Add a Traktor MK2 blog post

This blog post explains the current state of implementation for the
Traktor MK2 decoder.

Author: jclsn

content/images/news/offset-modulated-signal-with-derivative.png

@@ -0,0 +1,209 @@
+title: "How Does Timecode Vinyl Actually Work? (Pt. 3)"
+authors: Jan Claußen
+tags: traktor, timecode, dvs, vinyl control
+status: draft
+math: yes
+
+Since its release in 2011, the **Traktor Control Vinyl MK2** has sparked
+curiosity among digital DJs and audio developers alike. Its timecode format
+stands apart from Serato’s, which we explored in the previous posts. With the
+MK2 system, Native Instruments introduced a more advanced timecode that boosts
+resolution and accuracy by applying cryptographic methods for both decoding
+and error correction.
+
+In this post, we’ll break down how it actually works.
+
+---
+
+## Table of Contents
+
+1. [Recap: How Serato Timecode Works](#recap)
+2. [The Traktor MK2 Signal](#traktor-mk2-timecode)
+3. [Pitch Detection](#pitch-detection)
+4. [Demodulation Techniques](#demodulation)
+5. [The Code](#the-code)
+6. [What’s Next](#whats-next)
+
+---
+
+## Recap: How Serato Timecode Works <a name="recap"></a>
+
+Serato’s timecode is built around a 
+[Linear Feedback Shift Register](https://en.wikipedia.org/wiki/Linear-feedback_shift_register),
+modulated onto a 1 kHz carrier using 
+[amplitude modulation (AM)](https://en.wikipedia.org/wiki/Amplitude_modulation)
+— a legacy method from radio transmission.
+
+The demodulation process is relatively simple: when one stereo channel crosses
+the x-axis, the other hits a peak. If that peak exceeds a certain threshold,
+the system reads it as a 1; if not, it’s a 0.
+
+![Serato Timecode Signal]({static}/images/news/serato-control-cd.png)
+
+We covered this in more detail in 
+[DVS Internals Pt. 1]({filename}/news/2021-11-21-dvs-internals-pt1.md) 
+and [Pt. 2]({filename}/news/2021-12-22-dvs-internals-pt2.md).
+
+---
+
+## The Traktor MK2 Signal <a name="traktor-mk2-timecode"></a>
+
+Below is a generated signal that resembles what you’ll find on the Traktor MK2
+Control CD.
+
+The carrier wave operates at **2500 Hz**, a significant increase from Serato’s
+**1000 Hz**.
+
+> **Advantage 1:** The higher carrier frequency allows for ~2.5× greater resolution.
+
+![Offset-modulated Signal]({static}/images/news/offset-modulated-signal.png)
+
+Upon inspection, this waveform clearly doesn’t use amplitude modulation — the
+amplitude remains constant. Instead, it appears to be **offset-modulated**,
+where the signal is shifted vertically from the x-axis. This is a non-standard
+technique not commonly used in typical modulation schemes.
+
+On the original vinyl version (not shown here due to copyright), the offset
+can be so large that the signal floats entirely above the x-axis for multiple
+cycles — making zero-crossing detection impossible.
+
+Even when that doesn’t happen, the offset causes the time difference $d_t$
+between zero-crossings to become irregular, introducing audible pitch flutter.
+
+To decode the signal, we must solve:
+
+1. How to filter the signal to enable pitch detection
+2. How to demodulate this non-standard modulation
+3. What exactly is encoded in this bitstream?
+
+---
+
+## Pitch Detection <a name="pitch-detection"></a>
+
+> **Note:** If you're unfamiliar with pitch detection in DVS systems, revisit
+> [DVS Internals Pt. 1]({filename}/news/2021-11-21-dvs-internals-pt1.md).
+
+Our goal is to produce a signal that oscillates evenly around the x-axis. This
+filtered waveform can then be processed using standard pitch detection
+algorithms.
+
+A simple derivative operation achieves this:
+
+$$y[n] = x[n] - x[n-1]$$
+
+When applied to the offset-modulated signal, we get:
+
+![Offset-modulated signal with derivative]({static}/images/news/offset-modulated-signal-with-derivative.png)
+
+The resulting waveform oscillates cleanly around zero, which is ideal for
+analysis. It also makes it easier to pinpoint the half-cycle peaks needed for
+bit detection.
+
