3 SAW spectrometer

At present, digital auto-correlation and acoustic-optic spectrometers are in common use as spectrum analyzing systems for radio astronomy. The digital auto-correlation spectrometer provides a flexible selection of bandwidths and resolutions and has convenient digital components. However, its practical application for wide bandwidth and high resolution is limited by the micro-electric technique and the processing speed. The alternative acoustic-optical spectrometer also has its own limitations. As an optical system, its stability is susceptible to influence by the environment. Attempts have been made to develop new type of spectral analyzing system with better stability and reliability in structure and with simplicity of design. The SAW CZT-based spectrometer described below may have the desirable characteristics.

3.1 The CZT algorithm

The CZT algorithm for Fourier transform was developed in 1960's. Since then research on the algorithm from theoretical principle to practical application has flourished. Comprehensive discussions can be found in various review articles (Jack et al. 1978; Jack et al. 1980). To understand the structure of the SAW spectrometer in our spectral receiving system, we summarily depict the CZT algorithm blow.

For a spectral analyzing system, a signal $F(\omega)$ in frequency domain may be expressed in terms of a Fourier integral:

$$F(\omega)=\smallint _{-\infty }^{+\infty }f(t){\rm e}^{-j\omega t}{\rm d}t.$$ (1)

Let us now make a equivalent relation $\omega =2\pi \mu \tau$ between frequency $\omega$ and delay $\tau$, where $\mu$ is a chirp slope or a rate of frequency and delay. Using the identity 2t$\tau =t^2+\tau ^2-(t-\tau )^2$, Eq. (1) can be rewritten

$$\begin{eqnarray} F(\omega){=}F(2\pi \mu \tau){=}{\rm e}^{-j\pi \mu \tau ^2}\cdot... ...u t^2}]\cdot\,{\rm e}^{j2\pi \mu (\tau -t)^2}{\rm d}t \nonumber\\ \end{eqnarray}$$

or

$$F(2\pi \mu \tau )=\{[f(\tau )\bullet ch^{-}(\tau )]\otimes ch^{+}(\tau )\}\bullet ch^{-}(\tau )$$ (2)

where $ch\pm$ denote Z factors e$^{\pm j\pi \mu \tau ^2}$ and $\bullet$ and $\otimes$ are multiplication and convolution, respectively.

This transform can be realized by a pre-multiplication (M) of input signal f(t) with a down chirp waveform e$^{-j\pi \mu \tau ^2}$, followed by a convolution (C) with a up chirp signal, and finally multiplied by a down chirp signal (as shown in Fig. 2) (Zhang et al. 1996). The signal processing system is named by the M-C-M configuration of CZT or the SAW chirp filter. The post-multiplication, used to correct the phase of the output, can be omitted when only power spectrum is required and reduced to the M-C structure. The CZT algorithm appears to be a frequency axis replaced by a time axis. The spectral components in an input signal are dispersed into a set of pules with different delay and amplitude corresponding to the frequency and the input power, respectively, when they pass the SAW chirp filter.

 

Figure 2: M-C-M configuration of the CZT. The post-multiplication, used to correct the phase of the output, can be omitted and then reduced to the M-C structure when only power spectrum is interested in

3.2 The structure of the SAW spectrometer

A diagram of the SAW CZT-based spectrometer consisting of three parts (I, II and III) is shown by Fig. 3 (Chen et al. 1990). Pre-amplifiers and mixers constitutes the first stage with two highly stable L.O. (f1 = 710 MHz, f2=690 MHz). The operating frequency and bandwidth of SAW spectrometer are limited by the technology of SAW devices. So input signals are first split into two bands, A and B, 20 MHz each and then they are down-converted to IF 171 MHz. Part II is the SAW CZT processor containing four parallel CZT subsystem (A1, A2, B1 and B2). Each subsystem operates in a bandwidth 20 MHz with 50% working duty cycle and a frequency resolution 39 KHz. The SAW CZT processor, therefore, has a bandwidth of 40 MHz and 100% duty cycle. The equivalent transformation rate is greater 1024 points/66.6 $\mu$s. The dynamical range of SAW CZT processor is determined by the sidelobes of impulse response. Hamming weighting is employed to reduce the sidelobe to 35 dB. Part III is a digital processor to carry out the A/D conversion and digital integration. The longest integration is about 300 ms. The integration time and the beginning of the integration can be controlled by an I/O interface. Table 2 gives the properties of the SAW CZT processor. Performances of the spectrometer, such as bandwidth, frequency resolution, accuracy of frequency, dynamical range, and temperature behavior were carefully examined and these results have been published in relevant articles.

 

Figure 3: The structure of the SAW CZT spectrometer consists of three parts: Part I include mixers, pre-amplifiers and filters to split input signals into two bands and down-convert to IF 171 MHz; Part II is the SAW CZT processor. Part III is a digital processor to carry out the A/D conversion and digital integration

 

Table 2: Properties of the SAW CZT spectrometer