Hi all,

I'm currently trying to make my own reverb unit in pd, however I'm really struggling to understand some of the key concepts/components.

I understand that the basic Schroeder design (which is what I'm trying to re-create) consists of an input signal which feeds through 4 parallel comb filters, and then 2 linear all pass filters. However, the actual workings of these filters is baffling me.

I've been reading/researching for endless hours now, trying to get my head around the workings however I'm still struggling to grasp them.. I'm not the best at picking up these types of academic subjects, not to mention I'm slightly dyslectic which doesn't help as everywhere seems to explain the relevant concepts using big words, complicating diagrams, and complex equations, which simply confuse me more.. None the less I'm determined to grasp it!

I was hoping that someone could explain to me (in a 'for dummies' language fashion) how these filters are constructed/work. In fact if someone would even care to take the time to detail a complete explanation of the Schroeder reverberator itself in the same fashion it would be greatly appreciated! Please, feel free to patronise me!

Don't get me wrong- I'm not just looking to gain a general knowledge of the subject. I really wish to understand it in as much depth as possible. I just need someone to break it down for me and explain the concepts in ways that I can get my head around- at least to begin with. As theres not much point in me even attempting to start building a Schroeder in pd, until I can actually understand and grasp the relevant concepts first!

Kind regards,
Beanz

https://ccrma.stanford.edu/~jos/pasp/Comb_Filters.html
https://ccrma.stanford.edu/~jos/pasp/Allpass_Two_Combs.html
https://ccrma.stanford.edu/~jos/Delay/Schroeder_Allpass_Filters.html
Z^(-M) is a delay of M samples, a is a gain, b is a gain. So basically what the above allpass diagram says is to add a delayed (by M samples) version of itself multiplied by -a and feed it into the delay line again, and also to multiply it by b and add it to the delay line output.
if you want to understand this stuff really well I would recommend his books e.g.
https://ccrma.stanford.edu/~jos/filters/Analysis_Digital_Comb_Filter.html

I always found the CCRMA stuff a little difficult to understand. I'm not a mathematician, so it's sometimes hard to make intuitive sense of rigorous mathematical language.

Basically a comb filter is just a delay with feedback, which produces a repeating echo. If you consider a single comb filter, you can easily observe that a longer delay has a higher modal density (less metallic sound) and lower echo density (smaller number of discrete echoes per second), while a shorter delay has a lower modal density (more metallic sound) and higher echo density. For good quality reverberation, you want both high modal and echo densities.

The most obvious way to get this is to sum multiple comb filters. This increases both modal density and echo density additively, resulting in a smoother and less metallic frequency response and denser pattern of echoes, so long as the delay lengths are "mutually incommensurate" (coprime numbers of samples). You can get reasonably good sounding reverberation this way if you use something like 100 comb filters. But this isn't really efficient. Putting something in series will multiply the echo density, since the impulse responses are convolved. An allpass filter (feedback comb filter with a feed-forward patch, resulting in flat frequency response) is used here. It increases echo density but doesn't change modal density. By combining these, you can get acceptable modal and echo densities without using too many delays. Freeverb is a pretty good example of this.

For a good sounding decay, feedback gains should be scaled according to delay length, and filters can added inside the feedback loops.

Schroeder reverbs ultimately aren't very good. The echo density doesn't increase over time (as you would find in an actual acoustic space), series allpass filters result in a metallic sound with unnatural onset, and it takes too many comb filters to achieve high echo density. A Householder matrix is a simple modification to this that makes a huge improvement. But it's a little hard to understand why. And there are many other topologies that give better results.

Jasmin Frenette's Master's thesis gives the clearest and most comprehensive overview of reverberators that I've seen: freeverb3.sourceforge.net/doc/thesis.pdf‎