Convolution calculator

Enter value and click on calculate. Result will be displayed.
Enter first data sequence :
Enter second data sequence :
Result:
Data Sequence :

What is a Convolution Calculator?
A convolution calculator is a tool used to compute the convolution of two functions or sequences — a fundamental operation in mathematics, signal processing, and machine learning. Convolution combines two sets of data or functions to produce a third set, representing how one modifies or influences the other.

For discrete signals, the convolution of two sequences x[n] and h[n] is given by:

For continuous functions, convolution is represented as:

Why use a Convolution Calculator?

  • Saves time: Automates lengthy and complex calculations.
  • Reduces errors: Minimizes mistakes in signal processing.
  • Visualizes signals: Helps understand how two signals interact.
  • Essential for applications: Used in filtering, image processing, neural networks, and more.

How does a Convolution Calculator work?

  1. Input sequences or functions: Two sets of numbers (discrete) or mathematical functions (continuous).
  2. Reverse and shift: One sequence (or function) is reversed and shifted.
  3. Multiply and sum: Pairwise multiplication of overlapping values, summed up.
  4. Output the result: A new sequence or function showing the combined effect.

Example (Discrete Convolution):
Given:
x[n] = [1, 2, 3]
h[n] = [0, 1, 0.5]

The convolution y[n] is calculated as:

y[0] = (1)(0) + (2)(1) + (3)(0.5) = 0 + 2 + 1.5 = 3.5

Repeating this for each shift gives the full result.

When is a Convolution Calculator used?

  • Signal processing: Filtering and transforming audio, video, and sensor data.
  • Image processing: Applying filters like edge detection and blurring.
  • Neural networks: Calculating feature maps in convolutional layers.
  • Physics and engineering: Describing systems’ responses to inputs.
  • Probability: Determining the distribution of sums of random variables.