# Why is a transfer function denoted by 'H'?

1. Dec 12, 2011

### Gonzo17

During a basic lecture about system design the transfer function H(s) was discussed. The question was raised why the letter 'H' is used for this...

Sounds weird, but I did start to think about it... Indeed in many books and publications the letter H (besides sometimes G(ain)) is used to describe the transfer function.

I googled around but I didn't come further than the fact that H(s) is the Laplace transform of the impulse response, denoted by h(t). Lovely explanation, but of course it moves the problem to where 'h' comes from in the impulse response...

Maybe I am looking over something extremely trivial, but I can't seem to get around it. Anybody any idea what the (historical) reason for this mysterious 'H' is?

2. Dec 12, 2011

### Travis_King

Might have something to do with Hilbert Transforms.

3. Dec 12, 2011

### I like Serena

Just a wild guess.

The transform tables are typically based on F and G.
H is the next letter in the alphabet that has no other significant meaning.
So I suspect H was chosen to avoid ambiguity with F and G (and other symbols).

An alternative interpretation is that a typical simple electronic circuit filter looks like an H on its side.

4. Dec 12, 2011

### Travis_King

That's probably right ^
Just a whimsical notation that stuck

5. Dec 12, 2011

### Gonzo17

Thanks for the suggestions...

It is possible that it's just the boring F-G-H-thing mentioned above. But if anybody knows of another story, I'll be more than happy to hear it! :-)

6. Dec 12, 2011

### I like Serena

Once upon a time I googled why U is sometimes used for voltage instead of V.
The only thing I could find, is to distinguish the unit volt from the quantity voltage.
I'd still be interested in a better explanation. ;)

7. Dec 12, 2011

### Travis_King

Also T wouldn't work because transfer functions are often functions of time, you can have H(t), and h(t), but it's confusing to have T(t) and t(t)