How are difference equations solved in DSP?

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In summary, the speaker is having trouble understanding how difference equations are solved in DSP. They explain that they understand how differential equations are solved in the continuous domain, but they are struggling with solving them in the discrete domain. They ask for advice and provide an example from a video lecture on YouTube. The example represents a Linear Time Invariant Casual (LTIC) system and the speaker is confused about the value of y when n is -1. They ask for clarification and provide a word file with the equation for reference.
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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.
 

Related to How are difference equations solved in DSP?

1. What is a difference equation?

A difference equation is a mathematical equation that describes the relationship between the current value of a variable and its previous values. It is commonly used in fields such as physics, economics, and engineering to model dynamic systems.

2. How is a difference equation different from a differential equation?

A difference equation deals with discrete values, while a differential equation deals with continuous values. In other words, a difference equation describes the change in a variable over a set interval, while a differential equation describes the change in a variable at a specific point in time.

3. What methods are used to solve difference equations?

There are various methods used to solve difference equations, including direct substitution, characteristic equations, and generating functions. The appropriate method to use depends on the complexity and type of the difference equation.

4. Can difference equations be used to model real-world situations?

Yes, difference equations can be used to model real-world situations, such as population growth, interest rates, and chemical reactions. They are useful for predicting the behavior of a system over time.

5. What are some common applications of solving difference equations?

Solving difference equations is used in a wide range of fields, including physics, biology, economics, and engineering. It is commonly used to study and understand dynamic systems and make predictions about their behavior. Some specific applications include predicting stock prices, analyzing population dynamics, and modeling climate change.

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