# Unit-Pulse Response for Discrete Time System

• hoser1000
In summary, the question is asking to compute the unit-impulse response h[n] for n=0,1,2,3 for the given discrete-time system. The equation can be rewritten as y[n]=2delta[n]-y[n+1]. By definition, the impulse response is the zero state response when the input is an impulse, so y[0] = 0. By substituting x[n] with the impulse function and solving iteratively, the values for y[1], y[2], and y[3] can be obtained. The same reasoning applies to a similar equation with more terms, and the z-transform method can also be used.
hoser1000
The question is: Compute the unit-impulse response h[n] for n=0,1,2,3 for each of the following discrete-time systems.

Equation:
y[n+1] + y[n] = 2x[n]

I am trying to figure out how to solve this equation. I understand the example in the book but I don't understand what to do when it calls a future value (n+1)

I rewrote the equation as:
y[n]=2delta[n]-y[n+1]

When n=0 delta[n] is 1 so:
y[0]=2*1-y[1]<-----This is where I am getting confused. Doesn't y[1] refer to my answer when I use the value n=1? How can I get a solution if each equation will refer to the next future equation? The example in the book uses y[n-1] so for each value of n it refers to the previous answer for y[n].

Any help would be much appreciated!

hoser1000 said:
The question is: Compute the unit-impulse response h[n] for n=0,1,2,3 for each of the following discrete-time systems.

Equation:
y[n+1] + y[n] = 2x[n]

I am trying to figure out how to solve this equation. I understand the example in the book but I don't understand what to do when it calls a future value (n+1)

I rewrote the equation as:
y[n]=2delta[n]-y[n+1]

When n=0 delta[n] is 1 so:
y[0]=2*1-y[1]<-----This is where I am getting confused. Doesn't y[1] refer to my answer when I use the value n=1? How can I get a solution if each equation will refer to the next future equation? The example in the book uses y[n-1] so for each value of n it refers to the previous answer for y[n].

Any help would be much appreciated!

It is exactly the contrary of what you did. You should write y[n+1] as a function of y[n] and x[n].
By definition, the impulse response of a system is the zero state response of that system when the input is an impulse, so you have y[0] = 0.
Now substitute x[n] by the impulse function and solve iteratively for y[1], y[2], y[3].

Why don't you use Z transforms. That'll provide you with some more insight.

Hey,

Does this same reasoning apply if the equation is:

y[n+2] + y[n+1] + y[n] = x[n+1] - x[n]

if so, i too am lost.

is there another way to describe it?
or could you just go through it step by step

draakon said:
Hey,

Does this same reasoning apply if the equation is:

y[n+2] + y[n+1] + y[n] = x[n+1] - x[n]

if so, i too am lost.

is there another way to describe it?
or could you just go through it step by step

x[n] = x[-1] = 0
x[n+1] = x[0] = 1
x[n+2] = x[n+3] = ... = 0
y[n] = y[-1] = 0
y[n+1] = y[0] = 0
...
Or, as unplebeian suggested, use the z-transform

## 1. What is a Unit-Pulse Response for a Discrete Time System?

A Unit-Pulse Response for a Discrete Time System is the output of a system when a unit pulse (a single impulse) is applied as the input. It is a representation of the system's behavior and characteristics.

## 2. How is a Unit-Pulse Response for a Discrete Time System calculated?

The Unit-Pulse Response for a Discrete Time System is calculated by taking the inverse discrete Fourier transform of the frequency response function or by using the convolution sum formula.

## 3. What information can be obtained from the Unit-Pulse Response for a Discrete Time System?

The Unit-Pulse Response for a Discrete Time System can provide information about the stability, causality, and time-domain behavior of the system. It can also be used to determine the system's transfer function, which describes the relationship between the input and output signals.

## 4. How does the Unit-Pulse Response change for different types of systems?

The Unit-Pulse Response can vary depending on the type of system. For example, a stable system will have a bounded and decaying response, while an unstable system will have an unbounded and growing response. Additionally, different types of systems, such as linear and non-linear systems, will have different types of responses.

## 5. Why is the Unit-Pulse Response for a Discrete Time System important in system analysis?

The Unit-Pulse Response for a Discrete Time System is important in system analysis because it provides a way to understand and analyze the behavior of a system. It allows us to predict the output of a system for any given input signal, which is crucial in designing and optimizing systems for specific applications.

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