Finding Impulse Response of Difference Equation

In summary, the conversation revolves around understanding the concept of convolution for discrete equations. The person seeking help has not shown any effort in their work, making it difficult for others to assist them. They are also unsure of the notation used for convolution (Y(n) or Y(z)). Several resources have been shared to aid in understanding, and the suggestion to try using Excel and different transforms is given.
  • #1
Nickpga
22
2
Poster has been reminded to show their work on schoolwork problems
Homework Statement
Part of a lab, but basically I need to find the impulse response from this difference equation

y[n] = x[n] + 0.7x[n - 64]
Relevant Equations
y(n) = x(n) convoluted with h(n)
Y(n)/X(n) = H(n)
And really that's all I know how to do myself. If someone can explain/lead me through this, that will be very helpful. Thanks
 
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  • #2
No, you really have shown no work, so we can't "lead" you through it. As you know, you are required to show some effort here before we can offer tutorial help on schoolwork.

What is the definition of convolution for discrete equations? Have you tried doing this in Excel at least, to see what the impulse response looks like?

http://www.astro.rug.nl/~vdhulst/SignalProcessing/Hoorcolleges/college03.pdf
 
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  • #4
Do they write it as Y(n)? I thought they might use Y(z) instead. Is it possible to write x[n-64] in a way that might be helpful for you to start with and are there any transforms you can try with your equation?
 

FAQ: Finding Impulse Response of Difference Equation

What is impulse response in the context of difference equations?

Impulse response in the context of difference equations refers to the output of a system when an impulse (a sudden and short-lived input) is applied to it. It is a mathematical representation of how the system responds to a sudden change or disturbance.

How is impulse response related to the transfer function of a system?

Impulse response is the inverse Fourier transform of the transfer function of a system. This means that by finding the impulse response, we can determine the transfer function and vice versa. The transfer function is a mathematical representation of the relationship between the input and output of a system.

Why is it important to find the impulse response of a difference equation?

Finding the impulse response of a difference equation is important because it allows us to analyze the behavior and stability of a system. It also helps us understand how the system responds to different inputs and how it can be controlled or manipulated.

What methods can be used to find the impulse response of a difference equation?

There are several methods that can be used to find the impulse response of a difference equation, including the direct method, the recursive method, and the z-transform method. The choice of method depends on the complexity of the difference equation and the desired level of accuracy.

How can the impulse response of a difference equation be applied in real-world scenarios?

The impulse response of a difference equation has various applications in fields such as signal processing, control systems, and communication systems. It can be used to design filters, predict the behavior of a system, and improve the performance of a system by adjusting its parameters.

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