I'm confused with the name of Howard's father.

Is it Sam Wolowitz or Joe Wolowitz? 

I was recently watching Season 4 Episode 04 - The hot troll deviation. In that episode at around 2:40 you can see that the initials on Howard's shirt are HWJ , in my opinion which should be Howard Wolowitz (Joe?), also in Season 4 Episode 07 - The apology insufficiency at around 12:50 Sheldon says Howard's full name as 'Howard Joel Wolowitz'.

In Season 8 Episode 20 Howards half brother Josh Wolowitz says that his fathers name is Sam Wolowitz , and even Howard agrees to it. 

So, what is the name of Howards father? Sam or Joe? or am I wrong here? It's Sam as stated by his second son.