Study on Quantum Complement Floating Point Representation and Operations of Digital Signals

‍ ‍A novel one-dimensional finite-length quantum digital signal representation model， Complement Floating-point Representation of Digital Signals （CFRDS）， based on two’s complement floating-point representation is proposed in this paper to enhance the flexibility of quantum digital signal representation. The model uses two sets of qubit sequences to represent position information and amplitude information independently. Position information is represented using signed fixed-point integers in two’s complement form， ensuring the accuracy of signal positions and the ability to handle negative values. Amplitude information is represented using floating-point numbers， with both the exponent and mantissa in two’s complement form， enabling the model to flexibly handle signals of varying amplitudes while maintaining high precision under extreme numerical conditions. This representation method also simplifies mathematical operations， enabling the processing of a broader range of signal types. The model greatly improves the range and precision of signal amplitude representation and demonstrates superior convenience in mathematical operations， making various signal processing algorithms more efficient and reliable. This enhancement makes the model suitable for more complex signal processing tasks， improving the overall signal processing efficiency. This paper presents the CFRDS model and designs the quantum preparation circuits and basic quantum digital signal operation circuits based on this model. These include sequence addition， sequence multiplication， and autocorrelation function sequence operations of two quantum digital signals. The complexity of these circuits is analyzed in depth， and the feasibility and effectiveness of the proposed scheme are validated in computer simulations.