Difference Between 1st and 2nd Degree All-Pass Filter - AVS Forum
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post #1 of 24 Old 08-06-2013, 08:06 PM - Thread Starter
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I'm starting to research DSPs for my theater build, and the first one I've come across is the Xilica XP series. One feature I'll need is an all-pass filter to add some decorrelation to my side surround array. I've looked at the XP manual, and it specifies that it includes a 1st degree and a 2nd degree all-pass.

Could someone explain the difference between these two filters?

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post #2 of 24 Old 08-07-2013, 04:56 AM
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The first question I would ask is "Why do you feel you need all pass filters?"

And exactly what you mean be "decorrelation"?

I think you are missing several points-but just want to be sure.I am understanidng the question properly
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post #3 of 24 Old 08-07-2013, 05:06 AM
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Quote:
Originally Posted by J_P_A View Post

I'm starting to research DSPs for my theater build, and the first one I've come across is the Xilica XP series. One feature I'll need is an all-pass filter to add some decorrelation to my side surround array. I've looked at the XP manual, and it specifies that it includes a 1st degree and a 2nd degree all-pass.

Could someone explain the difference between these two filters?

All other things being equal, higher order gets you a faster transition, or a narrower transition band. That's the biggie. In your application you appear to be using the all pass to compensate for something. You need to match the transition band to the effect you are trying to compensate for.
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post #4 of 24 Old 08-07-2013, 05:50 AM - Thread Starter
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Quote:
Originally Posted by Ivan Beaver View Post

The first question I would ask is "Why do you feel you need all pass filters?"

And exactly what you mean be "decorrelation"?

I think you are missing several points-but just want to be sure.I am understanidng the question properly

I'm planning for a side array in my theater. So both rows are planned to have their own pair of surrounds (one left, one right, for each row. Four total). The way I understand this, Simply time delaying the signals is not enough to prevent comb filtering or intelligibility issues associated with slightly delayed signals. The signals must also be decorrelated through randomized phase, which is what I "think" the all-pass filter does. Am I beginning with a faulty premise?

I'm just starting to research this, so I'm sure I'm missing quite a bit. I enjoy learning about it, though smile.gif
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All other things being equal, higher order gets you a faster transition, or a narrower transition band. That's the biggie. In your application you appear to be using the all pass to compensate for something. You need to match the transition band to the effect you are trying to compensate for.

I certainly see how this would apply to a low-pass, high-pass, or band-pass filter, but in the case of an all-pass filter I didn't think there was a transition?

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post #5 of 24 Old 08-07-2013, 05:54 AM
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Originally Posted by J_P_A View Post

Quote:
Originally Posted by Ivan Beaver View Post

The first question I would ask is "Why do you feel you need all pass filters?"

And exactly what you mean be "decorrelation"?

I think you are missing several points-but just want to be sure.I am understanidng the question properly

I'm planning for a side array in my theater. So both rows are planned to have their own pair of surrounds (one left, one right, for each row. Four total). The way I understand this, Simply time delaying the signals is not enough to prevent comb filtering or intelligibility issues associated with slightly delayed signals. The signals must also be decorrelated through randomized phase, which is what I "think" the all-pass filter does. Am I beginning with a faulty premise?

I'm just starting to research this, so I'm sure I'm missing quite a bit. I enjoy learning about it, though smile.gif
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Originally Posted by arnyk View Post

All other things being equal, higher order gets you a faster transition, or a narrower transition band. That's the biggie. In your application you appear to be using the all pass to compensate for something. You need to match the transition band to the effect you are trying to compensate for.

I certainly see how this would apply to a low-pass, high-pass, or band-pass filter, but in the case of an all-pass filter I didn't think there was a transition?

There surely is a transition band in an all-pass, its just in the phase curve since the amplitude curve is by defintion flat.
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post #6 of 24 Old 08-07-2013, 06:04 AM - Thread Starter
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Quote:
Originally Posted by arnyk View Post

There surely is a transition band in an all-pass, its just in the phase curve since the amplitude curve is by defintion flat.

