logajan@ns.UUCP (John Logajan x3118) (01/19/89)
Okay, so what does a Hilbert transform look like? I know some digital filters look like: |----------------------->[sum]---> out | ^ | | [constant]--->[multiply] [constant]--->[multiply] ^ ^ | | in >---->[sum]------------->[storage]----------------->[storage] ^ ^ | | | | v v | | [constant]--->[multiply] [constant]--->[multiply] | |___________________| | |________________________________________________| Where the four constants determine the characteristics of the filter. Would suitable constants transform this into a Hilbert filter???? -- - John M. Logajan @ Network Systems; 7600 Boone Ave; Brooklyn Park, MN 55428 - - ...rutgers!umn-cs!ns!logajan / logajan@ns.network.com / john@logajan.mn.org -
karn@ka9q.bellcore.com (Phil Karn) (01/20/89)
>Okay, so what does a Hilbert transform look like?
Because a Hilbert Transformer is not a linear-phase device, by far the
easiest way to build one in DSP is with a FIR (finite impulse reponse)
filter. Just load up the coefficients in a table and run through them like
any other FIR filter. Any of several standard texts on DSP, e.g., Rabiner
and Gold, can tell you how to compute the optimum coefficients for a FIR
Hilbert Transformer of a given length.
The FIR is much preferred over the IIR (infinite impulse response) filter
design you presented, because it allows the kind of precise control over
filter phase characteristics that is the whole point of the Hilbert
Transform.
Philgrosen@amadeus.ucsb.edu (Mark D. Grosen) (01/21/89)
[Phil talks about Hilbert transformers (filters)] Actually, a Hilbert transformer is linear-phase, just discontinuous at w = 0. It's phase response is -j for 0 < w < pi and +j for -pi < w < 0. It's magnitude is 1 for all frequencies. Analog people call it a 90deg. phase shifter. An FIR filter can realize the phase response exactly, but can only approximate the magnitude response. One approach to a design is to window the ideal impulse response of (2sin**2(pi n / 2))/ (pi * n). An IIR filter can achieve the unit magnitude characteristic (all-pass), but can only approximate the phase characteristic. One advantage of IIR is less overall delay. Mark Mark D. Grosen ARPA: grosen@amadeus.ucsb.edu Signal Processing Lab / Communications Research Lab ECE Dept. University of California Santa Barbara, CA 93106