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## Dividing by zero smoothly

Think of any real numbers x, y, and f and any program containing x=y/f. How can we change the program so that it never divides by zero? A popular answer is to change x=y/f to where is any tiny value. When then x is approximately y/f as expected. But when the divisor f vanishes, the result is safely zero instead of infinity. The transition between the two is smooth but some criterion is needed to choose the value of .This is may not be the only way or best way to cope with zero division, but it is a good way and it permeates the subject of signal analysis.

In the Fourier domain, X, Y, and F, are complex numbers. Then what do we do with X=Y/F? Multiply top and bottom by the complex conjugate ,and again add to the denominator. Thus
 (1)
Now the denominator must always be a positive number greater than zero, so division is always safe.

Next: Damped solution Up: HOW TO DIVIDE NOISY Previous: HOW TO DIVIDE NOISY
Stanford Exploration Project
1/13/1998