Description |
Overlap Save Method
In this method, the size of the input data blocks is N=L+M-1 and the DFTs and the IDFTs are of length L. Each Data Block consists of the last M-1 data points of the previous block followed by L new data points to form a data sequence of length N=L+M-1.An N point DFT is computed for each data block. The impulse response of the FIR filter is increased in length by appending L-1 zeros and an N-point DFT of the sequence is computed once and stored. The multiplication of the N-point DFTs for the mth block of data yields: Ym(k)=h(k)Xm(k).
Since the data record is of length N, the first M-1 points of Ym(n)are corrupted by aliasing and must be discarded. The last L points of Ym(n) are exactly the same as the result from linear convolution. To avoid loss of data due to aliasing, the last M-1 points of each data record are saved and these points become the first M-1 data points of the subsequent record. To begin the processing, the first M-1 point of the first record is set to zero. The resulting data sequence from the IDFT are given where the first M-1 points are discarded due to aliasing and the remaining L points constitute the desired result from the linear convolution. This segmentation of the input data and the fitting of the output data blocks together form the output sequence.
Note: The following method uses the block convolution algorithm to compute the convolution. |