The information in the knowledge base and the rest of the site is not intended to teach you DSP, it is for people that have a basic knowledge of DSP to learn how to implement audio specific structures in the FV-1.
It is also expected that the reader will spend a little time working out the details themselves so they have an understanding of what is going on. For example the one pole low pass at:
http://www.spinsemi.com/knowledge_base/ ... le_filters
Has the difference equation of:
Y(n) = Y(n-1)*K1 + X(n)*K2
which should be obvious by simply looking at the structure
Since K1+K2=1 so that there is no gain in the system we can say K1=1-K2
Substituting for K1 in the difference equation we get:
Y(n) = Y(n-1) - Y(n-1)*K2 + X(n)*K2
which simplifies to:
Y(n) = (X(n) - Y(n-1))*K2 + Y(n-1)
which we can see in the second drawing
If we look at this equation in a more generic manner we can say it is something like: (A-B)*C + B
Which maps to an RDFX instruction where ACC = A = X(n), REG[ADDR] = B = Y(n-1) and C = C = K2.
Note that RDFX is a generic instruction, it can be used to create a fixed LP filter but also other structures, other instructions could be used to make an LP filter, you would need to do an adjustable filter using different instructions, etc. It all depends on what you are doing as to which instructions to use.
As to coefficient range, that should also be obvious to someone with basic DSP knowledge.
F(-3db) can only range from 0Hz to Fs/2 so for example for a 32KHz sample rate it can only range 0Hz to 16KHz.
The coefficient is defined as : K1=e^-(2*pi*F*t)
t = 1/Fs so
K1=e^-(2*pi*F/Fs)
since the limits for F are 0 and Fs/2 the limits of the coefficient K1 are:
For F = 0
K1=e^-(2*pi*F/Fs)
K1=e^-(2*pi*0)
K1=e^-(0)
K1 = 1 since any number raised to the 0 power is 1 by definition
For F = Fs/2
K1=e^-(2*pi*(Fs/2)/Fs)
K1=e^-(2*pi*(1/2))
K1=e^-(pi)
K1=0.04321
If we want to implement the RDFX version of the LP using only K2 we can calculate K2 from K2=1-K1 so the coefficient ranges:
0 for 0hz
to
0.95679 for Fs/2