Recurrence Relation for Alpha beta filter

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SUMMARY

The alpha beta filter is defined by the equation Xn = AXn + BXn-1, which is confirmed not to be a recurrence relation. The discussion highlights that the growth of alpha beta filters is polynomial, specifically represented as Xn = C1 (B/(1-A))n. In contrast, the growth rate of exponential smoothing filters is questioned but not fully resolved in the discussion.

PREREQUISITES
  • Understanding of alpha beta filtering techniques
  • Familiarity with polynomial growth concepts
  • Knowledge of exponential smoothing methods
  • Basic grasp of recurrence relations in mathematical contexts
NEXT STEPS
  • Research the mathematical foundations of alpha beta filters
  • Study the properties and applications of exponential smoothing filters
  • Explore the implications of polynomial growth in filtering techniques
  • Investigate the differences between recurrence relations and non-recurrence relations
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Mathematicians, data scientists, and engineers interested in signal processing and filtering techniques will benefit from this discussion.

SpartanG345
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The alpha beta filter equation is given by this

Xni = AXn + BXn-1

Xn-1 is subscript

i want to figure the solution to this recurrence relation, but is it a recurrence relation?

i am wondering weather alpha beta filters grow faster than exponential smoothing filters.- i said it is a 1st order equation

where Xn = C1 (B/1-A)^n so alpha beta filtering grow polynomial
But i am not quite sure to find the grow rate of the exponential filtering equation
 
Last edited:
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sorry this is wrong, the alpha beta filter equation is not a recurrence relation..
 

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