This is the only other mention of the all-pass filters I can find in the manual (which is rather sparse, unfortunately)
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The EQ bandwidth ranges from 0.02 to 3.61 octaves in steps of 0.01 octave. The equivalent Q value is automatically shown besides the octave value. For 1st degree all-pass (AP-1) filter, the bandwidth will sets the phase shift at the centre frequency. This phase shift is gradually changed from 180 degrees above the centre frequency to the specified value.

Although, this doesn't exactly sound like what I want, either. I was under the impression that a randomized phase is what is required. I'm having a hard time visualizing how I would implement this in an intelligent way (other than trial and error).

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post #7 of 24 Old 08-07-2013, 01:10 PM
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Hi J_P_A,

I was scratching my head yesterday, trying to understand. Now, I think I do.
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Originally Posted by J_P_A View Post

. . . I've looked at the XP manual, and it specifies that it includes a 1st degree and a 2nd degree all-pass.

Could someone explain the difference between these two filters?
For digital IIR filters in general, a second degree filter is simply two IIR filters cascaded together in series. As Arny said, a second-order filter will give you steeper roll-off, but with an all-pass filter, it gives you two opportunities to adjust the phase, instead of just one.

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The first question I would ask is "Why do you feel you need all pass filters?"
. . . The way I understand this, Simply time delaying the signals is not enough to prevent comb filtering or intelligibility issues associated with slightly delayed signals. The signals must also be decorrelated through randomized phase, which is what I "think" the all-pass filter does.
Well, almost.

As opposed to a FIR filter, the phase-shift of a IIR filter is non-linear. But I would hesitate to call it "random", as the phase is fixed for any particular frequency. So I'm not sure it will get you the "decorrelation" that you're looking for. It would just change the comb-filtering, although that may be all you need.

The normal use of an all-pass IIR filter is to correct phase. A filter would be designed to create specific phase-shifts at specific frequencies to compensate for unwanted phase-shifts in other portions of the signal path. But designing an IIR filter to control phase is more difficult than designing it to control frequency response, and I don't (yet) know how to design one for phase correction.
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post #8 of 24 Old 08-07-2013, 01:37 PM - Thread Starter
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Quote:
Originally Posted by MarkHotchkiss View Post

.......
For digital IIR filters in general, a second degree filter is simply two IIR filters cascaded together in series. As Arny said, a second-order filter will give you steeper roll-off, but with an all-pass filter, it gives you two opportunities to adjust the phase, instead of just one.
Well, almost.

As opposed to a FIR filter, the phase-shift of a IIR filter filter is non-linear. But I would hesitate to call it "random", as the phase is fixed for any particular frequency. So I'm not sure it will get you the "decorrelation" that you're looking for. It would just change the comb-filtering, although that may be all you need.

The normal use of an all-pass IIR filter is to correct phase. A filter would be designed to create specific phase-shifts at specific frequencies to compensate for unwanted phase-shifts in other portions of the signal path. But designing an IIR filter to control phase is more difficult than designing it to control frequency response, and I don't (yet) know how to design one for phase correction.

Very informative. This is the thread that started the gears turning on this particular subject. I'm trying to setup a side array of surround speakers, and the more experienced members (as well as some of the linked material) suggested that decorrelating the pairs of surrounds is necessary.

I interpret that to mean that you want the same spectral content, but at different phases in order to simulate a much larger space.

Does anyone have any recommendations on how this is generally done?

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post #9 of 24 Old 08-07-2013, 04:46 PM
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You only have issues with combfiltering when you have THE SAME signal arriving at a location at different times.

When the signal is different (as would be with different channels of a surround system with normal program material-NOT test noise) the issue is going to be pretty much nonexistant.

How can you have cancellation-when there is nothing to cancel with?

Personally I would not worry about it.
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post #10 of 24 Old 08-07-2013, 05:09 PM - Thread Starter
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Quote:
Originally Posted by Ivan Beaver View Post

You only have issues with combfiltering when you have THE SAME signal arriving at a location at different times.

When the signal is different (as would be with different channels of a surround system with normal program material-NOT test noise) the issue is going to be pretty much nonexistant.

How can you have cancellation-when there is nothing to cancel with?

Personally I would not worry about it.

