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