# What is the bandwidth of product of two signals?

For signal $x(t)$ with bandwidth $B_x$ and signal $y(t)$ with bandwidth $B_y$, what will the bandwidth of the signal $z(t)=x(t)y(t)$ be?

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I think that the statement "The bandwidths simply add." needs some qualification since it does not necessarily hold for all definitions of bandwidth that engineers might use. If $B_x$ and $B_y$ are the supports of $X(f)$ and $Y(f)$ respectively, then it is true that the support of $Z(f)$ will be $B_x+B_y$, but (i) support is not the only measure of bandwidth (do $99\%$ containment bandwidths add?), and (ii) in many signal models, the support of $X(f)$ and $Y(f)$ is $(-\infty,\infty)$ and so adding supports is meaningless. –  Dilip Sarwate Oct 31 '12 at 12:39