Name: IMPULSE RESPONSE OF A GIVEN SYSTEM
Uploaded: 2022-12-15
Duration: 3 min 14 s
Description: IMPULSE RESPONSE OF A GIVEN SYSTEM. IMPULSE RESPONSE OF A GIVEN SYSTEM.

[Audio] IMPULSE RESPONSE OF A GIVEN SYSTEM. IMPULSE RESPONSE OF A GIVEN SYSTEM. 

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[Audio] In acoustic and audio applications, impulse responses enable the acoustic characteristics of a location, such as a concert hall, to be captured. Various packages are available containing impulse responses from specific locations, ranging from small rooms to large concert halls.. The impulse response is the response of a system to a single pulse of infinitely small duration and unit energy (a Dirac pulse). The frequency response shows how much each frequency is attenuated or amplified by the system. The frequency response of a system is the impulse response transformed to the frequency domain.. 

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Impulse Response of a Given System
Introduction:
In the theory of signal processing and control, a dynamic system's output in reaction to a brief
input signal known as an impulse (t) is known as the impulse response, or impulse response
function (IRF). An impulse response is, more broadly speaking, any dynamic system's response
to an outside change. The impulse response in both situations describes the system's response
as a function of time (or possibly as a function of some other independent variable that
parameterizes the dynamic behavior of the system).
In each of these scenarios, the dynamic system and its impulse response could either be
mathematical systems of equations defining such objects, or they could be real-world physical
objects.
Due to the fact that the impulse function contains all frequencies (see the Dirac Fourier
transform), showing infinite frequency bandwidth that the Dirac delta function has), the impulse
response defines the response of a linear time-invariant system for all frequencies.

[Audio] For both discrete- and continuous-time systems, the impulse response is useful because it allows us to calculate the output of these systems for any input signal; the output is simply the input signal convolved with the impulse response function. 

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Objectives:
The idea of an impulse response is to capture all of that information in one go, so you can
instantly recall that setting. This means that wherever you are, you can retain your preferred
tone, right down to the detail of your favorite mic placement and room sound An impulse is has
amplitude one at time zero and amplitude zero everywhere else. The output of a system in response
to an impulse input is called the impulse response, The impulse response is a very useful way to
describe the characteristics of a large and useful class of systems.

[Audio] Remember that v(t) is implicitly zero for t< 0 (i.e., it is multiplied by a unit step function). Also note that the numerator and denominator of Y(s) are of the same order, so a step of long division is necessary when performing the partial fraction expansion. Remember that v(t) is implicitly zero for t<0 (i.e., it is multiplied by a unit step function). Also note that the numerator and denominator of Y(s) are of the same order, so a step of long division is necessary when performing the partial fraction expansion. Remember that v(t) is implicitly zero for t<0 (i.e., it is multiplied by a unit step function). Also note that the numerator and denominator of Y(s) are of the same order, so a step of long division is necessary when performing the partial fraction expansion.. 

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[Audio] Since we know the response of the system to an impulse and any signal can be decomposed into impulses, all we need to do to find the response of the system to any signal is to decompose the signal into impulses, calculate the system's output for every impulse and add the outputs back together. This is the process known as Convolution. Since we are in Continuous Time, this is the Continuous Time Convolution Integral.. 

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[Audio] This is the code of the unit impulse response , and I use application is scilab. 

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[Audio] This is the graph when the code is running. 

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IMPULSE RESPONSE OF A GIVEN SYSTEM

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In acoustic and audio applications, impulse responses enable the acoustic characteristics of a location, such as a concert hall, to be captured

Various packages are available containing impulse responses from specific locations, ranging from small rooms to large concert halls.

The impulse response is the response of a system to a single pulse of infinitely small duration and unit energy (a Dirac pulse)

The frequency response shows how much each frequency is attenuated or amplified by the system

The frequency response of a system is the impulse response transformed to the frequency domain.

For both discrete- and continuous-time systems, the impulse response is useful because it allows us to calculate the output of these systems for any input signal

the output is simply the input signal convolved with the impulse response function

Remember that v(t) is implicitly zero for t<0 (in other words, it is multiplied by a unit step function).  Also note that the numerator and denominator of Y(s) are of the same order, so a step of long division is necessary when performing the partial fraction expansion.
 
Remember that v(t) is implicitly zero for t<0 (in other words, it is multiplied by a unit step function).  Also note that the numerator and denominator of Y(s) are of the same order, so a step of long division is necessary when performing the partial fraction expansion.
 
Remember that v(t) is implicitly zero for t<0 (in other words, it is multiplied by a unit step function).  Also note that the numerator and denominator of Y(s) are of the same order, so a step of long division is necessary when performing the partial fraction expansion.

Since we know the response of the system to an impulse and any signal can be decomposed into impulses, all we need to do to find the response of the system to any signal is to decompose the signal into impulses, calculate the system's output for every impulse and add the outputs back together

This is the process known as Convolution

Since we are in Continuous Time, this is the Continuous Time Convolution Integral.

This is the code of the unit impulse response , and I use application is scilab

This is the graph when the code is running