Convolution between two vectors. Length and normalization

1. What is normalized convolution?
2. How do you find the convolution of two sequences?
3. What is the difference between linear convolution and circular convolution?

What is normalized convolution?

The idea of normalized convolution is that of associating to each signal a certainty component expressing the level of confidence in the reliability of each measure of a signal. In the case of missing samples the certainty associated with them is equal to zero.

How do you find the convolution of two sequences?

The convolution of two finite sequences is defined by extending the sequences to finitely supported functions on the set of integers. When the sequences are the coefficients of two polynomials, then the coefficients of the ordinary product of the two polynomials are the convolution of the original two sequences.

What is the difference between linear convolution and circular convolution?

Linear convolution is the basic operation to calculate the output for any linear time invariant system given its input and its impulse response. Circular convolution is the same thing but considering that the support of the signal is periodic (as in a circle, hence the name).