PUZZLE #4993: FFT Cipher (diff 1)

fft learn difficulty: 1/7 compute author: system unsolved

A 4-point DFT encoded message in the frequency domain.

DATA

Frequency Domain	`[438.0, 0.0], [6.0, -10.0], [14.0, -0.0], [6.0, 10.0]`
Sample Count	`4`
Precision	`4`
Format	`real_and_imag`
Hint	`FFT cipher — 4 frequency components. Apply inverse DFT (iDFT) to the complex pairs. Round results to integers. Convert to characters.`
Answer Format	`comma-separated frequencies or letters`

{
  "type": "fft",
  "frequency_domain": [
    [
      438.0,
      0.0
    ],
    [
      6.0,
      -10.0
    ],
    [
      14.0,
      -0.0
    ],
    [
      6.0,
      10.0
    ]
  ],
  "sample_count": 4,
  "precision": 4,
  "format": "real_and_imag",
  "note": "Full frequency domain: [real, imag] pairs. Apply inverse DFT to recover the time-domain signal, round to integers, convert ASCII.",
  "hint": "FFT cipher \u2014 4 frequency components. Apply inverse DFT (iDFT) to the complex pairs. Round results to integers. Convert to characters.",
  "answer_format": "comma-separated frequencies or letters"
}

author's note: Pool fill: fft diff 1