Loading
/custom-emojis/emojis/contour-map.png
Templates
📚
Articles & Resources
📖
Guides & Support
🌵
CalcTree
Bust Common Myths About Java Programming
Loading
/custom-emojis/emojis/calculator.png
Tensile Strength and Capacity Control of the W-Shape Sections According to AISC 360-16
Loading
/custom-emojis/emojis/calculator.png
Concrete Cylinder Strength Vs Cube Strength
Loading
/custom-emojis/emojis/calculator.png
Earthquake Design Action Calculation
EM Wave Propagation Calculator
İKSA YAPILARI PROJELENDİRME HİZMET BEDELİ (2024)
section properties with units
GEOTEKNİK RAPOR (EK-B) ASGARİ HİZMET BEDELİ (2024)
Forward Kinematics of Robotic Arm with 6 Degrees of Freedom
ZEMİN İYİLEŞTİRME/DERİN TEMEL PROJELENDİRME ASGARİ HİZMET BEDELİ (2024)
İKSA YAPILARI PROJELENDİRME HİZMET BEDELİ (2023)
Loading
/custom-emojis/emojis/bending-moment.png
Dezi et. al (2010)
🤾
Projectile motion
Sitemap
Convolution Calculator's banner
/custom-emojis/emojis/calculator.png

Convolution Calculator

This calculator computes the outcome of convolving two sets of data sequences. You can input up to 9 data terms for each sequence, and the resulting convoluted sequence will be outputted.

Calculation

Input

First Data Sequence:


a1
:1.00​



a2
:2.00​



a3
:3.00​



a4
:4.00​



a5
:5.00​



a6
:0.00​



a7
:7.00​



a8
:8.00​



a9
:2.00​

Second Data Sequence:


b1
:1.00​



b2
:2.00​



b3
:3.00​



b4
:4.00​



b5
:5.00​



b6
:6.00​



b7
:7.00​



b8
:8.00​



b9
:3.00​

Where:
  1. 
    
    are the variables/data input for the first data sequence
  2. 
    
    are the variables/data inputs for the second data sequence
  3. The output is the resulting sequence from the convolution of the two data sequences

Output

Sequence_1 
1
2
3
4
5
6
7
8
Sequence_2 
1
2
3
4
5
6
7
8
Convolution_results 
1
4
10
20
35
50
72
102
123
134
134
122
97
112
64


Explanation

Convolution is a widely used mathematical concept with applications in pure mathematics, such as probability theory and differential equations, as well as practical applications in acoustics, geophysics, signal processing, and computer vision. In signal processing, the impulse response of a linear time-invariant system (like an amplifier) can be used to predict the system's output for any input using convolution.
Let's take a look at convolution in detail. First, we can consider two sequences represented like:

a=[a]n=0∞a=[a]_{n=0}^{\infty}

b=[b]n=0∞b=[b]_{n=0}^{\infty}
👉Note, the use of

here means that their lengths can be arbitrarily long.
We define the convolution of sequence

and

as the sequence

, represented by:

c=[c]n=0∞c=[c]_{n=0}^{\infty}

where:

cn=∑k=0nakbn−kc_n=\sum_{k=0}^{n}a_kb_{n-k}
The term

can be calculated by computing the products of terms whose indices sum up to

. Compute the products

,

, etc up to

.
👉Note, the indices change simultaneously, i.e. the first increases while the second decreases.
Add the terms above to get

. The first few terms are:
  1. 
    
    
  2. 
    
    
  3. 
    
    
  4. 
    
    

Example

We will compute the convolution of two data sets,

and

, using the formula above to find the cn terms.
  1. 
    
    
    
    
  2. 
    
    
  3. 
    
    
  4. 
    
    
  5. 
    
    
Therefore, the convoluted sequence from the two data sets will be

.

Related Resources

  1. 🔗 Prime Number Checker
  2. 🔗 Poisson Distribution Calculator
  3. 🔗 Polar-Cartesian Coordinate Calculator