Explanation:
In the context of signal processing and the Fast Fourier Transform (FFT) algorithm, decimation-in-time (DIT) refers to a specific approach for splitting a time-domain sequence into two smaller sequences. The given statement states that if we split an N-point data sequence into two N/2-point data sequences f1(n) and f2(n), where f1(n) corresponds to the even-numbered samples of x(n) and f2(n) corresponds to the odd-numbered samples, then this is known as the decimation-in-time algorithm.

Decimation-in-Time Algorithm:
The decimation-in-time algorithm is one of the most common approaches for implementing the FFT. It involves recursively splitting the time-domain sequence into smaller subsequences, performing the FFT on these smaller subsequences, and then combining the results to obtain the final frequency-domain representation of the signal.

Splitting the Data Sequence:
In the decimation-in-time algorithm, the data sequence is split into two smaller sequences by separating the even and odd samples. This splitting process is performed recursively until the sequences become single-point sequences, which are trivial cases. The splitting can be visualized as follows:

1. Start with the original N-point data sequence, x(n).
2. Separate the even and odd samples of x(n) into two sequences, f1(n) and f2(n).
3. Apply the decimation-in-time algorithm recursively to f1(n) and f2(n) until they become single-point sequences.

FFT Implementation:
Once the data sequence has been split into two subsequences, the decimation-in-time algorithm applies the FFT to each subsequence separately. The resulting frequency-domain representations are then combined to obtain the final frequency-domain representation of the original sequence.

The decimation-in-time algorithm has several advantages, including simplicity, efficient memory usage, and the ability to exploit symmetry properties of the FFT. It is widely used in various applications, including audio processing, image processing, and telecommunications.

Conclusion:
In summary, the given statement is true. If we split an N-point data sequence into two N/2-point data sequences corresponding to the even and odd samples, then this is known as the decimation-in-time algorithm. This algorithm is commonly used for implementing the FFT and involves recursively splitting the data sequence, applying the FFT to the subsequences, and combining the results to obtain the frequency-domain representation of the original sequence.