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muoinhohn
Joined: 05 Nov 2004
Posts: 211
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Location: Hanoi
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 06 Nov 2006 4:19 Bessel filter ? |
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HI all
Anyone can explain to me why a filter of linear phase (like Bessel) is considered the filter has the minimal distortion ?
In my mind, the distortion relates with the phase shift. A filter has a best (minimal) distortion if it has a minimal phase shift that may be linear or non-linear, is it right ?
Best regards
Muoinho
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bcl
Joined: 24 Sep 2006
Posts: 41
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06 Nov 2006 4:33 Re: Bessel filter ? |
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The "distortion" introduced by a passive filter onto a waveform, for example, a squarewave, is caused by the filter's non-linear phase shift within its passband. The non-linear phase shift translates into non-constant group delay by the following relationship: τd≈-dΦ/dω.
The Bessel filter is known for its linear phase response, i.e. constant group delay, hence, minimum "distortion."
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muoinhohn
Joined: 05 Nov 2004
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Location: Hanoi
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06 Nov 2006 4:46 Re: Bessel filter ? |
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Hi,
Thank you very much. I've understood.  .
Regards
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Kral
Joined: 28 Mar 2005
Posts: 1182
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06 Nov 2006 15:47 Re: Bessel filter ? |
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muoinhohn,
An easy exercise to demonstrate the effects of phase non-linearity is as follows. In Excel plot a waveform consisting of a fundamental and a third harmonic. Plot another waveform with the phase of the fundamental shifted 30 degrees, and the phase of the third harmonic shifted 90 degrees. You will see that the resultant waveform is delayed, but not distorted. Now repeat with the fundamental shifted 30 degrees, and the third harmonic shifted 60 degrees. You will see the distortion, even though the amplitudes of the fundamental and third harmonic have not been altered.
Regards,
Kral
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muoinhohn
Joined: 05 Nov 2004
Posts: 211
Helped: 1
Location: Hanoi
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07 Nov 2006 4:23 Re: Bessel filter ? |
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HI Kral
Thank very much for your suggest. In fact I've used Matlab and made one try of 2 sinwave. And i saw signal with distortion and signal without distortion.
In addition, i've found a explanation mathematically in detail about group delay and distortion in the course (on page 13)
http://inst.eecs.berkeley.edu/~ee247/fa06/lectures/L2_f06.pdf
Best regards
Muoinho
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