1D Convolution

Perform 1D convolution between an input signal and a kernel:

$$\text{C}[i] = \sum_{j=0}^{K-1} \text{A}[i + j] \cdot \text{B}[j]$$

The convolution operation slides the kernel over the input signal, computing the sum of element-wise multiplications at each position. Zero padding is used at the boundaries.

Input:

• Vector $\text{A}$ of size $\text{N}$ (input signal)
• Vector $\text{B}$ of size $\text{K}$ (convolution kernel)

Output:

• Vector $\text{C}$ of size $\text{N}$ (convolved signal)

Notes:

• $\text{K}$ is odd and smaller than $\text{N}$
• Use zero padding at the boundaries where the kernel extends beyond the input signal
• The kernel is centered at each position, with $(K-1)/2$ elements on each side
• This problem is adapted from KernelBench