Why do we often time reverse the impulse response of a signal while performing convolution sum?It can be done even without time reversing the impulse response.

By time reversing the impulse response how does it really helps us,what are the advantages of it?

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    \$\begingroup\$ Wikipedia has an article about this. When you click on this link, it should scroll down to the part of the page where it says, "Theory". \$\endgroup\$ – KingDuken Feb 17 '18 at 2:13
  • \$\begingroup\$ @KingDuken still finding it hard to understand...how does reversal of a signal really helps us? \$\endgroup\$ – Paran Bharali Feb 17 '18 at 7:48
  • \$\begingroup\$ It's a graphical interpretation of the convolution integral, which defines how a system produces a response to an input stimulus. \$\endgroup\$ – Chu Feb 17 '18 at 8:06
  • \$\begingroup\$ This question seems to be a duplicate of Flipping the impulse response in convolution at dsp.stackexchange.com. \$\endgroup\$ – Olli Niemitalo Aug 8 '18 at 12:56

Picture an input signal to an LTI system as being composed of an impulse train, where the individual strengths of the impulses are proportional to the instantaneous values of the signal.

The system responds to each impulse as and when it arrives, so the total system response at any instant of time will be the response to the present impulse plus all the remnants of the responses to the impulses that happened in the past.

The convolution sum is an intuitive graphical interpretation of this physical process.

Perhaps it's more intuitively appealing to time reverse ('fold') the input signal rather than the impulse response. This will produce exactly the same mathematical result, but the visualisation is then of the signal sliding through the system as time proceeds.


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