Signal Convolution Calculator

Formula

To calculate the convolution of two discrete signals:

\[ (f * g)[n] = \sum f[k] \cdot g[n - k] \]

Where:

\( (f * g)[n] \) is the convolution result at index \( n \)
\( f[k] \) is the value of the first signal at index \( k \)
\( g[n - k] \) is the value of the second signal at index \( n - k \)

What is Signal Convolution?

Signal convolution is a mathematical operation that combines two signals to form a third signal that represents the amount of overlap between the two as a function of time or spatial position. It is commonly used in signal processing to analyze systems, filter signals, and in many other applications where signals interact.

Example Calculation

Let's assume the following values:

First Signal \( f \) = [1, 2, 3]
Second Signal \( g \) = [0, 1, 0.5]

Step 1: Compute the convolution:

\[ (f * g)[0] = 1 \cdot 0 + 0 \cdot 2 + 0 \cdot 3 = 0 \]

\[ (f * g)[1] = 1 \cdot 1 + 2 \cdot 0 + 0 \cdot 3 = 1 \]

\[ (f * g)[2] = 1 \cdot 0.5 + 2 \cdot 1 + 3 \cdot 0 = 2.5 \]

\[ (f * g)[3] = 2 \cdot 0.5 + 3 \cdot 1 = 4 \]

\[ (f * g)[4] = 3 \cdot 0.5 = 1.5 \]

The Convolution Result is [0, 1, 2.5, 4, 1.5].