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Merge pull request #5 from RQM-Technologies-dev/copilot/add-quaternionic-signal-processing-note
Add 🔷 QSP page with styled ecosystem diagram
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‎docs/index.md‎

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!!! note "🔷 Quaternionic Signal Processing (QSP)"
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RQM now includes **Quaternionic Signal Processing (QSP)** — a framework for applying quaternion-based mathematics to signal processing tasks. See the [QSP Overview](qsp/index.md) for the full stack documentation.
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!!! tip "New: rqm-optimize"
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**rqm-optimize** is now part of the RQM ecosystem — an SU(2)-aware circuit optimization and compression layer. Insert `optimize(qc)` between translation and execution to reduce gate count before hardware runs. See the [Optimization guide](optimization.md).
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‎docs/qsp/index.md‎

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# 🔷 Quaternionic Signal Processing (QSP)
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**Status:** Active development · Production-ready architecture
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> **Apply quaternion mathematics to real-world signal processing.**
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QSP is a quaternion-native signal processing framework built on `qsp-core`. It provides FFT, filtering, modulation, and orientation estimation through a unified API that treats signals as quaternion-valued sequences.
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---
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## Stack Architecture
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<div style="border: 2px solid var(--md-primary-fg-color); border-radius: 10px; overflow: hidden; text-align: center; font-family: var(--md-code-font); max-width: 640px; margin: 1.5rem auto;">
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<div style="background: var(--md-primary-fg-color); color: var(--md-primary-bg-color); padding: 14px 16px; font-weight: bold; font-size: 1.05em; letter-spacing: 0.04em;">
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qsp-stack
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</div>
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<div style="display: grid; grid-template-columns: repeat(4, 1fr); border-top: 2px solid var(--md-primary-fg-color);">
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<div style="padding: 12px 8px; border-right: 1px solid var(--md-primary-fg-color); font-size: 0.9em;">
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<strong>qsp-fft</strong>
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</div>
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<div style="padding: 12px 8px; border-right: 1px solid var(--md-primary-fg-color); font-size: 0.9em;">
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<strong>qsp-filter</strong>
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</div>
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<div style="padding: 12px 8px; border-right: 1px solid var(--md-primary-fg-color); font-size: 0.9em;">
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<strong>qsp-modulation</strong>
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</div>
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<div style="padding: 12px 8px; font-size: 0.9em;">
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<strong>qsp-orient</strong>
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</div>
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</div>
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<div style="background: var(--md-primary-fg-color--light, #e8eaf6); color: var(--md-primary-fg-color); padding: 14px 16px; border-top: 2px solid var(--md-primary-fg-color); font-weight: bold; font-size: 1.05em; letter-spacing: 0.04em;">
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qsp-core
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</div>
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</div>
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---
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## Package Roles
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<div class="grid cards" markdown>
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- **`qsp-core`** — Foundation
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---
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Defines the quaternion-valued signal primitives, number types, and shared utilities that every other `qsp-*` package depends on.
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- Single source of truth for quaternion arithmetic
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- No external signal-processing dependencies
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- Designed for numerical correctness and testability
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- **`qsp-fft`** — Quaternionic FFT
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---
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Implements the quaternion Fourier transform and its inverse, enabling frequency-domain analysis of quaternion-valued signals.
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- Quaternion FFT (QQFT) and inverse
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- Spectral analysis for multi-channel signals
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- Depends on `qsp-core`
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- **`qsp-filter`** — Signal Filtering
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---
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Provides FIR and IIR filter designs that operate natively on quaternion signals, preserving inter-channel phase relationships.
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- Quaternion FIR and IIR filters
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- Hilbert-transform-based analytic signals
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- Depends on `qsp-core`
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- **`qsp-modulation`** — Modulation & Demodulation
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---
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Encodes and decodes information using quaternion phase-shift keying and amplitude modulation schemes.
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- Quaternion phase-shift keying (QPSK extensions)
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- Amplitude and phase modulation
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- Depends on `qsp-core`
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- **`qsp-orient`** — Orientation Estimation
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---
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Estimates rigid-body orientation from inertial or multi-antenna sensor streams using quaternion-domain filtering.
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- Attitude estimation from IMU data
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- Quaternion Kalman and complementary filters
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- Depends on `qsp-core`
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- **`qsp-stack`** — Umbrella Package
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---
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A convenience meta-package that installs the complete QSP ecosystem in a single step.
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```bash
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pip install qsp-stack
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```
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</div>
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---
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🌐 **Website:** [https://rqmtechnologies.com](https://rqmtechnologies.com)

‎mkdocs.yml‎

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- API:
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- rqm-core API: api/rqm-core-api.md
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- rqm-qiskit API: api/rqm-qiskit-api.md
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- Quaternionic Signal Processing:
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- Overview: qsp/index.md
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- Quantum Communication:
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- Overview: quantum-communication/index.md

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