Convolution is the function which is used to model filters; it is almost the same as correlation, except that one of the signals is mirrored in time before multiplication takes place. Essentially, if the input signal correlates well with the spectrum of the filter impulse response, then the value of the output signal is high; if not, the signal is attenuated.
The length of the impulse response may be thought of as the `echo' or delay effe ct of the filter. For each point in time, the operation of convolution involves the reflection of the signal (the `echo') in the filter window, multiplica tion of the reflected signal with the impulse response, and obtaining the sum of the product sequence for this window. The reason for reflecting the signal can be made intuitively clear.
Assume that the filter has length 
and slopes downward, and that the signal has length 
and is just a sequence of unit pulses of constant amplitude.
Then the first pulse passes through starting at time 
, producing a copy of the impulse response as the output signal.
But point for point, this is added to a copy of the impulse response at for the next pulse, and so on.
This means that in general, the value of the output signal will rise from zero until a stable value is reached when the number of pulses in the signal sequence reaches the number of positions in the pulse response, and will continue at this stable value until the end of the pulse train arrives and the output signal starts to decrease again, and the output signal finally reach zero again at position at time 
. The rise in amplitude at the beginning, and the fall at the end are known as the end effects.The number of values which are relevant for defining the convolution of the two signals is thus 
.
Reflection occurs because the input signal meets the filter response `end to end', like streams of traffic moving in opposite directions, and not, unlike operations such as correlation or Fourier series addition, completely synchronously, like streams of traffic moving in the same direction.
Convolution in the time domain corresponds to multiplication in the frequency domain, i.e. to a cascade of systems performing the Fourier transformation of two signals, multiplication. and inverse Fourier transformation of the product.