Dimension of impulse response

• asmani
In summary, the impulse response and step response of an electric circuit may have different dimensions, but in order for the convolution integral to work, the dimension of the impulse response must be the reciprocal of time.

asmani

Hi all

The impulse response h(t) of an electric circuit (maybe in some special cases) is the derivative of the step response s(t) of the same circuit. right?
So does it mean they have different dimension, namely if the dimension of s(t) is X, then the dimension of h(t)=ds/dt is x over second?

asmani said:
The impulse response h(t) of an electric circuit (maybe in some special cases) is the derivative of the step response s(t) of the same circuit. right?
So does it mean they have different dimension, namely if the dimension of s(t) is X, then the dimension of h(t)=ds/dt is x over second?

okay, let's say that your impulse response is for a device in which the dimension of the output is the same as the dimension of the input. like voltage-in, voltage-out (but it could be current in/out or something else).

then, for the convolution integral to work

$$y(t) = \int_{-\infty}^{+\infty} h(t-u) x(u) du = \int_{-\infty}^{+\infty} h(u) x(t-u) du$$

the dimension for $h(t)$ must cancel the dimension of the $du$ which we normally attach to "time". so the dimension of $h(t)$ is the reciprocal of time.

1. What is the dimension of impulse response?

The dimension of impulse response refers to the number of values or variables present in the response of a system to an impulse input. It is used to describe the characteristics of a system and can vary based on the type of system being studied.

2. How is the dimension of impulse response calculated?

The dimension of impulse response is typically calculated by taking the number of poles (roots of the transfer function) and adding it to the number of zeros (roots of the transfer function). This calculation can be done algebraically or graphically using a pole-zero plot.

3. What factors can affect the dimension of impulse response?

The dimension of impulse response can be affected by various factors such as the complexity of the system, the number of inputs and outputs, and the type of input being applied. Additionally, the presence of noise or disturbances can also impact the dimension of impulse response.

4. Why is the dimension of impulse response important in signal processing?

The dimension of impulse response is important in signal processing because it provides valuable information about the characteristics and behavior of a system. It can be used to analyze and design systems, as well as predict how the system will respond to different input signals.

5. Can the dimension of impulse response change over time?

Yes, the dimension of impulse response can change over time if the system being studied is dynamic or time-varying. In such cases, the dimension of impulse response may vary with different input signals or as the system parameters change.