How are difference equations solved in DSP?

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SUMMARY

This discussion focuses on the resolution of difference equations in Digital Signal Processing (DSP), specifically within the context of Linear Time Invariant Casual (LTIC) systems. The user expresses confusion regarding the application of general solutions, akin to those used for differential equations, to difference equations. A particular point of contention is the value of the output y when n is -1, which appears contradictory to the expected behavior of LTIC systems. The conversation highlights the necessity of understanding the initial conditions and constants involved in solving these equations.

PREREQUISITES
  • Understanding of Digital Signal Processing (DSP) concepts
  • Familiarity with Linear Time Invariant Casual (LTIC) systems
  • Knowledge of difference equations and their properties
  • Basic grasp of initial conditions in signal processing
NEXT STEPS
  • Study the methods for solving difference equations in DSP
  • Learn about the implications of initial conditions in LTIC systems
  • Explore the relationship between difference equations and differential equations
  • Review video lectures or resources specifically covering LTIC system analysis
USEFUL FOR

This discussion is beneficial for students and professionals in Digital Signal Processing, particularly those seeking to deepen their understanding of difference equations and LTIC systems.

Jag1972
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Hello Folks,
I am having some trouble understanding how difference equations are solved in DSP. I understand how differential equations are solved in the continuous domain using a general solution which is the sum of the complementary function and particular integral. I am solving the difference equation in the same manner. I would very much appreciate your comments and advice on the void I have understanding them. The example is taken from video lectures from youtube. The difference equation is representing a Linear Time Invariant Casual (LTIC) system. Which means that when n is below 0 there are all 0 values. However when solving the equation y is 2 when n is -1 (sample -1). This doesn't make sense or this just what we have to do in order to find out the values of the constants. I would very much appreciate some advice.
I have attached the equation on a word file. Thank you very much in advance.

Jag.
 

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Why don't you understand. It is explained in the text of the PDF file you linked.
 

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