Convolution Calculator

Signal 1 (x[n])

Signal 2 (h[n])

Input Signals
Convolution Result

Convolution Result:

Understanding Convolution

Basic Definition

(x * h)[n] = Σ x[k]h[n-k]

where * denotes convolution

Time Domain

Integration of product of signals

Frequency Domain

Multiplication of Fourier transforms

Properties

Commutative, associative, distributive

Applications

Signal Processing

  • Digital Filtering
  • Image Processing
  • Audio Effects

System Analysis

  • Linear Time-Invariant Systems
  • Impulse Response
  • Transfer Functions

Probability Theory

  • PDF of Sum of Variables
  • Statistical Analysis
  • Risk Assessment

Advanced Topics

Fast Convolution

Using FFT for efficient computation

2D Convolution

Image filtering and feature detection

Deconvolution

Inverse problem and applications