Introduction:
In the overlap-save method of long sequence filtering, the impulse response of the Finite Impulse Response (FIR) filter is extended with zeros before filtering the input sequence. These zeros are appended to the impulse response to ensure that the output sequence has the same length as the input sequence.

Explanation:
The overlap-save method is commonly used for filtering long sequences. It involves dividing the input sequence into smaller blocks, applying the filter to each block, and then combining the filtered blocks to obtain the final output sequence.

To ensure that the output sequence has the same length as the input sequence, the impulse response of the FIR filter is extended by appending zeros to it. The number of zeros appended depends on the length of the input sequence and the length of the filter.

In the overlap-save method, the length of the output sequence is determined by the length of the input sequence and the length of the filter. If the length of the input sequence is N and the length of the filter is M, the length of the output sequence will be N + M - 1.

To obtain the output sequence of length N, M - 1 zeros are appended to the impulse response. This ensures that the output sequence includes the entire filtered response for the input sequence.

Conclusion:
In the overlap-save method of long sequence filtering, M - 1 zeros are appended to the impulse response of the FIR filter to obtain the output sequence of the same length as the input sequence. This ensures that the filtered response for the entire input sequence is included in the output.