Espley???????? has described a convenient method for the numerical calculation of the harmonic output of a circuit containing a non-linear element, such as a valve, the characteristic of which is given for equally-spaced values of the input voltage. A difference table was formed from these data; the terms of the central line of this table were then multiplied by the values of certain functions dependent on the type of the harmonic wanted and the amplitude of the input, and finally the products were added. The present paper shows that a similar procedure can be applied to the determination of intermodulation products of two input frequencies. The factors which now appear as multipliers of the difference terms can be obtained from a multiplication table of such Espley functions. The procedure is summarized in Section 5. The derivation of the result makes use of the operator properties of Sheppard's symbols ???????? and ????????.
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