Estimating Gain and Phase Shift

The gain ratio, often gain for short, is the ratio of the amplitude of the output to the amplitutude of the input. It is best understood from sinusoidal forcing after any initial transients have died out, and the input and output sine waves reproduce exactly. Input and output may have different units. For example, the input might be voltage while the output might be temperature of the heating coil that gets that voltage. The intensity of the signal is normalized to get rid of the units. However, the gain ratio could be greater than one or less than one because of the proportionality of selecting the scales.
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