# Audio Math Explainer

> >

- **Type:** Skill
- **Install:** `agentstack add skill-kunitoki-sonic-skills-audio-math-explainer`
- **Verified:** Yes — security-reviewed for prompt injection and unsafe behavior
- **Seller:** [kunitoki](https://agentstack.voostack.com/s/kunitoki)
- **Installs:** 0
- **Category:** [Content & Media](https://agentstack.voostack.com/c/content-and-media)
- **Latest version:** 0.1.0
- **License:** Unlicense
- **Upstream author:** [kunitoki](https://github.com/kunitoki)
- **Source:** https://github.com/kunitoki/sonic-skills/tree/main/skills/audio-math-explainer

## Install

```sh
agentstack add skill-kunitoki-sonic-skills-audio-math-explainer
```

Requires the [AgentStack CLI](https://agentstack.voostack.com/docs/cli). Works with Claude Code, Cursor, and any MCP-compatible agent.

## About

# Audio Math Explainer

> **The rule:** DSP math is small and composable — each concept builds directly on the last.
> Start with what the user needs, then connect it to code they're writing.

## Step 1 — Identify the concept

| Topic | Core idea | Common "why" |
|-------|-----------|--------------|
| Fourier transform / DFT / FFT | Decompose signal into frequency components | "Why does my FFT output look wrong?" |
| Convolution | Weighted moving average; LTI system response | "How does an IR reverb work?" |
| Z-transform | Frequency-domain analysis of discrete systems | "How do filter poles/zeros work?" |
| Biquad / IIR filters | Recursive difference equation with feedback | "Why does my filter ring / go unstable?" |
| FIR filters | Non-recursive weighted sum | "How do I design a linear-phase filter?" |
| Windowing | Reduce spectral leakage in DFT | "Why are FFT edges smeared?" |
| Sample rate / Nyquist | Highest representable frequency = sr/2 | "What causes aliasing?" |
| Decibels | Log scale for amplitude/power ratios | "How do I convert gain to dB?" |

If the user's question maps to multiple rows, start with the most fundamental one and build up.

## Step 2 — Explain with three anchors

For each concept, give exactly these three things in order:

1. **Intuition** — one sentence a musician could understand
2. **Math** — the key formula (inline, no walls of derivation)
3. **Code** — one-line pseudocode or a real function call from common audio libraries

Keep each anchor to 1–3 lines. Cut anything that doesn't directly answer the question.

## Step 3 — Connect to the user's code

After the three anchors:
- Locate where the math appears in their implementation (coefficient calculation, loop structure, buffer size choice, etc.)
- Name the exact variable or line where theory becomes code
- If a value looks wrong, explain which part of the math it violates

## Quick connection table

| Math concept | Where it shows up in code |
|--------------|--------------------------|
| DFT basis frequencies | `bin_index * sr / N` — each FFT bin |
| Convolution sum | FIR tap loop: `y[n] = sum(h[k] * x[n-k])` |
| Z-plane pole radius | IIR feedback coefficients `a1`, `a2` |
| Nyquist limit | `if (freq > sampleRate / 2) clamp(...)` |
| Window function | Multiply `x[n] *= window[n]` before FFT |
| dB conversion | `gain_db = 20 * log10(amplitude)` |

## Output format

```
### [Concept name]

**Intuition:** [one sentence]

**Math:** `[formula]`

**Code:** `[one-liner]`

**In your code:** [where this appears and what it means for their specific question]
```

> See `references/dsp-math-reference.md` for full formula tables, gotchas, and property lists.

## Source & license

This open-source skill is cataloged on AgentStack and links to its original source — we do not rehost the code.

- **Author:** [kunitoki](https://github.com/kunitoki)
- **Source:** [kunitoki/sonic-skills](https://github.com/kunitoki/sonic-skills)
- **License:** Unlicense

Install and usage instructions live in the source repository linked above.

## Pricing

- **Free** — Free

## Security capabilities

Automated source analysis of v0.1.0 — what this tool can access:

- **Network access:** no
- **Filesystem access:** no
- **Shell / process execution:** no
- **Environment & secrets:** no
- **Dynamic code execution:** no

*"Yes" means the capability is present in the source — more access means more to trust, not that it is unsafe.*


## Versions

- **0.1.0** — security scan: passed — Imported from the upstream source.

## Links

- Listing page: https://agentstack.voostack.com/l/skill-kunitoki-sonic-skills-audio-math-explainer
- Seller: https://agentstack.voostack.com/s/kunitoki
- Browse the marketplace: https://agentstack.voostack.com/browse

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Listed on AgentStack — the marketplace for AI agent skills and MCP servers. Every listing is security-reviewed. Creators keep 70%.