Convolution of sign function with itself

Asked Jun 17 '18 at 12:19

Active Jun 20 '18 at 15:25

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How can we calculate the convolution of the following function $(M(f))$ with itself $(M(f) * M(f) )$

$$ M(f)=\begin{cases}\operatorname{sgn}(f) \,,~~~|f|\leq 3w \\ 0 \,,~~~|f|>3w \end{cases}$$

where $$ \operatorname{sgn}(f)= \begin{cases}1 \,, ~~~f>0 \\ 0 \,,~~~f=0 \\ -1 \,,~~~ f<0. \end{cases}$$

edited Jun 17 '18 at 13:34

Alastor

asked Jun 17 '18 at 12:19

Have you tried multiplying Fourier transforms? – J.G. Jun 17 '18 at 12:22
@J.G. they are the fourier transforms , thats why I didn't use t as the variable. Do you mean , I should do the fourier transform once more to the sgn(t)? If I wanted to calculate this by using the definition of convolution with the integral , how would I do it? – Jun 17 '18 at 12:24

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