KP-302/3002 High Frequency Speaker - Intermittent & Scratchy Sound - Resolved, Bad Cap' Connection

[captainbeefheart]

Let's simplify the mechanisms.

 

Phase shift is the time difference between two signals.

 

Between the input to the filter networks to each output you will have phase shift, the largest at crossover frequencies. That means the output of the filter network is no longer on the same time domain. The speaker voice coil moves in response to the output from the filter network. At the crossover frequencies is where you will find two drivers contributing to the total acoustic output of the same frequencies, the phase shift between the two drivers means they will not reach their peak at the same time.

 

That is all you really want in regard to phase, you want the leading edge of a transient wave form (square wave) to reach it's peak at the same time with both drivers. Both drivers will reach their peak excursion at the same time, that's the goal. The more phase shift between two drivers the longer the delay one reaches it's peak compared to the other.

 

So constant delay, constant phase, all this terminology just gets confusing, all you need to do is remember you want each driver to reach it's peak for the same shared frequencies at the same time.

[henry4841]

It is called accurate reproduction. Keeping the phase the same as source is what is wanted in the end. 

[Edgar]

1 hour ago, captainbeefheart said:

Let's simplify the mechanisms.

 

Holy cow, @captainbeefheart, I applaud any attempt to simplify the concept of phase response, but that might be too much simplification. Still, I don't know of any other way to describe it without things getting very deep very fast.

 

37 minutes ago, henry4841 said:

Keeping the phase the same as source is what is wanted in the end.

Again, perhaps an oversimplification, but there is really no simple explanation that is also accurate.

 

[henry4841]

16 minutes ago, Edgar said:

Again, perhaps an oversimplification, but there is really no simple explanation that is also accurate.

 

I do not think any engineer would intentionally create a phase shift in a speaker system. Just the opposite is what I think they are trying to achieve. Keeping the speakers in phase with each other in a system is almost if not impossible in reality but I still believe it is the goal of most engineers. This is an entertainment hobby so if there is an advantage of intentionally causing a phase shift I guess it is possible an engineer has tried doing so. Ideally a single speaker creating the entire audio band would be best but in the real world not technically possible. Some full range speakers do sound really good these days though.  

[Edgar]

10 minutes ago, henry4841 said:

I do not think any engineer would intentionally create a phase shift in a speaker system. Just the opposite is what I think they are trying to achieve.

Except that a speaker system is inherently a highpass filter, and all causal, nontrivial filters introduce phase shift. The objective is to manage that phase shift.

 

11 minutes ago, henry4841 said:

Keeping the speakers in phase with each other in a system is almost if not impossible in reality but I still believe it is the goal of most engineers.

By, "keeping the speakers in phase with each other" I suspect that you refer to the individual drivers; woofer and midrange, midrange and tweeter, etc. Ignoring individual driver responses for the moment, it is quite possible, and not even all that difficult, to create lowpass/highpass filter pairs that are in-phase with each other. The Linkwitz-Riley pairs exhibit this property, for example. And in digital signal processing, it is almost trivial to design perfect reconstruction filters.

[captainbeefheart]

I think people are talking about two different phase relationships here and that is what is getting confusing.

 

Sometimes we are referring to the input of the filter network to the outputs of the filter network phase shifts, and then myself especially talks about the phase shifts between two outputs. The latter is the only one that will make any difference. If the time difference between two outputs is different for the same given frequency that will create the misaligned peaks during transients, one lags behind the other.

 

You can view the phase shift from input of filter network to each output and figure out the differences between the outputs for any given frequency, it gives you the same answer as viewing the direct difference in phase from output to output.

[Edgar]

15 minutes ago, captainbeefheart said:

I think people are talking about two different phase relationships here and that is what is getting confusing.

 

I think you've identified a large part of the problem. In the context of a crossover network, the phase relationship between the two drivers that are "crossing over" is the issue here.

 

There are many other phase issues that can be addressed, but they are not part of this discussion.

[CWelsh]

While 98% of the stuff you guys talk about is over my head, I keep coming back to see where it is all going. Three weeks ago it would have been 99% incomprehensible, so I'm learning something. This is part of why I joined this site, so thank you all. This is fun.

[Edgar]

3 hours ago, captainbeefheart said:

At the crossover frequencies is where you will find two drivers contributing to the total acoustic output of the same frequencies, the phase shift between the two drivers means they will not reach their peak at the same time.

