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<blockquote data-quote="Michael John" data-source="post: 147987" data-attributes="member: 830">Re: FIR filtersHi Frank,Sorry for taking a few days to reply. I&#039;m juggling this great thread with family activities and my &quot;day&quot; job. Regarding the use of the Hilbert transform.... Your plot shows a gently increasing delay in it&#039;s peak toward lower frequencies and I think this might be the result of the minimum-phase behaviour in the calculation of each band.In Matlab I simulated 5 equally wide (on a log scale) gaussian bands.[ATTACH]154511[/ATTACH]I then used the Hilbert Transform, minimum phase filter design approach to create the impulse responses for each band.[ATTACH]154514[/ATTACH]Note how the IR&#039;s of the lower frequency bands peak later in time than the higher frequency bands.Taking the same bands (from the Frequency plot above) and just using a IDFT gives the linear phase impulse responses (shown before and after sample rotation) which all peak at the same time.[ATTACH]154512[/ATTACH][ATTACH]154513[/ATTACH]I suspect using the IDFT, rather than Hilbert Transform approach, would remove the rising delay in your plot and make it symmetric about the same moment in time.One condition for the Hilbert transform approach is that it requires a lower bound on the input magnitude response, so that the LOG() function works. For the plots above, I used a lower bound of 1e-20. Changing this lower bound causes a time shift to the minimum phase IR&#039;s (2nd plot above) of all the bands.Also, a colleague here in Sydney showed me how using two IDFT&#039;s per gaussian band - with one as is and the other pre-multiplied by complex &quot;i&quot; for a 90 deg phase shift - gives two impulse responses that can be combined to create a nice envelope follower. I can email you the Matlab code.Best,Michael</blockquote>

[QUOTE="Michael John, post: 147987, member: 830"] Re: FIR filters Hi Frank, Sorry for taking a few days to reply. I'm juggling this great thread with family activities and my "day" job. Regarding the use of the Hilbert transform.... Your plot shows a gently increasing delay in it's peak toward lower frequencies and I think this might be the result of the minimum-phase behaviour in the calculation of each band. In Matlab I simulated 5 equally wide (on a log scale) gaussian bands. [ATTACH=CONFIG]154511.vB5-legacyid=14064[/ATTACH] I then used the Hilbert Transform, minimum phase filter design approach to create the impulse responses for each band. [ATTACH=CONFIG]154514.vB5-legacyid=14067[/ATTACH] Note how the IR's of the lower frequency bands peak later in time than the higher frequency bands. Taking the same bands (from the Frequency plot above) and just using a IDFT gives the linear phase impulse responses (shown before and after sample rotation) which all peak at the same time. [ATTACH=CONFIG]154512.vB5-legacyid=14065[/ATTACH][ATTACH=CONFIG]154513.vB5-legacyid=14066[/ATTACH] I suspect using the IDFT, rather than Hilbert Transform approach, would remove the rising delay in your plot and make it symmetric about the same moment in time. One condition for the Hilbert transform approach is that it requires a lower bound on the input magnitude response, so that the LOG() function works. For the plots above, I used a lower bound of 1e-20. Changing this lower bound causes a time shift to the minimum phase IR's (2nd plot above) of all the bands. Also, a colleague here in Sydney showed me how using two IDFT's per gaussian band - with one as is and the other pre-multiplied by complex "i" for a 90 deg phase shift - gives two impulse responses that can be combined to create a nice envelope follower. I can email you the Matlab code. Best, Michael [/QUOTE]

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