## 1 Introduction  
The technology used for spectral analysis has evolved over many years, and has many applications in various regions. The early classical heterodyne spectrometer relies on the sweep frequency and narrow-band filtering [1]. By mixing the input signals with the known swept-frequency signal and then detecting the output of the narrow-band filters, the spectral information of the input signal can be measured. However the frequency resolution of the classical heterodyne spectrometer corresponds to the band-pass width of the narrow-band filter, which is usually difficult to improve. Also, the use of the sweep frequency technology limits its application in real-time signal processing when dealing with wideband signals. Another high-speed digital spectrometer is the Fast Fourier Transform (FFT) spectrometer, which has been investigated and applied widely in recent years [2; 3; 4]. Based on the theory of discrete Fast Fourier Transform, the FFT spectrometer can realize spectrum measurements with extremely high-resolution and high real-time performance. Usually, the power consumption of the FFT spectrometer increases rapidly with the increase of the frequency resolution and measured bandwidth. Also, using the FFT algorithm for high-speed digital signal processing in Field Programmable Gate Arrays (FPGs) may introduce instability when applied to onboard systems. Based on the technology of pulse compression, the chirp transform spectrometer was first proposed in the 1960s for high-resolution and real-time spectral analyses. Due to its advantages of low power consumption and high stability, CTS has been widely applied to onboard systems for radiation measurements. The technology of pulse compression was first developed in radar systems to resolve the conflict between detection capability and range resolution [5]. This technology was then extended by [PERSON] to include spectral analysis [6]. Afterwards, the demodulation of wideband, low-power FM signals based on pulse compression technology was realized by [PERSON] [7], and today, [PERSON]'s system is known as the chirp transform spectrometer system. In recent years, CTS systems have been developed for atmospheric sounding [8; 9; 10; 11; 12]. Some new, single-channel structures have also recently been developed [13; 14], which may have potential applications in the aerospace field. As a new passive detection method, the CTS backend has developed into a mature tool which is widely used in weather and astronomical observations. The frequency resolution of CTS system depends on the time-bandwidth product of the compressor, which means that larger time-bandwidths of surface acoustic wave (SAW) filters correspond to higher frequency resolution [15; 16]. In practice, the design and manufacture of SAW filters having large time-bandwidth products is challenging and extremely expensive. Meanwhile, the large bandwidth of SAW filters introduces large insertion loss, which influence the dynamic range and sensitivity of the system. The nonideal quadratic dispersion characteristic of SAW filters during the manufacturing process also degrades the frequency resolution. In CTS systems, the classical pull-push structure has two channels. Achieving a precise dispersion characteristic match between different SAW filters remains challenging. In general, even though the SAW filter has the advantage of lower power consumption, it inevitably comes with many problems. In modern radar systems, the SAW filter is generally replaced with the digital pulse compression method [17; 18]. However, the classical digital convolution algorithm in the time domain is only suitable for the pulse compression of narrow-band signals. Significant computation and hardware resources are required when dealing with large bandwidth compression. For large bandwidth compression, digital multiplication in the frequency domain is usually used.