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Mario Alexandre
Mario Alexandre

Posted on • Originally published at tokencalc.pro

Free Prompt Transformer: Convert Any Prompt to 6 Nyquist Bands

#ai #tools #promptengineering #webdev

Free Prompt Transformer: Convert Any Prompt to 6 Nyquist Bands

By Mario Alexandre
March 21, 2026
sinc-LLM
Prompt Engineering

What the Transformer Does

The sinc-LLM Prompt Transformer is a free online tool that takes any raw prompt and decomposes it into 6 specification bands following the Nyquist-Shannon sampling theorem. It identifies missing bands, suggests content for them, and outputs a structured prompt that is 97% more token-efficient.

x(t) = Σ x(nT) · sinc((t - nT) / T)

The tool is available at tokencalc.pro and is completely free to use. No account required.

How It Works

The transformer follows a three-step process:

Step 1: Band Detection

Analyzes your raw prompt to identify which of the 6 specification bands are already present: PERSONA, CONTEXT, DATA, CONSTRAINTS, FORMAT, TASK.

Step 2: Gap Analysis

Identifies missing bands and estimates the aliasing risk for each. CONSTRAINTS (42.7% quality weight) and FORMAT (26.3%) are flagged as high-priority if missing.

Step 3: Structured Output

Outputs a sinc JSON prompt with all 6 bands filled, ready to send to any LLM (ChatGPT, Claude, Gemini, open source models).

{
"formula": "x(t) = ... sinc((t - nT) / T)",
"T": "specification-axis",
"fragments": [
{"n": 0, "t": "PERSONA", "x": "..."},
{"n": 1, "t": "CONTEXT", "x": "..."},
{"n": 2, "t": "DATA", "x": "..."},
{"n": 3, "t": "CONSTRAINTS", "x": "..."},
{"n": 4, "t": "FORMAT", "x": "..."},
{"n": 5, "t": "TASK", "x": "..."}
]
}

Before and After Examples

Input: Raw Prompt

"Write a marketing email for our new product."
Band coverage: 1/6 (TASK only). Aliasing risk: extreme. The model must invent 5 specification dimensions.

Output: 6-Band Prompt

PERSONA: B2B SaaS email copywriter specializing in product launches
CONTEXT: [Fill: Company name, product type, target market, launch stage]
DATA: [Fill: Product name, key features, pricing, unique value proposition]
CONSTRAINTS:

  • Maximum 200 words
  • One clear CTA
  • No superlatives or hype language
  • Must include product name and pricing
  • Professional tone, not salesy
  • Compliance-safe (no unsubstantiated claims) FORMAT: Subject line + greeting + 3 short paragraphs + CTA + signature TASK: Write a cold outreach email announcing the product launch. Band coverage: 6/6. Aliasing risk: near-zero.

Use Cases

  • Prompt optimization: Paste existing prompts to find and fill specification gaps

  • Cost reduction: Identify noise tokens that can be removed without quality loss

  • Quality improvement: Ensure every prompt meets Nyquist rate before execution

  • Team standardization: Give your team a tool that enforces consistent prompt structure

  • Education: Learn the 6-band framework by seeing it applied to real prompts

Try It Now

The transformer is live at tokencalc.pro. Paste any prompt and see the 6-band decomposition instantly. No account, no cost, no data stored.

For programmatic access, use the CLI tool from the sinc-LLM GitHub repository:

py -X utf8 auto_scatter.py "your raw prompt" --execute
Or the HTTP API:

POST http://localhost:8461/execute
Content-Type: application/json
{"prompt": "your raw prompt"}
Read the full research paper for the theoretical foundation behind the tool.

Transform any prompt into 6 Nyquist-compliant bands

Try sinc-LLM Free

Related Articles

Real sinc-LLM Prompt Example

This is the exact JSON format that sinc-LLM uses. Paste any raw prompt at tokencalc.pro to generate one automatically.

{
"formula": "x(t) = Σ x(nT) · sinc((t - nT) / T)",
"T": "specification-axis",
"fragments": [
{
"n": 0,
"t": "PERSONA",
"x": "You are a Product manager for developer tools. You provide precise, evidence-based analysis with exact numbers and no hedging."
},
{
"n": 1,
"t": "CONTEXT",
"x": "This analysis is part of a production system where accuracy determines revenue. The sinc-LLM framework identifies 6 specification bands with measured importance weights."
},
{
"n": 2,
"t": "DATA",
"x": "Fragment importance: CONSTRAINTS=42.7%, FORMAT=26.3%, PERSONA=7.0%, CONTEXT=6.3%, DATA=3.8%, TASK=2.8%. SNR formula: 0.588 + 0.267 * G(Z1) * H(Z2) * R(Z3) * G(Z4). Production data: 275 observations, 51 agents."
},
{
"n": 3,
"t": "CONSTRAINTS",
"x": "State facts directly. Never hedge with 'I think' or 'probably'. Use exact numbers for every claim. Do not suggest generic solutions. Every recommendation must be specific and verifiable. Include at least 3 MUST/NEVER rules specific to this task."
},
{
"n": 4,
"t": "FORMAT",
"x": "Lead with the definitive answer. Use structured headers. Tables for comparisons. Numbered lists for sequences. Code blocks for implementations. No trailing summaries."
},
{
"n": 5,
"t": "TASK",
"x": "Write the product announcement for tokencalc.pro/sinc-llm, a free browser-based prompt transformer"
}
]
}Install: pip install sinc-llm | GitHub | Paper

Originally published at tokencalc.pro

sinc-LLM applies the Nyquist-Shannon sampling theorem to LLM prompts. Read the spec | pip install sinc-prompt | npm install sinc-prompt

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