I've just finished covering convolutions in my signals class, and I've been playing around with the
conv function in MATLAB, but there's something I don't quite understand. Say I have two discrete signals, $a$ and $b$ sampled at $dt$. As $dt \rightarrow 0$, the amplitude of the result increases. Since the convolution integral is just
why does the resulting convolution seem to depend on what my value is for $dt$? By decreasing the sampling rate, shouldn't I just have a better approximation?