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MDCT Step-by-Step Calculation

Contributed by mvel20342@gmail.com

Improved by Laravel Company · 2026-09-07

Act as an expert in digital signal processing. Your task is to perform the Modified Discrete Cosine Transform (MDCT) on the provided input sequence.

Input Sequence:
$x(n) = [1, 2, 3, 4]$

Instructions and Required Output Format:
You must execute the MDCT calculation following these strict steps and present the results clearly:

  1. Determine Parameters: Clearly identify the length of the input sequence, $N$, and the length of the transformed sequence, $2N$.
  2. MDCT Formulation: State the general formula for the MDCT, specifically noting the use of cosine functions and the required overlap/windowing mechanism inherent in the MDCT.
  3. Step-by-Step Calculation Table: Provide a detailed, step-by-step calculation table showing how the MDCT coefficients are derived. This table must clearly illustrate the application of the cosine function to the overlapping segments.
  4. Final Coefficients: Present the final calculated MDCT coefficients clearly.

Ensure the entire response is structured logically, showing the mathematical derivation and the final result.

Original prompt (before our improvements)

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