Why do we do convolution?

Why do we do convolution? What is the actual interpretation behind this?

why convolution?

Hi
see
https://mathworld.wolfram.com/Convolution.html
https://en.wikipedia.org/wiki/Convolution
regards

convolution why

Start by studying time-discrete convolution. FIR filters are a good example.

If you have grasped them (check that you understand linear phase FIR filters), you will have less trouble interpreting the time-continuous version.

Convolution is particularly useful for its property that convolution in the time domain is multiplication in the frequency domain, and vice-versa, i.e. convolution in the frequency domain is multiplication in the time domain. This allows us to understand the relation between frequency and transient response better.

why convolution

Suppose you have an LTI system described by it's impulse response h and there's an input signal x. The response of the system to x is y (the output). y is obtained by convoluting x and h.

x----->[system h]---->y

discrete fir convolution example

Idea is very simple if you understand response of FIR systems.
At some interval response will be sum of the effect of impulse from that monment , and effect from previous impulses. And that is just what convolution do.

One impulse with amplitude x(kT) at the input interacts with system and produces output signal which can exist some time intervals (say N), which is defined with impulse response h :
For example N=3:
...............................|
............................ | | |
...|... ->.................| | | | |
t=0 t=0 1 2 3 4
which can be written:
y(0)=x(0)h(0)=2
y(1)= x(0)h(1)=3,
y(2)= x(0)h(2)=1,
...
y(N)=x(0)h(N)=1

From the point of output at time N it is important impulse amplitude and time distance whern impulse appears. If it appears in that time interval it is weighted by h(0), if one interval earlier it is weighted by h(1), ...
What if there were more than one impulse x(0)?. Result will be sum of effect of previous impulses, whic has different time shift.
At time k
x(k) affects with x(k)h(0)
x(k-1) is one interval before and is weighted by h(1)
x(k-2) 2 interwals before and is weighted by h(2)

x(k-N) is N intervals before and is weighted by h(N)
... impulse before N time intervals does not affect - FIR!!!
When you write this as sum you can notice convolution.

why ?? convolution

A graphical example can illustrated by a Signal on CRO and the same Signal on any Specteral Device,Now if u have to multiply this analog signal to another one.

One Cro , multiply all infinite points,in Frequency Domain just multiply those Vertical Sticks and its done.

why convolution is performed

You can read Signal and Systems by Oppenheim

why convolution?

Read DSP by Oppenheim or Modern Analog and Communication Systems by BP Lathi.

why convolution?

Thanks for the explanation pixel.That is what i was asking about.

Re: why convolution?

Hi,

Convolution is a very powerful tool in determining a system's output from knowledge of an arbitrary input and the system's impulse response.

More you can read at: https://cnx.org/content/m11539/latest/

https://www.dspguide.com/ch6/2.htm

Re: why convolution?

to be very very simple...convolution is performed to determin the effect of one signal on another...or u can say when a signal passes through a channel ...the channel gives some responce to it...convolution is done between the input signal and the responcs of the system to get the output....sidra_maheen84@yahoo.com

why convolution?

For LTI systems, we can anticipate the output for arbitary input by using convolution

Re: why convolution?

Convolution is done so that the LTI system's output can be known for a specific input. Generally in DSP convolution is used in applications like filtering etc.