Filtering with the Discrete Fourier Transform

The discrete Fourier transform is often used to implement linear time-invariant filters in a computationally efficient manner. This is due to the availability of computationally efficient or fast algorithms for computing the discrete Fourier transform. You will learn about the overlap and add method for computing convolution in this lesson. Overlap and add exploits the efficient computation of the discrete Fourier transform to efficiently compute the output of a filter with finite duration impulse response and long or possibly infinite duration input signal. This and similar methods are often employed in applications with relatively limited computational resources.