Signal Theory Solver

Convolution Calculator

Compute linear convolutions ($y[n] = x[n] * h[n]$) of finite digital sequences instantly.

Enter Sequences

Output Sequence y[n]

[1, 1, -1, -1]

Discrete Sliding Window Multiplication:

y[0] = 1 × 1 = 1 y[1] = 1 × -1 + 2 × 1 = 1 y[2] = 2 × -1 + 1 × 1 = -1 y[3] = 1 × -1 = -1

What is the Convolution Calculator?

The Convolution Calculator is an advanced mathematical tool used primarily in electrical engineering, digital signal processing, and computer vision. It computes the discrete convolution of two sequences, determining how the shape of one signal is modified by another.

How It Works (Formula)

Discrete convolution involves flipping one of the sequences, shifting it iteratively across the other, and multiplying the overlapping values. The sum of these products at each shift position forms the final convoluted output sequence.

$$ (f * g)[n] = \sum_{m=-\infty}^{\infty} f[m] g[n-m] $$

The mathematical definition of a discrete 1D convolution.

How to Use It

Enter the data points for your first discrete sequence (x[n]) separated by commas. Enter the data points for your second sequence or impulse response (h[n]). The calculator will process the arrays and output the full convoluted signal sequence.