File:Spectroradiometric analysis of radio signals (IA scientificpapers47719geor).pdf

When a radiation, regularly repeated, is received by a simple circuit possessing inductance, capacity, and resistance, a current is induced in the circuit whose effective value may be measured, If, while the radiation continues, the circuit is tuned to various frequencies, the resulting currents observed and plotted against the resonant frequencies of the circuit, such a curve will be proportional to the spectral distribution of energy in the radiation if the circuit has a relatively high resolving power compared to the spectral structure of the wave. As a matter of fact, this is not usually the case, and to derive the energy distribution of the wave requires that a certain integral equation be solved in which the above-mentioned curve is the known function. Four different methods are here given for obtaining practicable solutions of this equation. The first gives the solution in terms of a double integral analogous to Fourier's. The second gives a series solution. The third solution is given in terms of differentiations and integrations of the given function, and has the advantage that the operations may be performed graphically. The fourth method consists in representing the observed function by empirical equations of certain simple types, the solution corresponding being easily obtained by subtracting the damping coefficient of the circuit from certain analogous parameters in the simple types of solutions used. This method is applicable to the limiting case of line spectra and is here applied to three different experimental curves.