That's exactly the issue I'm trying to deal with. I will have two side surrounds for row one left and right), and two more side surrounds for row two (left and right). As an example, the right side surround for row one will play the same sound as the right side surround for row two. The problem being that people in row one will hear the sounds from the row two surrounds, but delayed in time (and vice versa).

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post #11 of 24 Old 08-07-2013, 06:21 PM
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An all-pass filter does not decorrelate anything, as stated above. If you delay the signal to one set of speakers properly for one row, the next row will get a garbled mix from the two speakers (direct and delayed). You'd be better off just using a single surround pair in between the two rows. Unless they are very far apart, as in a large auditorium or theater. I was trying to remember the rule of thumb; I think it's about 10 ms, which equates to roughly 10 feet apart, but I may be wrong. That is, don't place speakers carrying the same signal closer than about 10'. There are many variables that play into a real system design, natch, including amplitude fall-off with distance (attenuation) that provides a little more isolation.

If the speakers are far enough apart and have sufficient isolation, you can delay the signal, but I think DSPs use a true time-delay function (shift register or clock-swallower circuit) rather than an all-pass filter. At least the ones I have been around, but DSP is not my main field by a long stretch.

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post #12 of 24 Old 08-07-2013, 06:37 PM
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Quote:
Originally Posted by J_P_A View Post

That's exactly the issue I'm trying to deal with. I will have two side surrounds for row one left and right), and two more side surrounds for row two (left and right). As an example, the right side surround for row one will play the same sound as the right side surround for row two. The problem being that people in row one will hear the sounds from the row two surrounds, but delayed in time (and vice versa).
And when you try to "fix a position in row 1-it WILL be worse in row 2 and vice versa.

You CANNOT fix both positions at the same time-no matter what "toys" you try to use.

If you have a position that has arrivals from 2 speakers- you can ONLY fix that one position. Any other position will be different-and very possibly worse.

No way around it.

So you either choose a "best sounding" position and forget bout every place else-or choose a "happy medium" and live with it.

With loudspeakers LESS is always more. You should only hear ONE loudspeaker producing a particular signal. If more than one is producing the same signal, there WILL BE cancellations.

Now how much depends on the relative levels between the two sources. The closer they are in level-the greater the amount of cancellations.

If there is more than one listening position- you must consider the other positions-or else totally ignore them. Your choice.

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post #13 of 24 Old 08-08-2013, 05:57 AM - Thread Starter
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The high end Erskine builds frequently use side arrays. Here's a post from Dennis addressing the question of when multiple side surrounds are necessary.
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Originally Posted by Dennis Erskine View Post

Anytime you have multiple rows of seats, don't want di/bipole speakers, and have some distance from the wall to the first ear on each side of the room.

I believe Toole mentions multiple surrounds in his book, but only in passing. IIRC, he indicates that the signals should be decorrelated. I'll have to look later to see if I can find the specific reference.

Here is another source that discusses the use of all-pass FIR filters to decorrelate signals. The goal being the simulation of more diffuse sounds fields and diminished comb filtering due to multiple delayed signals.

Ideas on how someone would calibrate a setup like this?

EDIT: Added the missing link

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post #14 of 24 Old 08-08-2013, 12:09 PM - Thread Starter
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A bit of an update. I pulled out Sound Reproduction by Floyed Toole, and found the section that I was referring to in my previous post. Section 16.3 addresses a room that is extremely close to what I am planning. Toole's recommendation is to apply a delay to the second set of speakers to decorrelate them from the first set. Specifically, he recommends beginning with about 10 ms.

I believe the terminology is causing me some issue here (and I believe I've been confused by this in the past as well). Applying a delay to a signal does not decorrelate it in the strictest sense. Those two signals will still have a correlation coefficient of 1 (in the absence of noise), but at a different lag. However, I believe I understand how the term is being applied here. Further, if the DSP has the ability to apply a randomized phase to the second signal, that would decorrelate the signals for all delays. I'm just not sure if that's a feature in a typical DSP.

