1. Research Scope in Analysis
and Synthesis of ARMA
Filters as Artificial
Intelligence Blocks
Sandip Ray
February 18, 2013

2. First order ARMA(Auto Regressive
Moving Average) filter
𝐴
y= .x
1+𝐵.𝑧−1

3. A simple ARMA(Auto Regressive
Moving Average) filter
𝑎+𝑏.𝑧−1 +𝑐.𝑧−2 +𝑑.𝑧−3 +𝑒.𝑧−4 +⋯
y= .x
𝑎+𝑏.𝑧−1 +𝑐.𝑧−2 +𝑑.𝑧−3 +𝑒.𝑧−4 +⋯

4. A more complex ARMA filter
𝑏+𝑐.𝑧−1 +𝑑.𝑧−2 +⋯
𝑎+ −1 +⋯ +𝑐.𝑧−2 +𝑑.𝑧−3 +𝑒.𝑧−4 +⋯
𝑑+𝑒.𝑧
𝑏+𝑐.𝑧−1 +
𝑓+𝑔.𝑧−1
𝑑+𝑒.𝑧−1 +
𝑓
y= 𝑐+𝑑.𝑧−1 .x
𝑎+𝑏.𝑧−1 + 𝑑 +𝑑.𝑧−3 +𝑒.𝑧−4 +⋯
𝑐+ 𝑒
𝑑+
𝑓
𝑒+
𝑓+𝑔.𝑧−1

5. Generalized ARMA filter
 Generalized ARMA filter where [.] represents a “tree” of regression and
moving average coefficients. The “tree” is a sparse matrix and can be
implemented by linked list on computer.
([A]+[B]+[C]+[D]+⋯ )
 y = ([A]+[B]+[C]+[D]+⋯ ).x
 (Note. Numerator and denominator “trees”([.]) are different though
shown same because of simplicity in typing.)

6. An example of a “tree”
representing [.] in Generalized
ARMA filter
a b c
a b c d e f g h
a b c d e
d a b c
a b c
a b c d a b c d e f

7. PROPOSAL 1
 “Any human emotion(like sorrow, joy, love, greed, passion,
motivation) can be modeled by ARMA filters of varying
averaging length and regression depth.”

8. PROPOSAL 2
 “3 basic ingredients of human emotions are,
 1) Intelligence, 2) Power and 3) Empathy.
 Depth of Regression in Numerator(Forward Path) =
Intelligence
 Depth of Regression in Denominator(Backward Path) =
Empathy
 Length of Averaging in Numerator and Denominator(Forward
and Backward Path) = Power”


9. CONCLUSION
 Artificial Intelligence Block(AIB) can be designed(or
simulated) by exploiting ARMA filters of various shapes.
This will enable us to create AIBs for machine intelligence
and robotics.

10. QUESTIONS
 Currently Linear Algebra and Vector Calculus deals with
Matrices of various sizes and shapes.
 Is there a scope of research in analysis and synthesis of
differently shaped “Trees” in ARMA filters resulting in
extension of Linear Algebra and Vector Calculus ?

11. Theorem of minimal terms
No Artificial Intelligence Block (AIB) of complexity ‘C’ can be
created with lesser than ‘N’ terms,
where M<N<P

12. Theorem of Conjugate Pairs
Every Artificial Intelligence Block(AIB) has a conjugate pair,
which when combined with original one, creates a stable
conjugate pair.

13. Theorem of Liquidity
Every Artificial Intelligence Block(AIB) has a solidity(static) and
a liquidity(dynamic) component.

14. Variable, Pseudo-variable and
Constant
Variable Pseudo- Constant
variable
Domain Time Time-Space Space
Operator Add, Multiply Add, Multiply, Subtract, Divide
Subtract, Divide
Law Darwinism Darwinism- Newtonian
Newtonian
Topic Biology Biology-Physics Physics
Process Slow Moderate Fast

15. Thank You
Cell : +91-9620204096
Email : sandipray05@yahoo.com
Skype : sandipliketotalk