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# hilb

FIR approximation to a Hilbert transform filter

### Syntax

`xh=hilb(n [,wtype [,par]])`

### Arguments

n

odd integer : number of points in filter

wtype

string : window type `('re','tr','hn','hm','kr','ch')` (default `='re'`)

par

window parameter for `wtype='kr' or 'ch'` default `par=[0 0]` see the function window for more help

xh

Hilbert transform

### Description

Returns the first n points of an FIR approximation to a Hilbert transform filter centred around the origin.

The FIR filter is designed by appropriately windowing the ideal impulse response `h(n)=(2/(n*pi))*(sin(n*pi/2))^2` for `n` not equal 0 and `h(0)=0`.

An approximation to an analytic signal generator can be built by designing an FIR (Finite Impulse Response) filter approximation to the Hilbert transform operator. The analytic signal can then be computed by adding the appropriately time-shifted real signal to the imaginary part generated by the Hilbert filter.

### References

`http://ieeexplore.ieee.org/iel4/78/7823/00330385.pdf?tp=&arnumber=330385&isnumber=7823`

A. Reilly, G. Frazer, and B. Boashash, "Analytic signal generation Tips and traps", IEEE Trans. Signal Processing, vol. 42, pp.3241-3245, Nov. 1994.

• window — compute symmetric window of various type
• hilbert — Discrete-time analytic signal computation of a real signal using Hilbert transform

### Examples

`plot(hilb(51))`