DC Blocker

# DC Blocker

This is a `sndkit` algorithm. A more up-to-date version can be found here.

### Introduction

This document outlines an implementation of a DC Blocker, a typical utility used to block out what is known as DC offset. DC Blockers are occasionally used to clean up recorded audio, but they are more often seen handling digital algorithms that tend to naturally introduce a lot of DC into their signal. This is common in the physical modelling family of DSP algorithms (Karplus-Strongs, waveguides, FDN reverberators, etc).

Without knowing how a DC blocker works, it would seem to have magical characteristics. A DC blocker has the ability to "drag down" a waveform of audio with DC offset so that it is centered. But how does it know how much to drag?

In truth, a DC blocker is typically nothing more than a recursive highpass filter whose cutoff set to be a sub-audio frequency. This has the effect of removing any slow moving waveforms that often are the culrpits of unwanted DC biasing.

### Difference Equation

The difference equation for a 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 the constant \$R\$. And that's it.

### Tangled Files

This program outputs two files: `dcblocker.c` and `dcblocker.h`. Using the macro `SK_DCBLOCKER_PRIV` will expose the main struct. Otherwise, it is opaque.

<<dcblocker.c>>=
``````#define SK_DCBLOCKER_PRIV
#include "dcblocker.h"
<<funcs>>``````

<<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``````

### Struct Definition

The 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` value storing the previous output value, and an `R` value storing the DC filter constant.

<<typedefs>>=
``typedef struct sk_dcblocker sk_dcblocker;``
<<structs>>=
``````struct sk_dcblocker {
SKFLT x, y, R;
};``````

### Initialization

The `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 DC coefficent value.

<<funcdefs>>=
``void sk_dcblocker_init(sk_dcblocker *dcblk);``

<<funcs>>=
``````void sk_dcblocker_init(sk_dcblocker *dcblk)
{
dcblk->x = 0;
dcblk->y = 0;
dcblk->R = 0.99; /* quite reasonable, indeed! */
}``````

### Computation

A single sample of audio is processed with the function `sk_dcblocker_tick`. It performs the arithmetic for the difference equation, updates the internal values, then returns the output.

<<funcdefs>>=
``SKFLT sk_dcblocker_tick(sk_dcblocker *dcblk, SKFLT in);``

<<funcs>>=
``````SKFLT sk_dcblocker_tick(sk_dcblocker *dcblk, SKFLT in)
{
dcblk->y = in - dcblk->x + dcblk->R*dcblk->y;
return dcblk->y;
}``````