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post #15 of 24 Old 08-08-2013, 03:35 PM
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Hi J_P_A,
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Originally Posted by J_P_A View Post

Here is another source that discusses the use of all-pass FIR filters to decorrelate signals.
But where's the source? wink.gif

The concept of an all-pass FIR filter is strange to me. The advantage of a FIR filter over an IIR filter is linear-phase (a constant delay). So a filter that doesn't affect frequency response (such as an all-pass filter) and also doesn't affect phase (such as a FIR filter) would be a filter that does nothing at all. Well, it would create a delay, but there are much easier ways to do that - as a FIR filter is computationally expensive, while a delay is computationally free.

Now, it is possible to create a FIR filter that does affect phase, and maybe that is what that 'source' of yours is discussing. So I'm interested in that source.


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. . . Further, if the DSP has the ability to apply a randomized phase to the second signal, that would decorrelate the signals for all delays. I'm just not sure if that's a feature in a typical DSP.
Randomizing phase is an interesting concept, but I'm not sure how that would be done in a DSP. I seems to me that it would require randomizing the filter coefficients in an IIR filter (randomizing coefficients in a FIR filter would not change the phase). Maybe a simpler approach might be a variable delay (a rubber-buffer) and maybe some reverb (as mentioned in your other thread).

I assume that this has been addressed by the big-boys, and that there is an algorithm out there that does what you want.
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post #16 of 24 Old 08-08-2013, 03:40 PM
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When you have two signal that arrive at the same location and have a different phase response (either by delay or "randomized phase-WHATEVER that is???????????) you will have cancellations. PERIOD.

Unless the phase is exactly the same (and the only way to have that is to have both loudspeakers in exactly the same location -NOT side by side or on top of each other-but IN the same physical position-which is impossible), there will be interference which will lower the overall quality.

NO way around it-no matter how "fancy" the term-sorry.

The use of delay for speakers that are covering different location-and trying to get ti signal arrivals the same-is a very real tool-BUT ONLY if done properly and designed properly.

Just doing 'random things" without a specific approach is NOT a good idea.

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post #17 of 24 Old 08-08-2013, 07:21 PM - Thread Starter
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Thanks for the feedback guys! I'm fairly new to the calibration side of things, so I'm trying to learn as much as I can as I go. I can't afford to hire a professional calibrator, so I think this will be a fun hobby to pick up.
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Hi J_P_A,
But where's the source? wink.gif

The concept of an all-pass FIR filter is strange to me. The advantage of a FIR filter over an IIR filter is linear-phase (a constant delay). So a filter that doesn't affect frequency response (such as an all-pass filter) and also doesn't affect phase (such as a FIR filter) would be a filter that does nothing at all. Well, it would create a delay, but there are much easier ways to do that - as a FIR filter is computationally expensive, while a delay is computationally free.

Now, it is possible to create a FIR filter that does affect phase, and maybe that is what that 'source' of yours is discussing. So I'm interested in that source.
Randomizing phase is an interesting concept, but I'm not sure how that would be done in a DSP. I seems to me that it would require randomizing the filter coefficients in an IIR filter (randomizing coefficients in a FIR filter would not change the phase). Maybe a simpler approach might be a variable delay (a rubber-buffer) and maybe some reverb (as mentioned in your other thread).

I assume that this has been addressed by the big-boys, and that there is an algorithm out there that does what you want.


Well, that's embarrassing. redface.gifHere's the article I intended to link to. I'll update the above post as well. I'm not sure how it's actually implemented in a DSP, but decorrelation filters (also called whitening filters) are pretty common in other signal processing applications. Transforming these signals to the frequency domain using FFTs can be done in near real time. I haven't read it in a while, but IIRC, that paper suggests manipulating the phase in the frequency domain because it can be done independently of the amplitude. By randomizing the phase, they claim
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The timbral coloration and combing associated with constructive and destructive interference of multiple delayed signals is perceptually eliminated.

which, unless I miss my guess, is what I'm after.

Also, I believe I've read that this is the technique used to simulate multiple channels from one source. Mono to stereo for example. Here's a dolby patent that Dennis linked to that describes a method of simulating multiple channels from a single channel using decorrelation filters.

