User`s guide
106
The result of FFT includes a real and an imaginary component. The magnitude (or power)
and phase of the FFT data is computed by
=
For example, at 10Hz, the magnitude of the function
has magnitude of
2, and a phase of or
; while the function
has a magnitude of 2
and a phase of 0 at 5Hz.
2.3.1.4 Properties of Fourier Transforms
The Fourier transform is linear. It possesses the properties of homogeneity and additivity.
That is, scaling in one domain corresponds to scaling in another domain, and addition in one
domain correspond to addition in another domain.
Figure 27 shows scaling and addition of
and mentioned in previous paragraph.
We can clearly see that scaling the input in time domain results in same scaling in magnitude, but
has no effect in phase. And addition of inputs in time domain correspond to a combination of
magnitude and phase of the two inputs’ frequency domain.
Time
Domain
Magnitude in Frequency
Domain
Phase in Frequency
Domain
-2
0
2
0 0.5 1
f(x)=2sin(20𝜋x)
0
1
2
3
0 5 10 15 20 25 30
-2
-1.5
-1
-0.5
0
0 5 10 15 20 25 30
-2
0
2
0 0.5 1
g(x)=2cos(10𝜋x)
0
1
2
3
0 5 10 15 20 25 30
0
0.5
1
0 5 10 15 20 25 30
Eq.54
Eq.55