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Prompts MDCT Implementation for Sequence [1,2,3,4]

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MDCT Implementation for Sequence [1,2,3,4]

Implement the Modified Discrete Cosine Transform (MDCT) for the input sequence x(n) = [1, 2, 3, 4]. Follow steps to identify N and 2N, apply the MDCT formula with clear cosine valu…

PROMPT 

Implement MDCT for the input sequence:

x(n) = [1, 2, 3, 4]

Steps:
1. Identify N and 2N
2. Apply MDCT formula
3. Show cosine values clearly
4. Display step-by-step calculation table
5. Give final coefficients

REQUIRED CONTEXT

  • input sequence

ROLES & RULES

  1. Identify N and 2N
  2. Apply MDCT formula
  3. Show cosine values clearly
  4. Display step-by-step calculation table
  5. Give final coefficients

EXPECTED OUTPUT

Format
table
Schema
table
Constraints
  • step-by-step calculation table
  • show cosine values clearly
  • identify N and 2N
  • final coefficients

SUCCESS CRITERIA

  • Identify N and 2N
  • Apply MDCT formula
  • Show cosine values clearly
  • Display step-by-step calculation table
  • Give final coefficients

FAILURE MODES

  • Use incorrect MDCT formula
  • Misidentify N or 2N
  • Fail to display table or cosine values

CAVEATS

Missing context
  • Mathematical formula for MDCT.
  • Confirmation of MDCT type and any windowing function.
  • Precision requirements for cosine values and calculations.
Ambiguities
  • Does not specify the exact MDCT formula or type (e.g., Type-IV MDCT).
  • Unclear how to determine N and 2N for input sequence of length 4 (typically 2N=4, N=2 for MDCT).

QUALITY

OVERALL
0.65
CLARITY
0.85
SPECIFICITY
0.75
REUSABILITY
0.20
COMPLETENESS
0.65

IMPROVEMENT SUGGESTIONS

  • Explicitly include the MDCT formula, e.g., 'X(k) = sqrt(2/N) * sum_{n=0}^{2N-1} x(n) * cos[π/(2N) * (2n+1+N+k)(2n+1)]' for Type-IV.
  • Clarify: 'For input length 4, set 2N=4, N=2.'
  • Replace specific x(n) with placeholder like 'x(n) = {sequence}' for reusability.
  • Define table format: 'Columns: k, n, cos value, x(n), x(n)*cos, running sum.'

USAGE

Copy the prompt above and paste it into your AI of choice — Claude, ChatGPT, Gemini, or anywhere else you're working. Replace any placeholder sections with your own context, then ask for the output.

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