Calculates a simple Hilbert transform of a real series.
HILB(series)
series |
- |
A real input series. |
A complex series or array.
W1: gcos(1000, 1/1000, 3)
W2: hilb(W1)
W3: gcos(1000, 1/1000, 3, -pi/2)
W4: imag(W2)
W1 contains a 3 Hz cosine wave.
W2 computes the complex Hilbert Transform. The real part is the original input series in W1. The imaginary part is the actual Hilbert Transform.
W3 creates the same cosine wave as W1 except the phase is shifted -90 degrees.
W4 is the Hilbert transform of W1. It is equal to the -90 degree phase shifted cosine in W3 to machine precision.
W1: gnorm(1000, 0.1)
W2: hilb(W1)
W3: real(W2)
W4: imag(W2)
The real part of HILB is the same as the input series. The imaginary part of HILB is the Hilbert Transform.
The Hilbert transform shifts each positive phase component of a series by -90 degrees and each negative phase component by +90 degrees.
The real part of HILB is the same as the input series. The imaginary part of HILB is the Hilbert Transform.
HILB uses the FFT and IFFT to calculate the Hilbert transform.