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Linear and nonlinear optimization. Linear and Nonlinear Optimization. Linear and nonlinear programming. Thus, according to embodiment in FIG. Delta adder introduces attenuation of 0.

Signal 1 , in FIG. Invention in FIG. After the squaring operation according to the invention in FIG. Time waveforms are shown in FIG. Signal 2 , in FIG. Spectral content is shown in FIG. Embodiment in FIG. The averaging time must be sufficiently long to allow filtering at the lowest frequencies of the operation desired.

## A High-resolution Δ-Modulator ADC with Oversampling and Noise-shaping for IoT

This invention enables three different implementation approaches: 1. The output signal of switching multiplier m t is fed into V ref input of DSM Alternatively, it is also possible to feed back the digital output B of gate 37 , connecting it directly to LPF In this case implementation becomes much simpler, by-passing delta adder 38 , phase shifter 34 and logic gates 36 and 37 of output C.

In this way output B of 37 produces required squaring rectifying operation , output of LPF 39 produces average DC , and switching multiplier produces reference input signal m t. Simulation results in FIG. Its DC output is fed into switching multiplier M to produce reference signal m t.

From FIG. The output of delta modulator X i is first averaged in After averaging 46, the demodulated signal x t is obtained.

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Corresponding waveforms are shown in FIG. Waveform 1 , signal x t , is the amplified analog input x t , signal 2. Waveform 3 is the demodulated DSM sequence X i non-amplified. We can see a good agreement between input 2 and demodulated 3 signals. The invention in FIG. This invention overcomes the attenuation of a cascade of delta adders [1].

Input signals are first DSM converted to produce sequences X n , Y n , and Z n by means of delta sigma modulators 47 , 48 , 49 respectively. Sequences X n and Y n , are added in the delta adder to produce sequence S 1. The last sequence Z n is added to feed-back sequence W n This is done to overcome the cascaded attenuation of two delta adders. In the case of an odd number of adders in the first layer, the second input of the last adder is terminated with idle sequence I 0. Idle sequence I 0 consists of periodic stream of minus one and plus one. After averaging of idle sequence the result is always zero.

It is important to note that every level has only one D-FF for the generation of C n-1 , the carry-out signal. In this example there are two levels of addition. The first level produces C n-1 1 , and the second level produces C n-1 2. The outputs of D-FF 52 and 54 are fed back to delta adders 50 and 53 respectively.

Waveform 1 , in FIG. We can see a good agreement between theory and simulation results. The sum and difference of sequences is processed in delta adders 62 and The delay line is adjusted electronically to achieve maximum correlation.

## Delta-sigma modulation - Wikipedia

This correlator employs only one filter which is a significant savings as compared to classic correlators. In particular, in low frequency applications such as environmental monitoring, seismic, bio-medical applications, control, instrumentation, etc. Furthermore, DSM is low power consuming and dedicated circuits operate directly on a serial pulse stream. Only one wire is needed for internal and external connections and the use of one bit communication lines increases reliability and reduces cost of the system. This is a significant advantage compared to existing 8 or 16 bit DSP hardware.

Hardware and operation of circuitry are very simple and special manuals or software is not needed to operate circuits. Only data sheets with operating conditions and pin-outs are needed.

Eventual debugging is much simpler and faster compared to n-bit DSP hardware. For example, if an error happens at the most significant or sign bit in an ordinary n-bit DSP system, then the system is out of order. This is not the case with a one bit processor because demodulation DAC is performed by a moving average filter.

Thus, it will be appreciated by those skilled in the art that the present invention is not restricted to the particular preferred embodiments described with reference to the drawings, and that variations may be made therein without departing from the scope of the present invention as defined in the appended claims and equivalents thereof. All rights reserved.

- Circuits and Systems Based on Delta Modulation;
- The European Revolutions, 1848-1851!
- Challenges for the 21st Century: Proceedings of the International Conference on Fundamental Sciences: Mathematics and Theoretical Physics, Singapore 13-17 March 2000.