Finding the difference equation given the impluse response

[lusher00]

This question is for a DSP class. I hope that I am posting somewhere appropriate.

So given the impulse response:

h[n]=((0.5)^n-(0.25)^n)u[n]

find y[n].

Where do I start? I don't need an answer, just a nudge in the right direction.

 

[CEL]

In order to obtain the output, you need the input waveform and the initial conditions. What are they?

 

[Mene]

I would approach this problem by first understanding the concepts involved. In this case, we are dealing with digital signal processing (DSP) and impulse responses, which are used to describe the output of a system in response to an impulse input.

To find the difference equation, we need to understand the relationship between the impulse response and the output signal. The impulse response represents the output of a system when an impulse input is applied, while the output signal is the response to any input signal.

One approach to finding the difference equation is to use the convolution sum, which states that the output signal is the sum of the input signal convolved with the impulse response. In other words, we can think of the output signal as the weighted sum of the input signal at different time instants, where the weights are given by the impulse response.

So, to find the difference equation, we can start by writing the convolution sum using the given impulse response and input signal. From there, we can manipulate the equation to isolate the output signal on one side and the input signal and impulse response on the other side. This will give us the difference equation in terms of the impulse response and input signal, which we can then use to find y[n].

I hope this helps nudge you in the right direction. It's important to have a strong understanding of the concepts involved in order to solve problems in DSP. Additionally, seeking guidance and clarification from your instructor or peers can also be helpful in understanding and solving this type of problem.