{
  "input": [
    1,
    2,
    0,
    -1
  ],
  "FIR": [
    "1/2",
    "1",
    "1/2"
  ],
  "P": 2,
  "Q": 3,
  "main": {
    "up_zero_inserted": [
      "1",
      "0",
      "2",
      "0",
      "0",
      "0",
      "-1"
    ],
    "full_FIR": [
      "1/2",
      "1",
      "3/2",
      "2",
      "1",
      "0",
      "-1/2",
      "-1",
      "-1/2"
    ],
    "output": [
      "1/2",
      "2",
      "-1/2"
    ],
    "direct_index_oracle": [
      {
        "output_index": 0,
        "high_rate_index": 0,
        "terms": [
          "1/2",
          "0",
          "0",
          "0"
        ],
        "sum": "1/2"
      },
      {
        "output_index": 1,
        "high_rate_index": 3,
        "terms": [
          "0",
          "2",
          "0",
          "0"
        ],
        "sum": "2"
      },
      {
        "output_index": 2,
        "high_rate_index": 6,
        "terms": [
          "0",
          "0",
          "0",
          "-1/2"
        ],
        "sum": "-1/2"
      }
    ],
    "phase": 0
  },
  "wrong_raw_every_third": [
    1,
    -1
  ],
  "all_bounded_length_ratio_phase_oracles": 640,
  "identity_ratio_impulse": {
    "up_zero_inserted": [
      "1"
    ],
    "full_FIR": [
      "1/2",
      "1",
      "1/2"
    ],
    "output": [
      "1/2",
      "1",
      "1/2"
    ],
    "direct_index_oracle": [
      {
        "output_index": 0,
        "high_rate_index": 0,
        "terms": [
          "1/2"
        ],
        "sum": "1/2"
      },
      {
        "output_index": 1,
        "high_rate_index": 1,
        "terms": [
          "1"
        ],
        "sum": "1"
      },
      {
        "output_index": 2,
        "high_rate_index": 2,
        "terms": [
          "1/2"
        ],
        "sum": "1/2"
      }
    ],
    "phase": 0
  },
  "invalid_cases_rejected": [
    "Pzero",
    "Qnegative",
    "boolratio",
    "emptyfilter",
    "NaN",
    "invalidphase",
    "overlength"
  ],
  "scope": "own finite exact zero-extension/full-convolution/phase-index exercise, not SciPy/polyphase optimization/anti-alias-quality/delay compensation/duration guarantee/real audio or Opera service test"
}