A pulse train can be delayed by a finite number of clock periods by using a serial in-serial out shift register.

Explanation:
A shift register is a digital circuit that is used to store and transfer data in a sequential manner. It consists of a chain of flip-flops connected in series, with the output of one flip-flop connected to the input of the next flip-flop. The input to the shift register is applied to the first flip-flop, and the output is taken from the last flip-flop.

Serial In-Serial Out Shift Register:
A serial in-serial out shift register is a type of shift register where data is entered one bit at a time in a serial manner and is shifted out in the same order. It has a single input line and a single output line. The input data is shifted through the register on each clock cycle.

Delaying a Pulse Train:
To delay a pulse train, we need to shift the pulses by a certain number of clock periods. This can be achieved using a serial in-serial out shift register by following these steps:

1. Connect the pulse train to the input of the shift register.
2. Set the number of clock periods to delay the pulse train. This can be done by controlling the number of flip-flops in the shift register.
3. Apply clock pulses to the shift register. Each clock pulse will cause the data to be shifted by one position in the register.
4. The delayed pulse train can be obtained at the output of the shift register.

Advantages of Serial In-Serial Out Shift Register:
- It is a simple and cost-effective solution for delaying a pulse train.
- It requires fewer components compared to other types of shift registers.
- It can be easily cascaded to achieve larger delay times.

Limitations of Serial In-Serial Out Shift Register:
- The delay introduced by the shift register is limited by the number of clock periods it can delay. If a larger delay is required, multiple shift registers may need to be cascaded.
- The delay is dependent on the clock frequency. Higher clock frequencies may result in smaller delay times.

In conclusion, a pulse train can be delayed by a finite number of clock periods using a serial in-serial out shift register. This type of shift register allows the input data to be shifted through the register in a serial manner, providing a simple and cost-effective solution for delaying the pulse train.