Linear Convolution Using DFT and IDFT


Using simple words it is said that the linear convolution of two sequences can be obtained as the inverse transform of the product of the individual transforms.

Explanation:

  • Take the input signal and impulse response as two separate single-row matrices.
  • Identify the DFT of the input signal.
  • Identify the DFT of the impulse response.
  • Obtain the product of the DFT transforms of input signal and impulse response.
  • The output convoluted sequence can be then obtained by performing inverse DFT to the product.

The step-by-step values for the provided input is shown at the bottom of the page:

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Enter the first sequence :



Enter the second sequence :







x(n) :




h(n) :




y(n) :


x(n) and h(n) :


Multiply the below sequences :


y(n) :