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Fig. 3. Mixing circuit.For frequency modulation we can vary an equivalent inductance through a gyration resistance which varies directly with a modulating voltage. Thus, any of the oscillator circuits of Fig. 1 can be appropriately designed to obtain a frequency modulator through suitable gyrator variation. From (3) we note that the variation can be made linear by varying only R,, but that it also can be quadratic if R, is also varied (though, of course, slowly with respect to variations in the current). As with frequency modulators, we can avoid using noniinearities of active devices in mixing circuitry. Such a mixing circuit is shown in Fig. 3, where a frequency of o1 is the input to the transistor, and a signal of frequency w 2 is used to modulate a gyrator parameter or parameters. By choosing the two capacitors on each side of the gyrator so that the resulting circuit is resonant when there is no modulating signal at, say, w1 -w2, a suitable mixing circuit results. The selection of the relevant frequencies is governed by precisely the same set of considerations as for any other mixer. If desired, the simple tuned circuit of the figure can be replaced by a double tuned circuit of the type described in [3].It should be pointed out that the idea presented here for obtaining oscillators is but one among many suitable for integrated circuit techniques. For example, one can use operational amplifiers [9] or bistable circuits [IO]. However, the circuits described here should have the advantage of being easily adjusted and varied as desired.Although lumped oscillators and frequency modulators have been constructed and satisfactorily operated using the philosophy of this letter, continued theoretical and experimental investigations are currently in progress. Abstract-W. R. Crorrther rad C. M e r have f o e d an eBcient linear e n c o d h g f o r v d e r c i m m e k w h i c b w e s t h e H~m a t r i x .~ t i o o o f e x p e c t e d m e r n s q a r u e m w~t o t h e c o a~t h . t t h e H a~ mtrixdi.gop.lizesthecovuipilcematrixoftheloguitbmof16vocoderchmels. 'Ibe reslllting covuinoee matrix has been computed for different choices of characteristic V P I W SRecently, Crowther and Rader' announced a bit reduction scheme for a sixteenchannel vocoder that is similar in some respects to the reduction scheme discussed by Kramer and Mathews2 In the first work,' the logarithms of the outputs of a sixteenchannel vocoder are combined linearly by a Hadamard m a t r i~.~ The resulting linear combinations are quantized into a number of levels that varies with the energy content, the 0th output being quantized into 32 levels and the 15th output into only 2 levels. After quantization of the spectrum, the adjoint transformation (which happens to be the same as the original) is applied to restore speech spectrum channels. The resulting vocoder speech which contains only 1650 bits per second is difficult to distinguish, it is stated, from speech produced with the unadulterated 4OOO bit per second representation.Because of this success it...