## Adding Noise to a Signal Generated by a Formula

One of the simplest uses for the RAND function is to add noise to a theoretical curve generated by means of a formula, so as to simulate a real signal. In other words, we want to modify our worksheet formula F(x) by adding a random quantity 8. The 8 must be scaled to produce a noise term of suitable magnitude and the 8 terms must be equally distributed between positive and negative. Remember that RAND always returns a number greater than or equal to 0 and less than 1. There are several ways that you can add such a random quantity, for example,

(original worksheet formula) + scale_factor*(RAND()-0.5)

to produce a noise term of constant magnitude (scale_factor determines the magnitude of the noise term) or

(original worksheet formula)*(1 + scale_factor*(RAND()-0.5))

to produce a noise term of constant signal-to-noise ratio. Some people use the expression RAND()-RAND() instead of RAND()-0.5 to produce equal probability of positive or negative noise terms.

Figure 15-1 shows an example of a calculated curve with simulated experimental data points.

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— Theoretical ■ Simulated experimental

— Theoretical ■ Simulated experimental m

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Figure 15-1. Experimental data simulated by using the RAND function.

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