Hilbert Transform

Does anyone else find it odd that the hilbert function does not compute the Hilbert Transform? According to the help:

X = HILBERT(Xr) computes the so-called discrete-time analytic signal X = Xr + i*Xi such that Xi is the Hilbert transform of real vector Xr.

In other words, if you want to take the Hilbert transform of Xr you need imag(hilbert(Xr)). This seems so backwards to me.

Answer 1

[Andrew Newell]

It is backwards if you just want the Hilbert transform, but hilbert is part of the Signal Processing Toolbox, and maybe the users of this toolbox always use a Hilbert transform this way. To quote the documentation, "The Hilbert transform is useful in calculating instantaneous attributes of a time series, especially the amplitude and frequency. The instantaneous amplitude is the amplitude of the complex Hilbert transform; the instantaneous frequency is the time rate of change of the instantaneous phase angle."

But you have a point - they could have named the function analyticsignal.

Answer 2

[Debejyo Chakraborty]

In signal processing, we need exactly what Hilbert gives. In this community, the Hilbert transform is used to create an analytic signal. So, the function as is makes sense.

[Daniel Shub]

But as Andrew said, why not call the function which produces the analytic signal analyticsignal and the function which produces the Hilbert transform hilbert?

[Debejyo Chakraborty]

Agreed. That is would have been a much better naming convention.