System Response Computation Using Overlap-Add and Overlap-Save Methods

In this paper, we employ overlap-add and overlap-save methods with a circular convolution length of N=8 to compute system responses. Circular convolution is a fundamental technique in digital signal processing, particularly useful for handling periodic signals and finite-length sequences. For implementation, these methods typically involve partitioning input signals into blocks of length L, with N-L zeros padded for frequency-domain multiplication using FFT algorithms. The overlap-add method computes linear convolution by adding overlapping output sections, while the overlap-save method discards invalid samples from circular convolution results. We process system responses using circular convolution to gain deeper insights into system characteristics and behavior. This study compares both methods' computational efficiency, memory requirements, and numerical accuracy, discussing their respective advantages and limitations. We also provide guidance on optimal application scenarios, such as when to prefer overlap-add for its simplicity versus overlap-save for reduced computational overhead in real-time processing systems. The implementation typically utilizes FFT-based convolution with careful handling of buffer management and overlap regions.