Discrete Time Convolution Calculator

Calculate Discrete Time Convolution



Formula

To calculate the Discrete Time Convolution:

\[ y[n] = \sum_{k} (x[k] \cdot h[n-k]) \]

Where:

What is Discrete Time Convolution?

Discrete Time Convolution is a mathematical operation used in signal processing and control systems to combine two sequences. It produces a third sequence that represents the area under the product of the two original sequences as a function of displacement. This operation is used to calculate the output of a system based on the input and the system's impulse response. It is essential in digital signal processing for implementing filters and other signal processing operations.

Example Calculation

Let's assume the following sequences:

Using the formula:

\[ y[0] = (1 \cdot 0) + (0 \cdot 1) = 0 \]

\[ y[1] = (1 \cdot 1) + (2 \cdot 0) = 1 \]

\[ y[2] = (1 \cdot 0.5) + (2 \cdot 1) + (3 \cdot 0) = 0.5 + 2 = 2.5 \]

\[ y[3] = (2 \cdot 0.5) + (3 \cdot 1) = 1 + 3 = 4 \]

\[ y[4] = (3 \cdot 0.5) = 1.5 \]

The Convolution Result (\(y[n]\)) is [0, 1, 2.5, 4, 1.5].