I am often seeing this notation \$x^*(t)=x(t)\$ or similar but I cannot remember when I saw it the first time and I cannot find anywhere that explains the meaning of that notation. What does it mean?
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\$x^*(t)\$ can also relate to a sampled signal, the \$*\$ is the means to distinguish it from a continuous-time waveform. – Verbal Kint Dec 11 '19 at 13:16
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\$x^*(t)\$ is the complex conjugate of \$x(t)\$
So, when \$x(t)\$ is defined as $$x(t)=a+bj$$ then $$x^*(t)=a-bj$$.
When $$x^*(t)=x(t)$$ it means
$$a+bj=a-bj$$
This is only true when \$b=0\$, so \$x(t)\$ has to be a real number.
Huisman
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\$x^*\$ means the complex conjugate, i.e. if \$x = a + jb\$, then \$x^* = (a + jb)^* = a -jb\$. So if \$x=x^*\$ obviously \$b\$ must be 0, i.e. then \$x\$ is real.
Curd
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