 

Again, phase is just not a simple issue. Both drivers "reaching their peak at the same time" doesn't even explain it adequately. For example, the 1st-order crossovers cause the LF and HF drivers to be 90° out of phase with each other at the crossover frequency. Yet they sum perfectly.

[Edgar]

Here's an example of how complicated the issue of crossover phase can be. In a Linkwitz-Riley crossover network, the lowpass section and the highpass section are perfectly in-phase at all frequencies. So you would expect that a square wave, passed through the crossover network and then recombined (lowpass output and highpass output added together), would still be a square wave. The attached graphic shows what happens when you do exactly that.

 

The weird thing is, there are numerous studies indicating that you can't hear the difference! That's right: a real square wave and the ugly mess that used to be a square wave, shown below, sound exactly the same (or so it is claimed).

[captainbeefheart]

3 hours ago, Edgar said:

Again, phase is just not a simple issue. Both drivers "reaching their peak at the same time" doesn't even explain it adequately. For example, the 1st-order crossovers cause the LF and HF drivers to be 90° out of phase with each other at the crossover frequency. Yet they sum perfectly.

 

I never said phase was a simple concept/subject, in fact earlier I said it's quite complex. You are talking about input of filter network to output of filter network phase. My simplification was only saying ideally you want each driver's peaks to be time aligned when they are reproducing the same frequencies. Is that not a valid statement?

[Travis In Austin]

So in my digging on my own, trying to understand why  "No sound in nature has constant phase): might be important, and can there be "too much" with FIR filters, etc. I ran across the information at the bottom on linear-phase and minimal-phase filters from the dspGuru site. I can understand the math, I can see the difference between linear-phase and minimum-phase, but there wasn't anything I could find that relates it to speaker or balancing network design in the real world except articles by Klipsch, Heyser, etc. With Mr. Klipsch, his experiments and designs seem to always ask: What does this do to the distortion? 

 

He also was constantly laying out in his publication for dealers "Dope From Hope" how you needed to apply theory to the practical application of loudspeakers. I.e., phase shift and delay effectOne quick quote, from hundreds of papers PWK wrote on the subject, this from DFH Vol.13, No. 3 (1973) [the footnote cites to his AES paper,  Delay Effects in Loudspeakers, JAES Volume 20 Issue 8 pp. 634-637; October 1972]:

 

 

 

 

Followed a few years later by this observation:

 

 

From the dspGuru site, the emphasis is mine:

FIR Filter Properties

2.1 Linear Phase

2.1.1 What is the association between FIR filters and “linear-phase?”

Most FIRs are linear-phase filters; when a linear-phase filter is desired, a FIR is usually used.

2.1.2 What is a linear phase filter?

“Linear Phase” refers to the condition where the phase response of the filter is a linear (straight-line) function of frequency (excluding phase wraps at +/- 180 degrees). This results in the delay through the filter being the same at all frequencies. Therefore, the filter does not cause “phase distortion” or “delay distortion”. The lack of phase/delay distortion can be a critical advantage of FIR filters over IIR and analog filters in certain systems, for example, in digital data modems.

2.1.3 What is the condition for linear phase?

FIR filters are usually designed to be linear-phase (but they don’t have to be.) A FIR filter is linear-phase if (and only if) its coefficients are symmetrical around the center coefficient, that is, the first coefficient is the same as the last; the second is the same as the next-to-last, etc. (A linear-phase FIR filter having an odd number of coefficients will have a single coefficient in the center which has no mate.)

2.1.4 What is the delay of a linear-phase FIR?

The formula is simple: given a FIR filter which has N taps, the delay is: (N – 1) / (2 * Fs), where Fs is the sampling frequency. So, for example, a 21 tap linear-phase FIR filter operating at a 1 kHz rate has delay: (21 – 1) / (2 * 1 kHz)=10 milliseconds.

2.1.4 What is the alternative to linear phase?

Non-linear phase, of course. 😉 Actually, the most popular alternative is “minimum phase”. Minimum-phase filters (which might better be called “minimum delay” filters) have less delay than linear-phase filters with the same amplitude response, at the cost of a non-linear phase characteristic, a.k.a. “phase distortion”.

A lowpass FIR filter has its largest-magnitude coefficients in the center of the impulse response. In comparison, the largest-magnitude coefficients of a minimum-phase filter are nearer to the beginning. (See dspGuru’s tutorial How To Design Minimum-Phase FIR Filters for more details.)

