The Symmetry Principle - Signals, Processes, and Systems - page 132

T ime domain

Sawtooth FFT IF F T

1,0
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0,0
1,0
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0,0

0.00 0.25 0.50 0.75 1.0

s

Time domain

Sawtooth FFT Cut off IF F T

1,0
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0,0
0,8

0,7
0,6

0,5
0,4
0,3

0,2

0.00 0.25 0.50 0.75 1.0

s

Illustration 95: FT and IFT: symmetrical FOURIER transformation

A periodic sawtooth signal with four Hz was selected as a test signal. You could, however, just as well take
any other signal, for example noise. Set as usual the sampling frequency and the block length at 1024
using the menu option A/D.
In the module "cut out" the frequencies 0 - 32 Hz were allowed to pass (in the case of the settings selected
the sample value is practically equivalent to the frequency). You see the highest frequency of 32 Hz as the
ripple content of the sawtooth: this "ripple" sine covers 8 periods with any sawtooth; in the case of 4 Hz
sawtooth frequency the highest frequency allowed to pass) has the value 4 < 8 = 32 Hz.
It is very important in this connection to set exactly the same "cut out" on both channels (frequency
domain).