The principle of inversion, Sign+ & Sign+ (c)RS
In principle one uses a wave inverter circuit to invert a Waveform,
Such a circuit is called a wave inverter or converter; A diode matrix <>
Maths of a positive integer form allow all positive values, Invert the wave & All Negative.
So what do you propose is the purpose of wave inverting a waveform on an Integer Processor?
All Integer values of Positive Value subtracted + Inversion = Remainder Negative value,
In our case we are using the number to compute the differential in a L - R = Center Value.
Larger number - Smaller number = All values positive, Inversion leaves us with the remainder on the positive & Negative Value Set..
Rather than invert we sign (1 Bit) & therefore can subtract the value from a larger value without using Negative Values in a whole line,
Principally A Sin, Cosine pair are both positive; Or we can invert with a single Bit.
NON-FPU, All Integer & Hence for a codec & Display unit we can use all positive Values in out maths & most objectives involving subtracting waves;
We can displace for 0.0> Values of a sub 0 value such as 0.001
https://science.n-helix.com/2018/01/integer-floats-with-remainder-theory.html
https://science.n-helix.com/2021/02/multi-operation-maths.html
https://science.n-helix.com/2021/03/brain-bit-precision-int32-fp32-int16.html
Useful here:
https://science.n-helix.com/2021/10/he-aacsbc-overlapping-wave-domains.html
https://science.n-helix.com/2021/10/eccd-vr-3datmos-enhanced-codec.html
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Precision & Inversion - Waveform delta, Timing, Scaling, Inversion & reversion in timing circuits & Computation, Audio, Video & Visual Systems (c)RS
Usage cases include : Defining Audio , World beating power grids , Computer Chips, AMP's & PreAMPS & Power chargers & power supply or packages.
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Such is called an inverted 4/3 Analog or digital Wave converter, Where in a Wave of high density is converted into a low frequency; Mostly about timing and precision,
Low to high conversion is mostly about smooth wave modulation and specifically for situations commanding Very precise tight waveforms of Factored precision on lower bit order processors & principally is used for timing clocks;
For example Red Laser light amplitude modulators & timers of the slow & thus high precision simple function with an almost impossible to beat TIME Precision,
Usage cases include : Defining Audio , World beating power grids , Computer Chips, AMP's & PreAMPS & Power chargers & power supply or packages.
"Inverted Driver Geometry (IDG), with the bass/mid driver sited above the treble unit rather than below. This aids time-alignment."
(c)RS
Examples :
Mission(tm) Accomplished A Classic British Speaker Brand : Wireless : https://www.forbes.com/sites/marksparrow/2021/09/30/mission-accomplished-as-classic-british-speaker-brand-goes-wireless/
(Principally, Because hay! in Napoli we like a good price)
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Sub-Banding Audio compression document
https://science.n-helix.com/2021/10/he-aacsbc-overlapping-wave-domains.html
Example use of -+ Signed Data Arrays:
SiMD 16Bit, 2 workflows+ exist:
16Bit positive 16Bit Negative, Use cases:
Antialiasing
Sharpening
Noise subtraction (Image+ -Noise, Quick) ANC
HDR, Low & high field arrays
HDR, High Pass & Low Pass, Light & Shadow (Light)
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Integers in Low frequency band Clean waveform deltoids.
Integer -+ Signed Data Arrays Example banding for lower frequency audio channel sub-banding.
Integer is a good clean vibrant Bing sound,
With clean sounds; Sin waves & Low wave frequency;
A clean FP16b or 16Bit is a good way to go!
If we have plenty of FP16b we can still convert to float, but this way integer has low data rate + high efficiency in CPU & GPU + AVX
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Sub-Band Fractioning Signed : Camera CMOS, Sensor & Codec Example:
Sub-Band Fractioning +- Array Line Input SiMD FastMath
By using sub-banding fractions (For Example SBC Codec)
Small values can be subtracted or added to values & interpolated:
16Bit value, -+ small value & Interpolate
(Interpolate + 32Bit In/Out Cache Memory value storage Array) processor instruction set
Example 16Bit Arrays + 32Bit Array processor instruction set
16Bit Value, -+ Sub-Band of lower or higher frequency + Interpolate in 32Bit,
Merging & Super-Sampling & filtering.
Example 16Bit Operations of -+ Sign Code: CPU, FPU, GPU with Sub-Banding Maths (c)RS
Firstly a - Signed integer does not need to be a - Value if we apply a Table with Value Band:
Variable Table Vectored Database Variable (c)RS
Definition Table: B = Sub-Band (Defined as a value of a valid 16Bit Value; That represents a High or Low bit of a Bit Depth
32Bit Value / 2 = (2 * 16Bit : -+ Signed &or B1 + B2)
or 2 = (2 * 16Bit : -+ Signed &or B1 + B2)
or 3 = ( 3 * 80Bit : -+ Signed &or B1 + B2 + B3)
or 4 = (4 * 16Bit = 64Bit : -+ Signed &or B1 + B2 + B3 + B4)
B0 +- Signed Line in Variable Table 16bit
B1 +- Signed Line in Variable Table 16bit
V1(16Bit) + V2(16Bit) line = V3(32Bit)
V1 & V2 Make 16Bit transfer & Store possible.
V3 can use a 32Bit Store & Math processor or 32Bit SiMD Unit.
This process is called : Value Banding Table : VBT (c)RS
We can obviously use this procedure with all BitDepths: 8Bit, 16Bit, 32Bit, 64Bit, 80Bit, 128Bit, 256Bit <>
Rupert S
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Math operations
Stereo audio (Single process)
Quickly inversion Sin, Cos, Tan Subtraction or addition,
Possible use : Single Array storage of lines of + & - Values
(For cache read (Quick) or storage space)
MP3, AAC, SBC, AptX Audio decompression,
Conversion & Storage or play with, Low Processor processing usage requirements.
Tiny DAC & Audio processor arrays for :
Bluetooth,
WiFi,
Headphones,
Radio DAB+
Clocks; etcetera.
