fexpr~ to gen translation

I'm presuming from the caption that $x1[0] means the current input sample, and $x1[-1] means the previous input sample; and $y1[-1] means the previous output sample.

In gen~ we can use [history] to get the value of the prior sample. If gen~ `in1` gives $x1[0], then `in1`->`history` gives $x1[-1]. Similarly, whatever is being set to the gen~ `out`, also feed that to a `history` and you'll get $y1[-1].

In genexpr (codebox), (a) is:

History x1;
out1 = 0.5*in1 + 0.5*x1;
out2 = 0.5*in1 - 0.5*x1;
x1 = in1; // update at end of code box to ensure the 1 sample delay.

and (b) is:

History y1;
out1 = 0.5*in1 + 0.5*y1;
y1 = out1; // update at end of code box to ensure the 1 sample delay.

This stuff is all pretty basic form for developing filters. Take a look at the gen~ biquad example, which uses both two feedforward and two feedback paths (that's what a biquad is).

The general form is $xN refers to [in N] (or `inN` in codebox), $yN refers to [out N] (or `outN` in codebox). The [0] means current value; [-1] means the value passed through a 1 sample delay via [history] (AKA the Z^-1 operation). To get longer histories than [-1], use a [delay].

Many thanks Graham, that was incredibly useful to get explained.
I'm working towards trying to make an LPC type breakpoint filter (alla AudioSculpt) slowly – and hoping I can do this with Gen. I just haven't seen LPC done in Gen, so I'm going from this diagram as a starting point:

that block-diagram looked like fun so i thought i'd try to do a 16-stage one, just patching-style in gen~(no codebox)... using a multislider to set the weights all-at-once here(plus crossfading through a history of them to tame clicks/pops at changes)...
i dunno if it's correct, but it sounds interesting:

(a codebox-version would help modularize to extend to larger sets more easily... i'm also wondering if it should maybe be done with a 'data' object... used instead of the 'history'-series(?))

a slight evolution(to take care of the clicks/pops when setting weights, i created a smooth crossfade out of the weights-history 😋):

Well, that's truly awesome, ... and maybe someday I will understand the principles behind it thx Raja

my pleasure... actually you got me thinking i could maybe comment it better, here's comments within the gen~ patcher, to show where the patch coincides with the picture/diagram that SmokeDoepferEveryDay posted above:

Yes, ... thanks for taking the time,.... this helps...
Whenever you are deciding to teach max stuff the cool way, ( it certainly doesn't have to be this patreon wormhole^^), I will be participating... all the best

Woah, R∆J∆ !!
I was not expecting this!? :D

thankyou so much. This has saved me days/weeks/months of fiddling. Especially the (w1) (w2) (wp-1) etc

So this begs the question(s) if this were to be codebox and [data] gave something up to an order of 30 coeffs could I then parameterize with a BPF [function] or would it need some additional smoothing/windowing than the crossfading? probably right?

This was my ideal, to have a type of visualised LPC formant mask like in AS but with realtime input:

it was fun, happy to lend a hand :)
unfortunately, i'm not very woke about filter-design/topology itself 😅, i think if you have the right coefficients here(specific for FIR filters), you can do anything! 💪🙌😜
..just kidding, i don't actually know for sure, i might not understand your question, either:
i think the diagram which i turned to gen~ so far is just an FIR filter(i should've titled the gen~ subpatcher something more like 16-stage-FIR, too... oh well, my ignorance is now uploaded for posterity 😋😇 - whereas "LPC formant mask" involves something much more advanced i wouldn't know about... although the patch does come out sounding like a formant mask... is that what it is?! i didn't even know! 😆)

so if you have a BPF function in 30 coefficients for FIR, then it's probably no prob, otherwise, for IIR, you'd have to redo the gen~-based filter-topology to incorporate a feedback section:
https://circuitglobe.com/difference-between-fir-filter-and-iir-filter.html

i was just so intrigued by the diagram, because it illustrates something i've been noticing from this type of audio equation (and also in the way
neural-networks for AI work: https://en.wikipedia.org/wiki/Artificial_neural_network)
in all the equations you'll find: 'w1', 'w2', 'a1', 'a2', 'b1', 'b2', all symbolize something like a 'bias'(or 'weight') we multiply various stages of input/output-feedback by, to get the filter/analysis we want(even on a political/philosophical level, too: we tend to introduce bias in our perceptions of other people in order to try and get them to fit the world we wish to perceive 🤔🤯).
🤓
sorry if i completely misunderstand, hope that helps though 🍻