Difference equation vs differential equation

In summary, the conversation is about a person trying to refresh their knowledge from a signals class in preparation for a controls class. They mention that in their controls class, they deal with continuous-time (CT) systems, while in the systems class, they focused on discrete-time (DT) systems. The person's professor derived a frequency response that includes a complex exponential, which is unfamiliar to the person because in their controls class, they never have exponentials in the frequency response. They ask for the CT equivalent of the DT term y(n-1) and wonder why a CT model would have a complex exponential in the solution. Another person responds with an explanation that the complex exponential comes from taking the Fourier transform of the equation y(t) = ay
  • #1
swraman
167
0
Hi,

Im trying to go back and relearn material from a signals class I took to prepare for my controls class.

In the controls class we always deal with CT systems, whereas in the systems class we focused on DT.

My prof derived a frequency response that was H(w) = 1/(1-a*exp(i*w)).

This dint look farmiliar as in my controls class we never have exponentials in the frequency response.

The complex exponential in the Freq response came from y(n) = y(n-1) + x(n), more particularly the y(n-1) part. Now I am guessing the reason this doenst look farmiliar to my controls work is that we always use CT in controls, so there will never be a y(n-1) in our answer. So my question is: What is the CT parallel for the DT term y(n-1)? What makes a CT model have a complex exponential in the solution (aside from actually having y(t) = y(t-1), as y(t-1) doesn't mean the same thing in DT as CT)?

Thanks
 
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  • #2
no one?
 
  • #3
hi
i think that the i.f t is coming from ..
y(t)-ay(t-1)=x(t)
so take f.t
y(w)*(1-aexp-jw)=x(w)
That's it i think where exp comes where no unit step function is found here
any question again if you need ...
 
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What is the difference between a difference equation and a differential equation?

A difference equation is a mathematical equation that describes the relationship between the values of a sequence at different time points. It is discrete in nature, meaning that it operates on a set of distinct values at specific time intervals. On the other hand, a differential equation is a mathematical equation that describes the relationship between the rate of change of a continuous variable and the variable itself. It is continuous in nature, meaning that it operates on a range of values and can be solved for any point within that range.

What are the applications of difference equations and differential equations?

Both difference equations and differential equations have various applications in different fields of science and engineering. Difference equations are commonly used to model discrete systems that evolve over time, such as population growth, stock market fluctuations, and chemical reactions. Differential equations, on the other hand, are used to model continuous systems, such as motion, heat transfer, and fluid dynamics.

Which type of equation is easier to solve?

In general, difference equations are easier to solve compared to differential equations. This is because difference equations involve discrete values and can often be solved using algebraic methods. Differential equations, on the other hand, involve continuous values and often require advanced mathematical techniques, such as calculus, to solve.

Can a differential equation be converted to a difference equation?

It is possible to convert a differential equation to a difference equation, but it may not always be accurate or appropriate. The process of conversion involves discretizing the continuous variable and approximating the derivatives using finite differences. This can result in loss of information and may not accurately represent the original system.

Which type of equation is more commonly used in real-world problems?

The choice between using a difference equation or a differential equation depends on the nature of the problem and the available data. In general, differential equations are more commonly used in real-world problems as they can better model continuous systems. However, difference equations are also widely used, especially in fields such as economics and computer science where discrete systems are more prevalent.

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