Enter the first input sequence and the second input sequence, shifted by k units, into the calculator to determine the output sequence.

Discrete Time Convolution Formula

The following formula is used to calculate the discrete time convolution of two sequences.

y[n] = Σ (x[k] * h[n-k])


  • y[n] is the output sequence x[k] is the first input sequence h[n-k] is the second input sequence, shifted by k units The summation Σ is over all k

To calculate the discrete time convolution, for each value of n, multiply each element x[k] of the first sequence by the corresponding element h[n-k] of the second sequence, shifted by k units. Then sum all these products to get the value y[n] of the output sequence at that point. Repeat this process for all values of n.

What is a Discrete Time Convolution?

Discrete Time Convolution is a mathematical operation used primarily in signal processing and control systems. It is a method to combine two sequences to produce a third sequence, representing the area under the product of the two original sequences as a function of displacement. In simpler terms, it provides a way to calculate the output of a system based on the input and the system's impulse response. It is a fundamental tool in digital signal processing, used to implement filters and other signal processing operations.

How to Calculate Discrete Time Convolution?

The following steps outline how to calculate the Discrete Time Convolution using the given formula:

  1. First, determine the values of the input sequences, x[k] and h[n-k].
  2. Next, calculate the product of each corresponding pair of values from x[k] and h[n-k].
  3. Then, sum up all the products obtained in the previous step.
  4. Finally, assign the resulting sum to the corresponding value of the output sequence, y[n].

Example Problem:

Use the following variables as an example problem to test your knowledge:

x[k] = [2, 3, 1]

h[n-k] = [1, 0, -1]

Find the value of y[n] for a specific value of n.