Confused in difference between calculations of convolution and multiplication?

1. What is the difference between the convolution and multiplication?
2. Why do we use convolution instead of multiplication?
3. What is the relationship between a convolution and a matrix multiplication?
4. What happens when you multiply two signals?

What is the difference between the convolution and multiplication?

d) Convolution is a multiplication of added signals. Explanation: Convolution is defined as weighted superposition of time shifted responses where the whole of the signals is taken into account. But multiplication leads to loss of those signals which are after the limits.

Why do we use convolution instead of multiplication?

Convolution, for discrete-time sequences, is equivalent to polynomial multiplication which is not the same as the term-by-term multiplication. Convolution also requires a lot more calculation: typically N2 multiplications for sequences of length N instead of the N multiplications of the term-by-term multiplication.

What is the relationship between a convolution and a matrix multiplication?

convolutions can be mapped as matrix multiplication operations by flattening and rearranging the weights and input features. As illustrated in Figure 2, 64 × 3 kernels with a size of 3 × 3 are mapped to a rearranged matrix with dimensions of 64 × (3 × 3 × 3).

What happens when you multiply two signals?

Multiplication of signals is exploited in the field of analog communication when performing amplitude modulation (AM). In AM, the message signal is multiplied with the carrier signal so as to obtain a modulated signal.