App-15
IM 701210-06E
Appendix
App
Appendix 5 User-Defined Computation
Hilbert Function (HLBT)
Normally, when we analyze a real time signal, it is convenient to think of this signal as
the real part of a complex function and do the actual analysis using the complex function.
If the real time signal is considered to be the real part of the function, the imaginary part
can be determined with the Hilbert transform of the real part.
The Hilbert transform does not change the order of the individual variables. Hilbert
transform of a time signal results in another time signal.
Hilbert transform is described below.
When transforming a signal in the time domain, the signal is transformed into the
frequency domain, first, using the Fourier transform. Next, the phase of each frequency
component is shifted by –90 deg if the frequency is positive and +90 deg if negative.
Lastly, taking the inverse Fourier transform completes the Hilbert transform.
Application Example
• Hilbert transform can be used to analyze an envelope waveform.
AM (amplitude modulation): SQRT(C1*C1+HLBT(C1)*HLBT(C1))
Demodulation of a FM signal: DIF(PH(C1,HLBT(C1)))
Phase Function (PH)
Phase function PH(X1,Y1) computes tan
–1
(X1/Y1).
However, the phase function takes the phase of the previous point into consideration and
continues to sum even when the value exceeds
±π
(ATAN function reflects at
±π
).
The unit is radians.
Preceding Point
Preceding Point
θ
2
θ
2
θ
2=
θ
1+
∆θ
2
θ
2=
θ
1-
∆θ
2
∆θ
2
∆θ
2
θ
1
θ
1
