## 1 Introduction  
The core of signal acquisition technology is the transformation of analog signals into digital signals. The Nyquist sampling theorem [1, 2] forms the critical basis of modern approaches to signal sampling and processing; it requires that the sampling frequency is greater or equal to twice the highest frequency of the effective signal, thus avoiding aliasing. In this way, the sampled signal can contain the information of the original signal and can be restored without distortion. In practical applications, the sampling frequency is usually 5-10 times the highest frequency of the signal. As signal frequency and bandwidth increase in modern technology (up to MHz rates for some sonars), the Nyquist sampling rate also increases linearly. This makes the amount of data increase dramatically. Not only does this bring difficulties to the acquisition system, but for signals with underlying repeatability, it also generates a large amount of redundant data, which increases the cost of signal transmission, storage, and processing.  
Compressive sensing (also called compressive sampling) [3, 4, 5, 6] differs from Nyquist sampling in that it combines the compression and sampling stages. It utilizes the characteristics of sparse representation of signals on a set of bases and realizes the perception of high-dimensional signals through non-correlated observations of low-dimensional space, low-resolution, and under-Nyquist sampled data to reconstruct the original signal by combining optimization methods. The compressive sensing method directly converts the samples from a continuous time signal while discarding redundant information in the Nyquist sampling. Then optimization is used to process the compressed samples.  
How to achieve the sampling of information using compressive sensing theory is a critical issue that needs a solution at present. Many studies have been carried out on this issue, such as: the observation matrix construction [7; 8; 9], analog broadband signal sampling [10; 11; 12], radar signal compression [13; 14], image compression technology [15; 16; 17; 18], and ultrasound transducer fields [19]. Some researchers [20; 21; 22] designed ultra-high-speed analog-to-digital converters, but their high level of complexity makes them difficult to implement in practice. Some researchers [11; 23] used an AIC (analog-to-information converter) structure to realize random observations. The main problem is that the clock frequency of the random symbol function is greater than the Nyquist sampling rate, which increases the difficulty of frequency mixing. The sampling method of AIC structure is quite different from the traditional sampling method; there is no compatibility between the AIC structure circuit and a traditional sampling circuit. Therefore, there is an urgent need for a compressive sensing acquisition method that is convenient for physical implementation.  
In this article, we first present the direct under-sampling compressive sensing (DUS-CS) method, summarizing the key points of the theory and how they can be implemented in hardware (Section 2). Next, we apply DUS-CS to simulated high-resolution data and compare different compression ratios (Section 3). The hardware designed for under-sampling and compressive sensing is presented in Section 4, and its application is presented in Section 5. The advantages and limits of this approach are summarized in Section 6.