#+TITLE: DC Blocker* IntroductionThis document outlines an implementation of a DC Blocker, atypical utility used to block out what is known as DC offset.DC Blockers are occasionally used to clean up recordedaudio, but they are more often seen handling digitalalgorithms that tend to naturally introduce a lot of DCinto their signal. This is common in the physical modellingfamily of DSP algorithms (Karplus-Strongs, waveguides,FDN reverberators, etc). Without knowing how a DC blocker works, it would seem to havemagical characteristics. A DC blocker has the ability to"drag down" a waveform of audio with DC offset so that it iscentered. But how does it know how much to drag? In truth, a DC blocker is typically nothing more thana recursive highpass filter whose cutoff set to be asub-audio frequency. This has the effect of removing anyslow moving waveforms that often are the culrpits ofunwanted DC biasing.* Difference EquationThe difference equation for a[[https://ccrma.stanford.edu/~jos/filters/DC_Blocker.html][DC blocker]] looks like this: $$y(n) = x(n) - x(n - 1) + Ry(n - 1)$$ Where $R$ is usually a constant between 0.9 and 1. This difference equation outlines the whole darn algorithm!What will be needed is a function that takes in an input,and stores the previous input, output, as well as theconstant $R$. And that's it.* Tangled FilesThis program outputs two files: =dcblocker.c= and=dcblocker.h=. Using the macro =SK_DCBLOCKER_PRIV= willexpose the main struct. Otherwise, it is opaque. #+NAME: dcblocker.c#+BEGIN_SRC c :tangle dcblocker.c#define SK_DCBLOCKER_PRIV#include "dcblocker.h"<<funcs>>#+END_SRC #+NAME: dcblocker.h#+BEGIN_SRC c :tangle dcblocker.h#ifndef SK_DCBLOCKER_H#define SK_DCBLOCKER_H#ifndef SKFLT#define SKFLT float#endif<<typedefs>>#ifdef SK_DCBLOCKER_PRIV<<structs>>#endif<<funcdefs>>#endif#+END_SRC* Struct DefinitionThe main struct for this DC blocker will be called=sk_dcblocker=. It only needs three parameters: an=x= value storing the previous input value, a =y= valuestoring the previous output value, and an =R= valuestoring the DC filter constant. #+NAME: typedefs#+BEGIN_SRC ctypedef struct sk_dcblocker sk_dcblocker;#+END_SRC#+NAME: structs#+BEGIN_SRC cstruct sk_dcblocker {    SKFLT x, y, R;};#+END_SRC* InitializationThe =sk_dcblocker= can be initialized with=sk_dcblocker_init=. It zeros out =x= and =y=, and sets=R= to be a value of =0.99=, which is a reasonable DCcoefficent value. #+NAME: funcdefs#+BEGIN_SRC cvoid sk_dcblocker_init(sk_dcblocker *dcblk);#+END_SRC #+NAME: funcs#+BEGIN_SRC cvoid sk_dcblocker_init(sk_dcblocker *dcblk){    dcblk->x = 0;    dcblk->y = 0;    dcblk->R = 0.99; /* quite reasonable, indeed! */}#+END_SRC* ComputationA single sample of audio is processed with the function=sk_dcblocker_tick=. It performs the arithmetic for thedifference equation, updates the internal values, thenreturns the output. #+NAME: funcdefs#+BEGIN_SRC cSKFLT sk_dcblocker_tick(sk_dcblocker *dcblk, SKFLT in);#+END_SRC #+NAME: funcs#+BEGIN_SRC cSKFLT sk_dcblocker_tick(sk_dcblocker *dcblk, SKFLT in){    dcblk->y = in - dcblk->x + dcblk->R*dcblk->y;    dcblk->x = in;    return dcblk->y;}#+END_SRC