Communications Toolbox

Designing Hilbert Transform Filters

The hilbiir function designs a Hilbert transform filter and produces either

• A plot of the filter's impulse response
• A quantitative characterization of the filter, using either a transfer function model or a state-space model

Example with Default Parameters

For example, typing simply

• hilbiir
  

plots the impulse response of a fourth-order digital Hilbert transform filter having a 1-second group delay. The sample time is 2/7 seconds. In this particular design, the tolerance index is 0.05. The plot also displays the impulse response of the ideal Hilbert transform filter having a 1-second group delay. The plot is in the figure Impulse Response of a Hilbert Filter.

To compute this filter's transfer function, use the command below.

• [num,den] = hilbiir
  
  num =
  
     -0.3183   -0.3041   -0.5160   -1.8453    3.3105
  
  
  den =
  
      1.0000   -0.4459   -0.1012   -0.0479   -0.0372
  

Here, the vectors num and den contain the coefficients of the numerator and denominator, respectively, of the transfer function in ascending order of powers of z^-1.

The commands in this section use the function's default parameters. You can also control the filter design by specifying the sample time, group delay, bandwidth, and tolerance index. The reference entry for hilbiir explains these parameters. The group delay is also mentioned above in Noncausality and the Group Delay Parameter.

Noncausality and the Group Delay Parameter

Raised Cosine Filters in Communication Systems