In this method the size of the input data block is L points and the size of the DFTs and IDFT is N=L+M-1.

Since the data record 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 as same as the result from linear convolution.

The input sequence has a length N=4 and impulse response has a length M=3. So, the response must have a length of 6(4+3-1).

The impulse 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.

From the figure given, it is clear that the last M-1 points of the first sequence and the first M-1 points of the next sequence are added and nothing is discarded because there is no aliasing in the input sequence. This is same as in the case of Overlap add method.

The four point DFT of h(n) is H(k)=1+2e-jkπ/2+3 e-jkπ (k=0,1,2,3)

In Overlap add method, to each data block we append M-1 zeros at last and compute N point DFT, so that the length of the input sequence is L+M-1=N.

In these two methods, the input sequence is segmented into blocks and each block is processed via DFT and IDFT to produce a block of output data. The output blocks are fitted together to form an overall output sequence which is identical to the sequence obtained if the long block had been processed via time domain convolution. So, Overlap add and Overlap save are the two methods for linear FIR filtering a long sequence on a block-by-block basis using DFT.

In this method, each data block consists of the last M-1 data points of the previous data block followed by L new data points to form a data sequence of length N=L+M-1.

From the figure given, we can notice that each data block consists of the last M-1 data points of the previous data block followed by L new data points to form a data sequence of length N+L+M-1 which is same as in the case of Overlap save method.