is given by:

P

k

=











1

n

2

|Y

0

|

2

for k = 0

1

n

2



|Y

k

|

2

+ |Y

n−k

|

2



for 0 < k < n/2

1

n

2





Y

n/2





2

for k = n/2 , even n only

(5.32)

which combines the power from positive and negative frequencies Y

k

and Y

n−k

into a single component of ...