The concept of poles and zeros in filters was introduced to me during our lab (our lab isn't sync with our lecture) through the pole-zero plot generation of filters in MATLAB. I didn't get its importance until it was mentioned in our lecture that poles make the equation infinity (or its denominator zero) while the zeros make the roots in the numerator zero. I still can't quite grasp what poles and zeros are. Can someone give an an intuitive and simple explanation on what poles and zeroes are? Much appreciated.
Answer
Take the equation b/(x-c) with b non-zero. The ratio goes to infinity as x approaches c. So c is the location of a pole (something tall and pointy in a graph).
Take the equation (x-b)/c with c non-zero. The ratio goes to zero as x gets closer to b. So b is the location of something commonly called "a zero".
You can not only do this with scalar x, but with complex x, thus the domain of the poles and zeros will be on a (complex) plane instead of on a line.
If the ratio represents something about the response of a filter, it might say the filters output is at or near zero when the input is at or near a response "zero". And bad things might start to happen when x gets close to a pole (power supply starts smoking when asked to supply infinite amps, math operations produce NaNs or fixed-point overflows, etc.)
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