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Feb 24, 2016 at 12:15 comment added Rajesh D I felt this is needless to say, as OP knows that Fourier series converges pointwise at all points except jumps,in this case.
Feb 24, 2016 at 12:09 comment added Rajesh D @user1952009 : original function $M$ is binary and hence has no zero set but only sign change points. Thats why all I have said is that the number of zeros of $f(M)$ would be equal to the sign changes, as long as cutoff is high enough. I agree the location of zeros of $f(M)$ do not exactly coincide with the jump points but convergence as the cutoff goes to $\infty$. (I could not comment right below your comment as I don't have enough rep now.
Feb 20, 2016 at 3:39 history edited Rajesh D CC BY-SA 3.0
added 16 characters in body
Feb 20, 2016 at 3:14 history answered Rajesh D CC BY-SA 3.0