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iterative convolution, discret convolution N times of the same

HI, I'm trying to do N time convulution of a density funtion called
"fd" with itself . I tried to write an algorithm as shown
For[i = 1; convn = fd, i <= N, i++,
 convn = DiscreteConvolve[convn, fd , x, m, Assumptions -> m > 0];

The initial function fd(x) has x as input variable. After the
convolution, the results convn(m) is in the function of m instead of
x. That's the reason why the algorithm I wrote doesn't work after the
first iteration since the DiscreteConvolve function couldn't find the
input in a function as x anymore.

I would like to ask a question is there a way to change the variable
of a function? for exemple: how can I replace a function y = x+1 by y=m
+1 ???? and is there another way to easily do a convolution N times of
the same function? Thank you very much.
Best regards,

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