App-10
IM 701830-01E
Hilbert Function (HLBT)
Normally, when we analyze a real time signal, it is convenient to think of this signal as the real
part of the complex function and do the actual analysis using the complex function.
If the real time signal is considered 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.
Example of an application
• Hilbert transform can be used to analyze an envelope waveform.
AM modulation: SQR(C1*C1+HLBT(C1)*HLBT(C1))
Demodulation of a FM signal: DIF(PH(C1,HLBT(C1)))
Phase Function
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
Appendix 6 About User Defined Computations
