(ffmpeg-user Digest, Vol 54, Issue 10)
" It was seen in Figure 2.7 that a sinusoidal function is a rotation
resolved in one axis. In order to obtain a purely sinusoidal motion, the
motion on the other axis must be eliminated. Conceptually this may be
achieved by having a contra-rotating system in which there is one
rotation at +w and another at -w. Figure 2.8(a) shows that the sine
components of these two rotations will be in the same phase and will
add, whereas the cosine components will be in anti-phase and will
cancel. Thus all real frequencies actually contain equal amounts of
positive and negative frequencies. These cannot be distinguished unless
a modulation process takes place. Figure 2.8(b) shows that when two
signals of frequency +/-w1 and +/-w2 are multiplied together, the result is
that the rotations of each must be added. The result is four frequencies,
+/-(w1 + w2) and +/-(w1 - w2), one of which is the sum of the input
frequencies and one of which is the difference between them. These
are called sidebands."
The fact is that there is no picture 2.7 in the book, yeeeeheeee !
First of all i don't get this sentence :
"Conceptually this may be
achieved by having a contra-rotating system in which there is one
rotation at +w and another at -w."
Can someone explain me please ?
=>Read up on Fourier analysis...
In yet other words, a real sinusoid has symmetric contributions from
positive and negative freqs:
cos(x) = (exp(ix)+exp(-ix))/2
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