2.2 Frequency Response

2.2.1 What is the Z transform of a FIR filter?

For an N-tap FIR filter with coefficients h(k), whose output is described by:

y(n)=h(0)x(n) + h(1)x(n-1) + h(2)x(n-2) + … h(N-1)x(n-N-1),

the filter’s Z transform is:

H(z)=h(0)z-0 + h(1)z-1 + h(2)z-2 + … h(N-1)z-(N-1) , or

2.2.2 What is the frequency response formula for a FIR filter?

The variable z in H(z) is a continuous complex variable, and we can describe it as: z=r·e^jw, where r is a magnitude and w is the angle of z. If we let r=1, then H(z) around the unit circle becomes the filter’s frequency response H(jw). This means that substituting e^jw for z in H(z) gives us an expression for the filter’s frequency response H(w), which is:

H(jw)=h(0)e^-j0w + h(1)e^-j1w + h(2)e^-j2w + … h(N-1)e^-j(N-1)w , or

Using Euler’s identity, e^-ja=cos(a) – jsin(a), we can write H(w) in rectangular form as:

H(jw)=h(0)[cos(0w) – jsin(0w)] + h(1)[cos(1w) – jsin(1w)] + … h(N-1)[cos((N-1)w) – jsin((N-1)w)] , or

2.2.3 Can I calculate the frequency response of a FIR using the Discrete Fourier Transform (DFT)?

Yes. For an N-tap FIR, you can get N evenly-spaced points of the frequency response by doing a DFT on the filter coefficients. However, to get the frequency response of the filter at any arbitrary frequency (that is, at frequencies between the DFT outputs), you will need to use the formula above.

2.2.4 What is the DC gain of a FIR filter?

Consider a DC (zero Hz) input signal consisting of samples which each have value 1.0. After the FIR’s delay line had filled with the 1.0 samples, the output would be the sum of the coefficients. Therefore, the gain of a FIR filter at DC is simply the sum of the coefficients.

This intuitive result can be checked against the formula above. If we set w to zero, the cosine term is always 1, and the sine term is always zero, so the frequency response becomes:

2.2.5 How do I scale the gain of a FIR filter?

Simply multiply all coefficients by the scale factor.

2.3 Numeric Properties

2.3.1 Are FIR filters inherently stable?

Yes. Since they have no feedback elements, any bounded input results in a bounded output.

2.3.2 What makes the numerical properties of FIR filters “good”?

Again, the key is the lack of feedback. The numeric errors that occur when implementing FIR filters in computer arithmetic occur separately with each calculation; the FIR doesn’t “remember” its past numeric errors. In contrast, the feedback aspect of IIR filters can cause numeric errors to compound with each calculation, as numeric errors are fed back.

The practical impact of this is that FIRs can generally be implemented using fewer bits of precision than IIRs. For example, FIRs can usually be implemented with 16 bits, but IIRs generally require 32 bits, or even more.

2.4 Why are FIR filters generally preferred over IIR filters in multirate (decimating and interpolating) systems?

Because only a fraction of the calculations that would be required to implement a decimating or interpolating FIR in a literal way actually needs to be done.

Since FIR filters do not use feedback, only those outputs which are actually going to be used have to be calculated. Therefore, in the case of decimating FIRs (in which only 1 of N outputs will be used), the other N-1 outputs don’t have to be calculated. Similarly, for interpolating filters (in which zeroes are inserted between the input samples to raise the sampling rate) you don’t actually have to multiply the inserted zeroes with their corresponding FIR coefficients and sum the result; you just omit the multiplication-additions that are associated with the zeroes (because they don’t change the result anyway.)

In contrast, since IIR filters use feedback, every input must be used, and every input must be calculated because all inputs and outputs contribute to the feedback in the filter.

