All right, the usual arguments against linear phase FIR vs. minimum phase IIR are the following:
1. High computation requirements vs. high CPU efficiency.
2. High latency vs. low latency.
3. Pre and post ringing vs. post ringing alone.
4. No phase distortion vs. phase distortion.
I am not going to discuss 1 and 2 to keep this post shorter. I generated these illustrations myself.
Let's take a square wave and apply a linear phase low pass filter and high pass filter to it. If we look at the LPF and HPF, we see that both filters have pre and post ringing. However, when the LPF and HPF are summed, the pre and post ringing disappears. Thus, LP filters rely on proper summation of LPF and HPF, otherwise pre and post ringing will be exposed.
What would cause the LPF and HPF to sum improperly? Here are a few causes:
1. Asymmetric HPF/LPF slopes
2. Improper time alignment between drivers
3. Different directivity different drivers which means they sum on-axis but not necessarily off-axis. Linkwitz made this observation.
4. High Q aggressive phase corrections. Putzeys made this observation.
I should add that the mathematical causes for pre-ringing are now well understood and there are algorithms that can reduce pre-ringing to negligible levels. Since you bring that up, let's look at the on-axis step response of my speaker.
We can see a little bit of pre-ringing. Now let's go 30 deg off axis:
See much difference in pre-ringing? Even if there was, there is the phenomenon of pre-masking where any signal, provided it is low in amplitude and occurs less than 20ms before the main signal will be masked by the main signal.
Now let us look at what happens if we were to use a min phase filter. Let us take a square wave again and apply min phase LPF and HPF to it.
Look at the output. The phase is completely distorted, and the post ringing does not go away. Now, you could argue that phase distortion is not audible, and post-ringing is masked by the main signal. Ohm's Acoustic Law and all that. 99.99% of speakers in the world use minimum phase instead of linear phase, and all of them distort phase in the same way. Quite simply we are used to hearing phase distortion like this.
Now I will wander into more controversial territory. I have the capability to generate both min phase and lin phase filters. I have directly compared them. There is no contest, linear phase sounds so much cleaner. The last time we met (maybe you have forgotten) you mentioned Bohdan Raczynski. You might be interested in
what he has to say about linear phase. He cites a number of sources that show that there is increasing research that shows that phase distortion is audible.
So, do we choose linear phase, with negligible and inaudible pre-ringing? Or minimum phase with unavoidable phase distortion and twice as much post-ringing which can never be removed?
To wrap up - we should ask ourselves why should we choose FIR rather than IIR. FIR allows us to use min phase or lin phase. IIR forces us to use min phase only. We can get halfway there with mixed phase, but with very limited FIR taps. The ONLY valid reason to avoid using FIR is to avoid latency which is critical in AVR's so there are no lip sync issues. The other reason of course is so that you can use underpowered SHARC DSP chips which can't do high tap count FIR, put it into products like MiniDSP and sell it for cheap.
I am not letting DEQX off the hook here. I think it is incredibly overpriced for what it delivers. I will be meeting Kim and Alan tomorrow and I will have a chat with them.
