Linear convolution of discrete signals with defined lengths

1. How do you find the length of a linear convolution?
2. What is discrete linear convolution?
3. How do you compute linear convolution of two DT sequences?

How do you find the length of a linear convolution?

The linear convolution of an N-point vector, x , and an L-point vector, y , has length N + L - 1. For the circular convolution of x and y to be equivalent, you must pad the vectors with zeros to length at least N + L - 1 before you take the DFT.

What is discrete linear convolution?

The Discrete-Time Convolution (DTC) is one of the most important operations in a discrete-time signal analysis. The operation relates the output sequence y(n) of a linear-time invariant (LTI) system, with the input sequence x(n) and the unit sample sequence h(n), as shown in Fig. 1.

How do you compute linear convolution of two DT sequences?

Pad the two original sequences with zeros to length N. Compute the N-point DFT to obtain H[k] and X[k]. Compute the point-wise product: Y [k] = H[k]X[k] k = 0,... (N − 1).