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Convolution vs mixing

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vishnu36

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Hi

This is the elementary question. Difference between convolution and mixing. . I am looking for the analogies with reference to chemical process. I guess that mixing is eqvt of addition of two signals. But what does convolution mean in terms of real process. Is it multiplication?
 

vishnu36 said:
what does convolution mean in terms of real process. Is it multiplication?
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Think of convolution as the shape of the maximum value of sum of 2 signals in opposite directions over time. It may have no physical analogous ir real world, but you have to keep in mind that mathematical operations in transformed domains are often mere shortcuts to outcome to results in a simpler way.
 

Convolution is basically: the output of a system at time=t is the sum of the system's affect on all (or for causal systems, all previous) inputs.

So if the input is three pulses -- one at t=0, one at t=1, one at t=2, then the output of the system at t=10 seconds is the effect the first pulse has after 10 second plus the effect of the second pulse after 9 seconds plus the effect the third pulse has after 8 seconds.
This is also why the argument to the impulse response has the subtraction.

"mixing" is sometimes used to mean simple multiplication. Although some fields use it to mean addition.
 

Ok, Am I to understand that in mixing like for eg HCL, concentration of individual element (Viz. H and CL) remain intact, whereas in convolution the output is totally different from its input. Secondly why doe we flip input or even response for performing convolution. Also any analytical method to derive the impulse response of the system? ( is it just the derivative of step response?)
 

Not sure in terms of chemistry. Unless you can provide context, I think you are trying to force "convolution" to have a common example in the field of chemistry. Maybe it does? It has more examples in physics/mechanics/electronics/math.

(f*g)(t) = integral_over_tau( f(tau) g(t - tau) dtau)

f(tau) -- this is a function of the variable we are integrating over, not much to see here.
g(t-tau) -- this is a function of t-tau. this is a function of "how far in the past tau is from t". Or equally "how far in the future t is from tau".

thus this is the sum of the function f(tau) weighted by how much an input at tau would affect the output at time t.
 

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