why if we pad any signal with enough zeros we can get the same result

if we pad any signal with enough zeros we can get the same result as linear convolution whilst using the fft function we compute circular convolution. Why?

• It's usually thought of as the other way around. The windowing you choose impacts a trade-off between frequency and time resolution regarding non-stationary data. You may have to prioritize. – hotpaw2 Nov 1 '13 at 18:03
• can you explain more plz? – fransisco Nov 1 '13 at 20:56
• Just curious, in practical implementations, is there a relationship between the time resolution and frequency resolution? @hotpaw? – freak_warrior Nov 4 '13 at 0:14

Hint: try computing the linear convolution of $~[1\quad 1\quad 1]~$ and $~[0\quad 1 \quad 1]~$ by hand and the circular convolution of the zero-padded versions $~[1\quad 1\quad 1 \quad 0\quad 0\quad 0]~$ and $~[0\quad 1 \quad 1\quad 0\quad 0\quad 0]~$ also by hand (or via FFTs if you are desperate enough).