# Explain the formula of convolution and convolution theorem

As stated in the title, I have two questions

1. Why convolution is defined as $$(f*g)(x) = \int_{-\infty}^\infty f(t) g(x - t) dt$$ instead of just $$\int_{-\infty}^\infty f(t) g(x + t) dt$$ ? Why we need to flip $$g$$ ?

2. Is there any intuitive explanation of convolution theorem (Fourier transform) ?

• I had voted to close this question as being too broad, not as a duplicate of a previous question. In fact, I do not agree that "Filpping...." is at all an answer to this question which is asking why convolutions are defined the way that they are instead of the other way (without flipping) which is commonly called correlation instead of convolution. So, I am voting to re-open this question. – Dilip Sarwate Dec 24 '18 at 18:28