2.5 What special types of FIR filters are there?

Aside from “regular” and “extra crispy” there are:

• Boxcar – Boxcar FIR filters are simply filters in which each coefficient is 1.0. Therefore, for an N-tap boxcar, the output is just the sum of the past N samples. Because boxcar FIRs can be implemented using only adders, they are of interest primarily in hardware implementations, where multipliers are expensive to implement.
• Hilbert Transformer – Hilbert Transformers shift the phase of a signal by 90 degrees. They are used primarily for creating the imaginary part of a complex signal, given its real part.
• Differentiator – Differentiators have an amplitude response which is a linear function of frequency. They are not very popular nowadays, but are sometimes used for FM demodulators.
• Lth-Band – Also called “Nyquist” filters, these filters are a special class of filters used primarily in multirate applications. Their key selling point is that one of every L coefficients is zero–a fact which can be exploited to reduce the number of multiply-accumulate operations required to implement the filter. (The famous “half-band” filter is actually an Lth-band filter, with L=2.)
• Raised-Cosine – This is a special kind of filter that is sometimes used for digital data applications. (The frequency response in the passband is a cosine shape which has been “raised” by a constant.) See dspGuru’s Raised-Cosine FAQ for more information.
• Lots of others.

[captainbeefheart]

Pretty much exactly how I explained it, phase and delay are one in the same because if two drivers producing the same frequency are out of phase they reach their peaks at different times giving a time delay. Paul feels you can get away with 4mS delay but I think his prior mention of 2 feet or 2mS is closer to accurate because when we were discussing delay and chorus effects for pro audio the majority go down to 500uS or 1mS which is still audible. I certainly agree anything under 1mS delay is purely academic as it shouldn't be noticed or heard.

 

1mS is about 1 foot at 1kHz

[Edgar]

21 minutes ago, captainbeefheart said:

My simplification was only saying ideally you want each driver's peaks to be time aligned when they are reproducing the same frequencies. Is that not a valid statement?

Nope, for exactly the reason that I offered with my example of the 1st-order crossover network. The lowpass portion and the highpass portion are 90° out of phase with each other at the crossover frequency, meaning that the peak of the sinewave coming out of the highpass filter is displaced in time by ¼ wavelength relative to the peak of the sinewave coming out of the lowpass filter. Yet the two sum perfectly to the original waveform.

[captainbeefheart]

2 minutes ago, Edgar said:

Nope, for exactly the reason that I offered with my example of the 1st-order crossover network. The lowpass portion and the highpass portion are 90° out of phase with each other at the crossover frequency, meaning that the peak of the sinewave coming out of the highpass filter is displaced in time by ¼ wavelength relative to the peak of the sinewave coming out of the lowpass filter. Yet the two sum perfectly to the original waveform.

 

You are making the same exact point I am. That the input of filter to output filter phase doesn't really matter it's the summed output to output that is important. I don't know how much clearer I could have stated that but we are saying the same damn thing.

[Edgar]

1 hour ago, captainbeefheart said:

 

You are making the same exact point I am. That the input of filter to output filter phase doesn't really matter it's the summed output to output that is important. I don't know how much clearer I could have stated that but we are saying the same damn thing.

 

I don't see how "ideally you want each driver's peaks to be time aligned when they are reproducing the same frequencies" equates to "the input of filter to output filter phase doesn't really matter it's the summed output to output that is important". 

 

Also, unless the lowpass and highpass outputs are perfectly in-phase at all frequencies, they may sum to unity at and near the crossover frequency on-axis but they won't sum to unity off-axis. Not a big problem in most living rooms, but a big problem in an auditorium.

[captainbeefheart]

21 minutes ago, Edgar said:

I don't see how "ideally you want each driver's peaks to be time aligned when they are reproducing the same frequencies" equates to "the input of filter to output filter phase doesn't really matter it's the summed output to output that is important". 

 

If you don't understand that I have no idea how to continue the conversation. I feel it's fairly clearly stated. The delay issue is between two drivers correct? So the phase difference is between the two outputs connected to those two drivers, not the difference between the output and filter network input.

[Edgar]

1 minute ago, captainbeefheart said:

I have no idea how to continue the conversation.

 

That is something upon which we can both agree. I don't understand what you're trying to say and you don't understand what I'm trying to say, so there is no reason for either of us to say anything more.

[captainbeefheart]

Just now, Edgar said:

That is something upon which we can both agree. I don't understand what you're trying to say and you don't understand what I'm trying to say, so there is no reason for either of us to say anything more.

 

That is not entirely true, I do know exactly what you are saying but you don't know what I am saying. I will try and think of a different way to show you with some actual examples.

[001]

good lord, 10 pages of unrelated discussion to the OPs problem!  start a new thread!  i gave up on following the thread after about page 2 or 3... did the OP ever resolve his issue with the bad tweeter ??