+You may notice that the derivative’s zero-crossings don’t align perfectly with
+the original peaks. That’s due to a delay introduced by the filter. Smoothing
+the signal first, then compensating for the delay (e.g., by selecting
+<br>$x[n-3]$), yields better results.
+
+For greater accuracy, one could analyze the phase response $\phi(\omega)$,
+which shows how delay varies with input frequency—but for most use cases, a
+fixed delay works well enough.
+
+---
+
+## Demodulation Techniques <a name="demodulation"></a>
+
+To extract bits from the signal, we detect the zero-crossings and sample the
+amplitude of the sinusoid at those moments.
+
+![Offset-modulated signal with
+zero-crossings]({static}/images/news/offset-modulated-signal-with-zero-crossings.png)
+
+The filtered signal can cross the x-axis in two directions—positive to
+negative or vice versa. Based on the direction, we determine which half-cycle
+contains the encoded bit.
+
+![Offset-modulated signal with readings]({static}/images/news/offset-modulated-signal-with-readings.png)
+
+Demodulation is then as simple as applying a threshold: amplitudes above it
+are **1**, and below it are **0**.
+
+![Offset-modulated signal with timecodes]({static}/images/news/offset-modulated-signal-with-timecodes.png)
+
+On actual vinyl, the physical behavior of the needle causes the offset to
+decay over time. This decay complicates bit extraction.
+
+To compensate, we analyze the **slope** between subsequent readings:
+
+$$slope[n] = reading[n] - reading[n-1]$$
+
+This method helps isolate the encoded signal from the floating zero line
+caused by mechanical drift.
+
+---
+
+## The Code <a name="the-code"></a>
+
+> **Note:** A deeper explanation of LFSRs can be found in [DVS Internals Pt. 2]({filename}/news/2021-12-22-dvs-internals-pt2.md)
+
+Interestingly, the Traktor MK2 system also uses a Linear Feedback Shift
+Register (LFSR) — but with very different parameters. While Serato’s LFSR has a
+20-bit length, Traktor’s appears to use a **110-bit** register.
+
+The number of unique states an LFSR can generate is:
+
+$$n_{max} = 2^m -1$$
+
+Hence for the Serato timecode
+
+$$n_{serato} = 2^{20} -1 = 1\,048\,575$$
+
+and for the Traktor MK2 timecode
+
+$$n_{mk2} = 2^{110} -1 = 1.298 \cdot 10^{33} = 1\,298\,074\,214\,633\,706\,907\,132\,624\,082\,305\,023$$
+
+That’s an astronomically high number—far beyond what’s required for this
+application.
+
+But how many states are actually needed?
+
+With a 2500 Hz carrier, you get 2500 bits per second. For 12 minutes of
+timecode:
+
+$$12 \,min \cdot 60 \,s = 720 \,s$$
+$$720 \,s \cdot 2500 \,states/s = 1\,800\,000 \,states$$
+
+This already exceeds the maximum state range of Serato’s 20-bit LFSR.
+
+> **Advantage 2:** The MK2 timecode supports ~1.8× more states than Serato’s system.
+
+However, a downside appears: each 110-bit state must be stored in 128 bits (4
+× 32-bit integers).
+
+So for 12 minutes:
+
+$$1\,800\,000 \,states \cdot 128 \,bit = 230\,400\,000 \,bit = 28\,800\,000 \,byte = 27.46 \,MB$$
+
+And for a 25-minute CD:
+
+$$4\,500\,000 \,states \cdot 128 \,bit = 576\,000\,000 \,bit = 72\,000\,000 \,byte = 68.66 \,MB$$
+
+> **Disadvantage 1:** The memory footprint is large—even a single side of timecode can exceed 27 MB.
+
+This makes storing a full lookup table impractical in production software.
+
+Nonetheless, this technique works and it represents the current state of
+implementation of the xwax library used that is used for vinyl control in
+Mixxx.
+
+---
+
+## What’s Next <a name="whats-next"></a>
+
+Fortunately, there are mathematical methods to reduce the memory requirements.
+This requires diving deeper into the crypthographic theory. First tests show
+that this can possibly be achieved by decimating the bitstream over a 110-bit
+window. This collapses the sequence into a 22-bit alternating 
+[Gold code](https://en.wikipedia.org/wiki/Gold_code). 
+The implementation of this technique is far more complex and not completed yet.
+
+We’ll explore those strategies in the next part of this series.