Alex_Zapantis
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Απάντηση: DEQX hdp-express
Αντιγράφω από εδώ:
http://www.weiss.ch/eq1/brochures/eq1lp.pdf
Linear phase IIR filters
Contrary to common belief, non-minimum phase IIR systems are realizable, this usually involves a minimum-phase section followed by a linear all-pass section with any arbitrary phase response.
Thus, a linear-phase system would have a minimum-phase system followed by an all-pass system designed to have a phase response which, when added to the minimum-phase, will result in a linear phase response.
This can (theoretically) be done in the analogue as well as the digital domain.
However, there are certain practical problems which make this method difficult, if not impossible.
FIR filters
There is no direct way to transform analogue equalizer parameters to digital FIR systems, though there are algorithms that try to emulate a specific frequency response on a FIR system.
These yield quite exact copies of the amplitude (and perhaps even the phase) response.
FIR filters also have certain properties:
1. A finite impulse response, resulting in a fixed length output when excited by an input pulse.
2. Most design algorithms produce a linear phase response (just as IIR designs result in minimum phase responses).
3. A delay.
So linear phase response is almost a by product of FIR filters.
But IIR filters are favoured over FIR filters in audio equalizers because of several reasons:
1. The delay of the FIR systems is usually not acceptable for audio processing.
2. The parameters of analogue equalizers are easier maintained in IIR than FIR filters.
3. There is a considerably larger hardware expense involved for tuneable FIR audio equalizer than for the IIR equivalent.
4. Digital signal processing for audio band FIR filters is computationally more intensive than for IIR filters.
FIR filters are used mainly for applications requiring extremely narrow transition bandwidths combined with no effects (i.e. phase shifts) in the pass band.
Examples (in audio applications) are interpolation filters for sample rate conversion and band-split filters for crossovers.
In order to avoid the technical and commercial drawbacks of FIR systems for audio equalizers, the Weiss Gambit EQ1-LP uses yet another scheme for linear phase response based on the following property of IIR filters: if one processes a sample with any IIR system, then time-reverses this sample and processes it again with the same IIR system, one will effectively have cancelled out the phase response of the IIR system, while squaring the amplitude response.
The solution lies in the time-reversed (noncausal) filter of this algorithm.
So effectively, the EQ1-LP is a time machine, sending the audio signal backwards through time...
On a side note, this algorithm was experimentally implemented by Weiss Engineering in 1995, but only now is current DSP hardware powerful enough to realize the seven band 96kHz requirements of the EQ1-LP.
Συνεπώς, ακόμα και αν δε μας ενδιαφέρει και τόσο η δυνατότητα χρήσης FIR φίλτρων αυτή καθεαυτή, η ύπαρξή τους εντός ενός μηχανήματος (ή software) μπορεί να είναι επιθυμητή κυρίως ως ένδειξη στιβαρής "μπαταρίας" υπολογιστικής ισχύος, που, με τη σειρά της αυξάνει σοβαρά τις πιθανότητες "ικανοποίησης της μαντάμ πχιότητας".
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Αντιγράφω από εδώ:
http://www.weiss.ch/eq1/brochures/eq1lp.pdf
Linear phase IIR filters
Contrary to common belief, non-minimum phase IIR systems are realizable, this usually involves a minimum-phase section followed by a linear all-pass section with any arbitrary phase response.
Thus, a linear-phase system would have a minimum-phase system followed by an all-pass system designed to have a phase response which, when added to the minimum-phase, will result in a linear phase response.
This can (theoretically) be done in the analogue as well as the digital domain.
However, there are certain practical problems which make this method difficult, if not impossible.
FIR filters
There is no direct way to transform analogue equalizer parameters to digital FIR systems, though there are algorithms that try to emulate a specific frequency response on a FIR system.
These yield quite exact copies of the amplitude (and perhaps even the phase) response.
FIR filters also have certain properties:
1. A finite impulse response, resulting in a fixed length output when excited by an input pulse.
2. Most design algorithms produce a linear phase response (just as IIR designs result in minimum phase responses).
3. A delay.
So linear phase response is almost a by product of FIR filters.
But IIR filters are favoured over FIR filters in audio equalizers because of several reasons:
1. The delay of the FIR systems is usually not acceptable for audio processing.
2. The parameters of analogue equalizers are easier maintained in IIR than FIR filters.
3. There is a considerably larger hardware expense involved for tuneable FIR audio equalizer than for the IIR equivalent.
4. Digital signal processing for audio band FIR filters is computationally more intensive than for IIR filters.
FIR filters are used mainly for applications requiring extremely narrow transition bandwidths combined with no effects (i.e. phase shifts) in the pass band.
Examples (in audio applications) are interpolation filters for sample rate conversion and band-split filters for crossovers.
In order to avoid the technical and commercial drawbacks of FIR systems for audio equalizers, the Weiss Gambit EQ1-LP uses yet another scheme for linear phase response based on the following property of IIR filters: if one processes a sample with any IIR system, then time-reverses this sample and processes it again with the same IIR system, one will effectively have cancelled out the phase response of the IIR system, while squaring the amplitude response.
The solution lies in the time-reversed (noncausal) filter of this algorithm.
So effectively, the EQ1-LP is a time machine, sending the audio signal backwards through time...
On a side note, this algorithm was experimentally implemented by Weiss Engineering in 1995, but only now is current DSP hardware powerful enough to realize the seven band 96kHz requirements of the EQ1-LP.
Συνεπώς, ακόμα και αν δε μας ενδιαφέρει και τόσο η δυνατότητα χρήσης FIR φίλτρων αυτή καθεαυτή, η ύπαρξή τους εντός ενός μηχανήματος (ή software) μπορεί να είναι επιθυμητή κυρίως ως ένδειξη στιβαρής "μπαταρίας" υπολογιστικής ισχύος, που, με τη σειρά της αυξάνει σοβαρά τις πιθανότητες "ικανοποίησης της μαντάμ πχιότητας".
