Implement 1D Convolution | Dataford Interview Questions

IBM watsonx.ai preprocessing pipelines may need lightweight signal transformations before model inference. Implement a valid one-dimensional convolution without using numerical libraries.

Given a non-empty numeric signal and a non-empty numeric kernel, return their valid convolution. Valid convolution uses no padding and includes only positions where the entire kernel overlaps the signal. The kernel must be reversed before multiplication, so the result at position i is:

output[i] = sum(signal[i + j] * kernel[m - 1 - j] for j in range(m)), where m = len(kernel).

Formal Specification

Input: signal, a list of integers or floating-point values, and kernel, another such list.
Output: A list of numeric values with length len(signal) - len(kernel) + 1.
Preserve exact arithmetic for integer inputs. Do not mutate either input list.

Constraints

1 <= len(kernel) <= len(signal) <= 10^5
Each value is an integer or floating-point number in the range [-10^6, 10^6]
Inputs are non-empty lists
The input lists must not be mutated

Function Signature

def valid_convolution(signal, kernel):

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