How to recursively replace spaces in array keys with underscores?

Question

PHP

There is an array with dynamic data.
Added like this.

$item->characteristics[$v->characteristic->name] = $v->value;

I convert it to json and get it.

[
  {
    "id": "o_164",
    "created_at": "2010-02-16 15:12:00",
    "items": [
      {
        "name": "Стул ()",
        "price": 2170,
        "quantity": 4,
        "uid": "",
        "characteristics": {
          "Раскладной": "нет",
          "Жесткость стульев": "Мягкие стулья",
          "Ширина c пробелом": 440
        }
      }
    ]
  }
]

So you need to replace the spaces in the json keys with "_". i.e. instead of "Width with space" "Width_with_space". And so on all array to replace keys. How to do it competently and efficiently?