1. What is Linear Convolution?

Linear convolution is a mathematical operation that combines two sequences to produce a third sequence. It's fundamental in signal processing and system analysis, representing how a linear time-invariant system responds to an input signal.

2. How Does the Calculator Work?

The calculator uses the linear convolution formula:

Where:

• \( f[k] \) — First input sequence
• \( g[k] \) — Second input sequence
• \( y[n] \) — Output convolved sequence
• \( n \) — Index of the output sequence
• \( k \) — Index of summation

Explanation: For each output index n, the calculator sums the products of overlapping samples from the two sequences.

3. Importance of Linear Convolution

Details: Linear convolution is essential for digital signal processing, including filtering, system analysis, and image processing. It helps understand how systems modify signals.

4. Using the Calculator

Tips: Enter two sequences as comma-separated values (e.g., "1, 2, 3"). The calculator will compute their linear convolution and display the result.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between linear and circular convolution?
A: Linear convolution is used for aperiodic signals, while circular convolution is for periodic signals and uses modulo indexing.

Q2: How is convolution related to multiplication?
A: Convolution in time domain is equivalent to multiplication in frequency domain (Convolution Theorem).

Q3: What determines the length of the output sequence?
A: For sequences of length M and N, the convolution result has length M+N-1.

Q4: Can I use this for image processing?
A: Yes, 2D convolution is used in image processing, which is an extension of this concept.

Q5: How does convolution relate to impulse response?
A: The convolution of an input signal with a system's impulse response gives the system's output.