I suppose I need to reread that as well. I have a feeling there is a simple answer to this, and I may just be using the wrong terms to describe the problem.
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When you have two signal that arrive at the same location and have a different phase response (either by delay or "randomized phase-WHATEVER that is???????????) you will have cancellations. PERIOD.

Unless the phase is exactly the same (and the only way to have that is to have both loudspeakers in exactly the same location -NOT side by side or on top of each other-but IN the same physical position-which is impossible), there will be interference which will lower the overall quality.

NO way around it-no matter how "fancy" the term-sorry.

The use of delay for speakers that are covering different location-and trying to get ti signal arrivals the same-is a very real tool-BUT ONLY if done properly and designed properly.

Just doing 'random things" without a specific approach is NOT a good idea.

I'm not sure what "random things" you are suggesting that I am intending to try, but I'm just trying to learn how this particular situation is addressed during calibration. Based on the documents that I've linked to and referenced it's clear that more can be done than just adding a delay to these signals to improve things. I'm just not clear on how it's done in a DSP. Dennis recommend QSC components to do this. If time aligning the signals is all that's required, there's certainly no need for that much processing power, so I think it's safe to assume they're doing a little more.

While I agree that there will always be some constructive or destructive interference where multiple signals are present, I think the intent of this is to simulate a sound field that would have originated from a much larger space (destructive interference included).

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post #18 of 24 Old 08-10-2013, 03:27 PM
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Hi J_P_A,

Thanks for the link. I just finished reading it, and it makes a lot of sense. I now understand what it takes to decorrelate your surrounds.

All it takes are two FIR filters. But instead of using "real" values for the magnitude-response as we normally do when computing a FIR filter, we use "complex" values. The "imaginary" portion of the complex values contain the phase, and the key to decorrelating the audio is to generate random phases in those values. The "real" portions of the complex values, the magnitudes, are all set to unity, producing an all-pass filter with random phase.

Said another way: A normal FIR filter would have all phase information (the imaginary portions) set to zero, thereby causing those values to contain magnitude information only (the real portions). The FIR filter needed for decorrelation includes random phase, so we are simply performing our usual iDFT on complex values instead of real values when building the filter.

As Ivan said, nothing you can do will prevent comb-filtering, but according to the author, the decollelation causes the combing to be less noticeable. I don't understand why, but the science of audio-perception is beyond me - I just do math.

Bottom line:
Any DSP that can take an audio-stream and put it through two FIR filters, producing two audio streams can do the job. A single stereo DSP at each side would do. Unfortunately, many audio DSPs are limited to IIR filters, and wouldn't be suitable. The OpenDRC or miniSHARC products made by miniDSP can do FIR.
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post #19 of 24 Old 08-10-2013, 06:10 PM - Thread Starter
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Thanks Mark!

Just to clarify, are you saying that I would need to apply two FIR filters to each extra channel (i.e. two filters for the extra surround right, and two filters for the extra surround left), or is this one FIR filter for each channel? If it's the former, can you clarify why?

Also, I've never worked with a DSP like this, so I'm not sure of the details of setting up an FIR filter. Does the DSP have a function for generating the random values built in, or would I need to manually set the values for each frequency?

Not knowing any better, I thought I would be looking for an 8 input (for a 7.1 system), 10 output (at a minimum) DSP to calibrate the entire system.

Thanks again!

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post #20 of 24 Old 08-10-2013, 07:05 PM
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Hi J_P_A,
Quote:
Originally Posted by J_P_A View Post

. . . Just to clarify, are you saying that I would need to apply two FIR filters to each extra channel (i.e. two filters for the extra surround right, and two filters for the extra surround left), or is this one FIR filter for each channel? If it's the former, can you clarify why?
Yes, it is the former. The output meant for the left-surround would go into the DSP (maybe two inputs of the DSP), and then go through one FIR filter for the first-row's left-surround, and also through a second FIR filter (in parallel) for the second-row's left-surround. You would have the same arrangement for the right-surround.

You can probably decorrelate by having only one FIR filter for row-two, but you would then need to delay row-one's speaker by an amount equal to the group-delay of row-two's filter. A FIR filter can add considerable delay to a signal, and having two filters is a simple way of keeping the delays equal.

