# Impulse response of the hilbert transform

Started by March 30, 2009
```hi there, i was going through a paper on using hilbert transform for edge
detection in image processing.It said over there that the hilbert transform
works better than differentiation for edge detection as it has longer
impulse response which helps reduce the effect of noise.I am new to the
subject and dont understand what exactly does a longer impulse response
mean.??.and how does the impulse response of a system determine its
susceptibility to noise..??..and ya what is the impulse response of the
hilbert transform..i think its [-j.sgn(f)].correct me if i am wrong but
does a longer impulse response mean that it covers a larger band of

```
```On Mar 30, 8:02&#4294967295;am, "Anex" <anex.stormri...@gmail.com> wrote:
> hi there, i was going through a paper on using hilbert transform for edge
> detection in image processing.It said over there that the hilbert transform
> works better than differentiation for edge detection as it has longer
> impulse response which helps reduce the effect of noise.I am new to the
> subject and dont understand what exactly does a longer impulse response
> mean.??.and how does the impulse response of a system determine its
> susceptibility to noise..??..and ya what is the impulse response of the
> hilbert transform..i think its [-j.sgn(f)].correct me if i am wrong but
> does a longer impulse response mean that it covers a larger band of

Hello Anex,

You can find the impulse response of a Hilbert transform in this
paper. It gives the theoretical response. It is essentially 1/t.

http://www.claysturner.com/dsp/HilbertTransforms.pdf

But you can design via a Parks-McClellan algorithm practical varsions
of Hilbert transforms.

But since you say you are doing edge detection, you may find this