How to Write Better AI Prompts: A Signal Processing Approach

The Problem with Prompt Advice

Most prompt advice is vague: "be specific," "give context," "use examples." That advice is not wrong. But it is not enough. It does not tell you how specific, how much context, or which examples. It gives you no way to check if your prompt is done.

My sinc-LLM framework swaps vague advice for a clear checklist. A prompt is complete when it covers all 6 parts well. No more guessing.

The 6 Things Every Prompt Needs

Based on my research studying 275 real prompts, every good prompt covers 6 parts:

1. PERSONA: Tell the AI who it is. Not just "helpful assistant." Say something like "a data scientist who works with time series data."
2. CONTEXT: Give the situation. What project is this? What stage are you in? What have you already tried?
3. DATA: Share the real inputs. This could be code, numbers, a document, or examples.
4. CONSTRAINTS: This is the most important part (42.7% of output quality). Write the rules, limits, and things to avoid. Put the most words here.
5. FORMAT: Say exactly what the answer should look like. JSON? Bullet points? How long?
6. TASK: The actual instruction. By the time you fill in the other parts, this is usually just one sentence.

Before and After: Real Examples

Bad Prompt (1 band sampled)

"Analyze this data and give me insights."

This only covers TASK. The AI has to guess the persona, the context, the data, the constraints, and the format. Every guess can lead to a wrong answer.

Good Prompt (6 bands sampled)

PERSONA: Senior business analyst for e-commerce
CONTEXT: Q4 2025 sales data, comparing to Q3. Company sells B2B SaaS.
DATA: [attached CSV with columns: date, revenue, churn_rate, new_signups]
CONSTRAINTS: Focus on churn trends only. Do not speculate on causes
  without data support. Flag any metric that changed more than 15%.
  Max 500 words.
FORMAT: Executive summary (3 bullets), then detailed analysis
  with one table comparing Q3 vs Q4 metrics.
TASK: Analyze churn trends and identify the top 3 actionable findings.

The CONSTRAINTS-First Method

Here is the surprising finding from my 275 observations: start writing your prompt with CONSTRAINTS, not TASK. Here is why:

• CONSTRAINTS drive 42.7% of the quality of the answer.
• Writing constraints makes you think about tricky cases before the AI does.
• Constraints are the part people most often skip, so the AI has to fill them in by guessing.
• A prompt with great constraints and a weak task beats a prompt with a great task but no constraints.

Simple rule: if your CONSTRAINTS section is shorter than your TASK section, your prompt is missing its most important part.

Tools to Help

You do not have to do this by hand every time:

• sinc-LLM Transformer: Free online tool. Paste any prompt and it breaks it into the 6 parts for you.
• sinc-LLM GitHub: Open source code you can add to your own workflow.
• My Research Paper: 275 observations, math proofs, and ablation studies.

The gap between a good prompt and a great one is not creativity. It is completeness. Cover all 6 parts, and the AI does the rest.

{
  "formula": "x(t) = Σ x(nT) · sinc((t - nT) / T)",
  "T": "specification-axis",
  "fragments": [
    {
      "n": 0,
      "t": "PERSONA",
      "x": "You are a practical AI coach who helps beginners get dramatically better results from ChatGPT, Claude, and Gemini. You focus on immediate, actionable improvements."
    },
    {
      "n": 1,
      "t": "CONTEXT",
      "x": "The reader has been using AI chatbots for 6 months and gets 'okay' results. They know their prompts could be better but do not know where to start. They have never heard of sinc-LLM or prompt frameworks."
    },
    {
      "n": 2,
      "t": "DATA",
      "x": "Average user prompt: 12 words. Average sinc prompt: 68 words. Quality improvement: 24% (composite score). The single biggest improvement comes from adding CONSTRAINTS (42.7% of quality)."
    },
    {
      "n": 3,
      "t": "CONSTRAINTS",
      "x": "Write at a 10th-grade reading level. No jargon. Every tip must include a before/after example. Limit to 5 tips maximum. Each tip must be usable in under 30 seconds. Do not mention the word 'framework' or 'methodology.'"
    },
    {
      "n": 4,
      "t": "FORMAT",
      "x": "Return: (1) The One Thing Wrong With Your Prompts (1 paragraph). (2) 5 Tips with Before/After examples. (3) The Template they can copy-paste."
    },
    {
      "n": 5,
      "t": "TASK",
      "x": "Write 5 practical tips for writing better AI prompts that a beginner can apply immediately, based on the sinc-LLM finding that CONSTRAINTS carry 42.7% of quality."
    }
  ]
}