Also, having control of the FIR coefficients of both outputs allows you to specify the correlation measure of the outputs. The author's technique for controlling the correlation measure is to create two random-phase sequences and then mixing them in particular proportions in order to get the desired correlation measure. But that might not be necessary if you want a correlation measure of zero.
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Also, I've never worked with a DSP like this, so I'm not sure of the details of setting up an FIR filter. Does the DSP have a function for generating the random values built in, or would I need to manually set the values for each frequency?
The FIR filters inside the DSP are pretty generic in their operation. Typically, the only difference in the operation of FIR filters is the number of terms that the filter uses (which you specify). It is the coefficients of those terms that produce a band-pass, an all-pass, a phase-correcting or any other type of FIR filter. Those coefficients are pre-calculated in a computer and then downloaded into the DSP.

The DSP manufacturers provide software to calculate and download the filter coefficients for you. As an alternative, you could use Matlab, MathCad or even Excel to calculate the coefficients. When I design a filter, I typically write a MathCad document to produce my coefficients. That way, I know exactly how they were calculated, which isn't always the case when you're depending on someone else's software. The DSP's software then needs to support the downloading of user-designed coefficient files.
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post #21 of 24 Old 08-10-2013, 07:24 PM - Thread Starter
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AMAZING POST! This explained a lot of things I've been curious about, but didn't know where to begin to ask!
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..........A FIR filter can add considerable delay to a signal, and having two filters is a simple way of keeping the delays equal.

Got it! Makes perfect sense.

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The DSP manufacturers provide software to calculate and download the filter coefficients for you. As an alternative, you could use Matlab, MathCad or even Excel to calculate the coefficients. When I design a filter, I typically write a MathCad document to produce my coefficients. That way, I know exactly how they were calculated, which isn't always the case when you're depending on someone else's software. The DSP's software then needs to support the downloading of user-designed coefficient files.

This is a very useful nugget. I've been wondering how the filters for a DSP were "Designed." It seemed very limiting to only be able to set a bandwidth and center frequency, and I couldn't understand why it would cost so much for a DSP that only allowed basic filtering like that. The operation manuals I've looked at are very minimal in what they explain. Now that I know this piece, I can see where I can directly apply the topics in that paper to an actual filter in a DSP! I just need to dig out my filter design textbook and brush up on all my poles and zeros smile.gif

Sorry, I'm a little excited about this prospect! smile.gif

EDIT: I'm digging into the MiniDSP page, and I see they have lots of options available! Multiple I/O configurations. Looks promising. Thanks for the tip.

Thanks again for the info!

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post #22 of 24 Old 08-10-2013, 10:13 PM
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Hi J_P_A,

A word of warning: I don't think you will be able to do it all with a single DSP, unless it's possible to do the decorrelation with IIR filters. A single FIR filter can use more computational bandwidth then a dozen IIR filters, so it would be one powerful DSP that could do both of your surrounds. Notice that most of the miniDSP products can't do FIR at all, and the ones that can are limited to two channels.

It could be interesting to talk to the different DSP manufacturers to ask if they can do decorrelation , if for no other reason but to see the blank stares. You might get lucky, and find someone who supports it.
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post #23 of 24 Old 08-11-2013, 02:03 PM - Thread Starter
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Mark,

I can't say I'm surprised. There's never a free (or even cheap) ride when you're talking AV smile.gif

I'll check in to some of of the other cheaper DSPs. Xilica comes to mind. I think their XD series and Neutrino both provide FIR filtering capabilities. They're still not cheap, at least by my standards, but about 1/2 the price of the QSC stuff IIRC.

I suppose this puts the QSC equipment into better perspective as it apparently has a fixed latency regardless of the number of filters. IIRC, it's pretty low as well.

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post #24 of 24 Old 10-11-2013, 07:28 AM - Thread Starter
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The topic of calibrating a side surround array comes up from time-to-time and this thread has a couple of excellent posts by Nyal Mellor about decorrelating the side surrounds using IIR filters rather than FIR filters. It's a short thread, but well worth the read if you are interested in calibrating side arrays.

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