The French forward arrived in North London fresh from winning Ligue 1 with Montepellier but initially struggled to score goals for the Gunners.
Giroud has now struck four times in his last five matches including braces against Brighton & Hove Albion and West Ham United.
The 26-year-old believes that he is on the right path to help Arsenal fans forget the loss of Robin van Persie last summer.
He told Eurosport: "The Premier League is the most physical championship in the world, you must adapt to prove that you can impose yourself. Above all I have to prove that I can follow a big player like Van Persie.
"I had a difficult time in November, I struggled to score but then I didn't play as much as I do now. I'm a bit like a diesel engine, when I started to play more I felt better and became more efficient.
"I think you can see that on the pitch, 14 goals and 10 assists is a good balance sheet but I don't want to stop there. I think I can still make progress, there is more to come from me."
Giroud has scored nine Premier League goals in 24 appearances this season.