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Hilbert Transformer FIR Design
Syntax y = hilbert(Ntaps) ("RECTANGULAR" assumed)
Syntax y = hilbert(Ntaps,wintype) (all windows except "GAUSSIAN" and "KAISER")
Syntax y = hilbert(Ntaps,wintype,winparam) ("GAUSSIAN" and "KAISER" windows only)
Include: include spt\hibert.oms
See Also linfir , pwlfir , rcfir , srrcfir , pbfir

ARGUMENTS:
   INPUTS:
      Ntaps    = INPUT, scalar, any numerical type. Filter length in
                 [taps]. Coerced to INTEGER.
      wintype  = INPUT, string. One of ["RECTANGULAR"|
                 "TRIANGULAR"|"HAMMING"|"HANNING"|"NUTTALL"|
                 "BLACKMAN"|"GAUSSIAN"|"KAISER"].
      winparam = INPUT, scalar, any numerical type. Parameter
                 used by GAUSSIAN or KAISER window functions.
                 Coerced to DOUBLE.
   RETURN: Returns DOUBLE column vector Hilbert Transformer FIR
           filter of length Ntaps.

Description

Designs and returns a Hilbert transformer FIR digital filter as a column vector.

Creates a linear phase, windowed Hilbert Transformer FIR filter of length 'Ntaps'. Function returns a column vector of type DOUBLE. 'Ntaps' may be of any numerical type and is coerced to INTEGER before local processing. 'Ntaps' must be ODD-valued, and must be >=3 or novalue is returned.

The ideal Hilbert transformer is a filter with unity gain and a phase shift of 90 degrees at all frequencies. The Hilbert transform is useful in creating 'analytic' signals and generally where quadrature related signals are required. The Hilbert transform of a sinewave is another sinewave delayed by 90 degrees. The Hilbert transformer FIR has an additional delay of (Ntaps-1)/2 samples due to the causality of the filter.

A window function may be applied to the resulting FIR filter. 'wintype' is a string specifying the window type to be applied. 'winparam' is the numerical parameter used with the GAUSSIAN and KAISER window functions. If you leave off 'wintype' and 'winparam', a "RECTANGULAR" window is assumed. For windows other than "GAUSSIAN" and "KAISER", 'winparam' may be omitted. Error handling is done by 'winddata()' function.

Example
Make a 31-tap Hilbert transformer.


Ntaps = 31                       # Number of taps
win   = "TRIANGULAR";            # Window Type
fs    = 10d3                     # sampling rate
h     = hilbert(Ntaps,win)       # HAMMING
h
t     = seq(Ntaps)-1d0;          # Tap index
M     = 100;                     # Number points for freq response
fmin  = 10d0;                    # freq min plot
fmax  = fs/2-1d0;                # freq max plot
df    = (fmax-fmin)/M;           # freq increment
f     = (seq(M+1)-1d0)/M*fs/2d0; # freq vector
HdB   = db20(gainz(h,1,f,fs));   # dB response

 The filter taps are:

{
-0.00297465
0
-0.0102969
0
-0.0202817
0
-0.0347042
0
-0.0573682
0
-0.0981634
0
-0.193352
0
-0.669296
0
0.669296
0
0.193352
0
0.0981634
0
0.0573682
0
0.0347042
0
0.0202817
0
0.0102969
0
0.00297465
}

 Plots of the filter and it's frequency response are:



Reference

Stearns & David