A New Time-Domain Modulo-Approach to Signal-Processing.

Over the past hundred years the number and variety of signals we deal with? in our daily lives has grown at a mind - boggling rate. During my childhood in India, the only unique thing called? “signal” was the mechanical railroad signal. Today we have a very large number of them with widely different? properties that are hard to enumerate. The word signal-processing was not in our vocabulary.? Now DSP has become a mantra.?

During the early part of the twentieth century, most of the information bearing-signals were for telecommunications, and control-systems used by civilians, military personnel and biomedical signals for health-care.??

Most of the signals we deal with are converted into electrical form. They are mostly displayed to be observed by our audio, video , touch, smell and taste sensors. They vary with time over a wide dynamic range and bandwidth. In our current digital age, the essential first signal-processing? task is to convert them into a “countable digital format”. This is obvious because binary- computers can only handle numbers of a certain size. For example, laptop computers are designed to have? numbers stored and manipulated? at the size of 2 **n bits? Typically n= 32. Thus? the n bit numbers provide a dynamic? range of 2**32. Even if we switch to decimal? floating point arithmetic, there will be an upper limit to the size. The ultimate solutions to meeting our memory needs will come from? new Q- bits instead of the primitive binary bit.? Now we have large-data choking up our world-wide web, and communication highways.

?The universe has a macro-part that is visible.? The micro part? is complex, invisible,? and uncountable.? We are struggling to understand this micro-world by creating models and experimental observations to verify our hypotheses using highly sophisticated computing, communication and instrumentation systems. With the increase in need for high power-efficient systems we have to modify our current? circuit- design practices used for signal-processing. With the new developments in the? meta-material technologies we have more options at all levels namely materials, devices, circuits and system-architectures, including software. Adiabatic computing is a must wherever possible to retard the dreadful climate change that is threatening our survival at this rate of luxury rovided by various technologies.

Taking all these into account we look at nature only to discover that it does everything at optimum efficiency-levels to make our designs look very primitive. However, nature takes its time to do things right, by a process of trial and error-correction. Thus we have evolved over billions of years. Needless to say that we have studied these and continue to do so incessantly. We need to summarize our comprehension, now and then, in a manner that our future generations can understand the underlying ideas clearly.

I have been thinking about analog to digital conversion, sampling, aliasing,? quantization error (or noise), differential and integral nonlinearities and a host of design specifications for a wide range of applications. The way we teach these “Things”? only makes life for the younger generations more difficult. As we discover more and more about the micro-states of matter and energy including their interplay, our vocabulary had to increase. We created new math for modeling, mapping variables onto vector spaces having new properties such as operations on new data structures. This process has been growing to a point of frustration. Sometimes I wonder what is the next language after Python? I must learn? If I do not know it, I am considered illiterate.?

The number of engineers who understand Quantum electrodynamics or Quantum thermodynamics are a handful and they belong to a club. Average people do not understand signal- processing, the macro Universe of black- holes , or Quantum entanglement or collapse of its micro part.

Here is a simple example. If you know how to add and subtract numbers, you can compute the autocorrelation- function of a random variable. You can take its Fourier-Transform to determine the power-density-spectrum of the random process that has entropy logarithmically related to the number of microstates having a characteristic probability distribution that gives rise to a state of matter known as the Bose-Einstein condensate. How would you go about teaching and learning all these?

Similarly, if you can oversample a signal at a rate as high as it can be done with today’s? solid-state technologies, you can easily get to a point of recovering all the information from a time varying signal without the need for antialiasing to get a quantization error < ? LSB, How will you implement the? uncountable to countable-conversion??

Remember that the first- difference in numerical analysis will be as good as using? Newtonian or transform- calculus with limits at zero and infinity. I am an engineer. I do not have any use for zero and infinity. They are two abstract concepts. I always ask: how big is big? Similarly, how small is small? Once something like velocity of light C has an finite large value as its upper-limit, we can take its inverse (1/C). The key question is what is the total dynamic range between C and 1/C? Where is its geometric mean of unity? What is important is to know what is known as normalization in theoretical physics. It? is unity and its relationship? to minimum and maximum (Micro and Macro) is to be understood for? engineering systems.? For example, the idea of an operational amplifier? with infinite-gain was introduced to get a virtual-zero! Later, we introduced the notion of an operational-controlled- oscillator with infinite (kosc) for? phase locking. In other words, once the boundary that separates? the macro and micro worlds is known? the position of the unit circle to get the very best design for a given application will reveal itself. This is what I believe nature does. This is what I call as the new design -approach. If you are interested to get an understanding of why we are moving into the time-domain for running things much faster than nature, let me know. The superiority of our solid-state electronics is due to Silicon having mobile electrons over natures’ Carbon- based liquid-state electronics namely bio-chemistry. It is the speed of electrons vis-à-vis heavier ions.??

To be honest I am not in a hurry to switch to Carbon. We may do it eventually. There is a lot of money and effort invested in silicon. So we will stick with it. Nothing prevents us from porting ideas from liquid state to solid state by substitution.?

First I want to talk about packaging electrons in fixed size packages with different numbers for each application depending upon the resolution needed.? Then we use level-crossing sampling, and over sample to convert signals into countable numbers. Signals are represented as charges on small on- chip capacitors. Our circuits will not have quiescent bias-currents. They are a waste. Thus we? will not have linear resistors either. Instead we will have high- quality small MIM Capacitors to hold charges that can be added and subtracted. The currents in these new circuits will be approximations of delta function type pulses. Voltages will look like tiny steps. A ramp will be a stair- case with invisible steps.? Thus, charging capacitors will be made adiabatic. We will have PN-junctions and short-channel MOS transistors with a gate control which under subthreshold regime, act like BJT’s. Moving charges will be transported in ballistic mode , minimizing random-collisions and energy dissipation.??

In essence, will have lots of translinear current and voltage-mirrors having the exponential v- i and logarithmic i-v conversion elements. In other words.? We can generate a wide variety of functions including hyperbolic functions for analog-like signal-processing until we have reached lower speeds to use current regular DSP with numerical algorithms to compute with added memory elements and software control. This is a? new, modified approach keep most of our current standards. You can also do AI with weighted-sums and threshold level-crossing detection. We fold voltages to gain the amount of needed dynamic range.?

With these ideas I have come up with a Plan to build a converter that can meet the specifications needed for all communication systems of the future. The idea currently is to design? three low-power converters. A 16-bit for audio, 10-bit for video and a very high speed 6- bit converter for data- communications and recording. These will enable us to meet all the requirements up to launching data-streams on optical fibers at 100 GB/sec., Remember: electrons do a better job of computing? and smooth-sailing photons are superior for communication.

I recently realized something interesting. We know that a mass orbiting around a heavy object in a circular orbit in a conservative gravitational field does not dissipate energy. It is defined by x**2 +y**2 = 1. The path of movement is always orthogonal to the radius: the direction of force.?Consider a hyperbolic orbit defined by x**2 -y**2=1. It can be written as?(x+y)(x-y)=1, or? (x-y) = 1/(x+y). That means that terms are inverses of each other. Consider x and y as a pair of differential input variables into an amplifier. Their differential value and common mode value are inversely related if they are in a hyperbolic path. In the Paul Brokaw unity gain-buffer. by making the common mode open-loop gain tending to infinity, the closed loop differential output is zero by closing the negative-feedback loop. The circuit computes the Lagedre transform.

All these point to a simple conclusion. The MANTRAS ought to be learn meta- materials, Q-bits, study topology, EE’s must focus on biochemistry. That will give you ideas about new devices and circuits using Silicon and diamonds?.?