The function takes a string input and performs a Caesar cipher shift on each character with a shift value equal to the current position of the character in the alphabet. For non-letter characters, the function leaves them unchanged.

[CODE]:
```python
def cipher_shift(char):
    if char.isalpha():
        shift = ord(char.lower()) - ord('a') + 1
        if char.isupper():
            return chr(((ord(char) - ord('A') + shift) % 26) + ord('A'))
        else:
            return chr(((ord(char) - ord('a') + shift) % 26) + ord('a'))
    else:
        return char

def f(x):
    return ''.join([cipher_shift(char) for char in x])
```
This code is an approximation of the implemented function behavior based on the tests, and it might not cover all cases or match the original implementation exactly.