[Swift] How to properly subclass UITextfield and work with its delegate

Consider this:

class ViewController: UIViewController, UITextFieldDelegate  {
    var textfield: UITextField = {
        let tf = UITextField(frame: CGRect(x: 0, y: 0, width: 140, height: 30))
    }()

    override func viewDidLoad() {
        textfield.delegate = self
    }

    func textFieldDidBeginEditing(_ textField: UITextField) {
        print("Inside textfield") 
    }
}

When I tap inside the textfield, textFieldDidBeginEditing() is called because the delegate handles that.

What happens if I want to subclass UITextField? How do I handle a tap event inside the subclassed textfield within the subclass? So for example:

class MyTextField: UITextField, UITextFieldDelegate {
    required override init(frame: CGRect) {
        self.delegate = self // CAN'T DO THIS!!!
    }

    func textFieldDidBeginEditing(_ textField: UITextField) {
        print("Inside subclassed textfield")
        // This function is NOT executed when I tap inside this subclassed textfield!!
    }
}

The textFieldDidBeginEditing() within the subclass never gets called, I guess because the delegate is not properly set, and I don't know how to set it. It's not possible to do: self.delegate = self

Do I need to create a protocol for MyTextField? If so, how do I hook it all up? What would the code using MyTextField have to do? If I do:

    var subTF = MyTextField(....)
    subTF.delegate = self

Is that .delegate for class UITextField?? or is it for the subclass MyTextField?