edge detection of 1-D signals

Would you please introduce me to some methods (or references) to do edge detection on some pulses (rectangular pulses embedded in noise). At first I apply some filters to smooth the signals, then I need edge detection. I have to say that they are 1-d signals (not images).

I should say that in the next stage, I have to implement the optimal method on an ARM micro-controller.

• Could you tell us more about the filters you use to smooth signals? In the linear setting, smoothing and edge detection can be merged, and how signals are smoothed is important – Laurent Duval Oct 28 '18 at 13:11
• I apply different filters such- (Both IIR and FIR filters ) Butterworth, Chebyshev, etc. -Moving average filters, recursive filters; finally I have to choose the best one. – Reza Mahjoob Nov 1 '18 at 17:29
• Dear Duval, unfortunately I did not understand what you said. E.g., how can I combine filtering and edge detection?(suppose a moving average filter and then taking difference) Please explain more if it is possible. thanks. – Reza Mahjoob Nov 3 '18 at 10:02
• If the smoothing operation is implemented with a linear filter, and you then use a standard discrete derivative (which is a linear filter as well), both can in general be combined, since convolution (in common practice) is commutative. So you can convolve your signal directly with the derivative of the smoothing filter. – Laurent Duval Nov 3 '18 at 10:38
• One issue though: smoothing is often not optimal with rectangular pulses, depending on their sharpness – Laurent Duval Nov 3 '18 at 10:47

$$d[n] = x[n]-x[n-1]$$
where large values of $$|d[n]|$$ signifies edge locations assuming noise is reduced.