"ABEFAR" <
[email protected]> wrote in
news:
[email protected] oups.com:
> i'm very pleased that it is possible to build a hilbert transformer
> I'd like to start building a new hilbert transformer in my master study
>
> could you please help me in drawing flow chart for what to start with
> abdullah
>
>
Hilbert transformers are very easy using the odd length FIR filter
method.
This is illustrated in Rick Lyon's book: Understanding Digital Signal
Processing (second edition).
Basically you create antisymmetric coefficients around the center of your
FIR. The output of this filter with be the Q part. You can take the
center tap of the delay line to get the I part.
The catch to hilbert transformers of this type is that the FIR will be a
bandpass. If you need a wide hilbert transformer, you need a long FIR.
This makes some sense if you think about it. How would you delay to
create 90 degrees at DC (about an infinite number of taps).
The other catch to hilbert transformers is that the amplitude response of
the Q section will not be exactly 1. It will always have some ripple. You
extend the length to improve both the frequency response and bandwidth.
The FIR can be created using a windowing method or remez exchange. The
windowing method has an interesting property in that 1/2 of the
coefficients are 0 anbd therefore you can omit them from your
calculation. The center of the hilbert bandpass will be 1/4 the sampling
rate. I use Kaiser windows when using the window method. The trick I
learned recently is that the there will be the same number of 0 values
for a filter length of 4n-1 as 4n+1. Therefore you might create a 4n+1
filter and then truncate to 4n-1 length. I got better results in my last
application for exactly the same computation requirements.
The remez exchange will have non zero vaues for each tap, but may yield a
flatter response for a wider bandwidth.
I use hilbert transformers all the time to make detectors, since SQRT(I^2
+ Q^2) is the magnitude. In many cases, I skip the SQRT since a
comparision to a known value might be all that is important (MS vs RMS)
--
Al Clark
Danville Signal Processing, Inc.
--------------------------------------------------------------------
Purveyors of Fine DSP Hardware and other Cool Stuff
Available at
http://www.danvillesignal.com