The Design of Nonlinear Chirp Based on the DSP Builder Technique

This paper, by analyzing the function Chirp, studies the software design and realization of the function. It offers a design plan based on the nonlinear Chirp signal of DSP Builder technique and designs the signal generator of the nonlinear Chirp based on the design flow of Matlab/Simulink/DSP Builder/Quartusll. It also conducts simulation verification using the development software Matlab/Simulink and Quartusll, proving that the design can well realize the signal source Chirp. The experiment proves that the DSP Builder technique can modify the starting frequency, bandwidth and the frequency resolution of linear frequency modulation signals by changing the programming parameters. The method is proved to be simple in designing, convenient in modification, low in cost and it doesn’t involve any programming; therefore, it is easy to realize.


Introduction
The non-linear FM pulse signals are the ones whose instantaneous frequencies change with the time, i.e., the sine waves whose instantaneous frequencies change with the time in a range1.They are widely used in such fields as communication, radar, sonar for their wonderful bandwidth efficiency [2]3.The study of the realization of the wireless fuze signals Chirp in FPGA is significant for the research of wireless fuze system4. The test of stress waves based on the theory of chirp signals is widely used in engineer quality nondestructive testing. A large number of experiments have proved that the testing instruments developed on the basis of the study are effective in engineer testing.
Most of the Chirp signal sources commonly used in the current market are designed with the dedicated chips DDS[5]5 [7]. They have wide output frequency and excellent high frequency performance. But they cannot meet the requirements for the fixed signal wave forms, functions and controlling modes produced by the dedicated DDS chips. Therefore, it is desirable to integrate one or several DDS core circuits and the other parts on a FPGA by using a programmable logic device. In this way, programming can be done on the chip and will be highly flexible and reconfigurable.

Chirp mathematical expression
The instantaneous frequencies of Chirp change with the time, i.e., it is a time function. Its math expression is as follows.
In equation 3,  is a constant, 0 f is the initial output frequency, n is a sampling site.
For the non-linear Chirp function, the relationship expression in a continuous time domain is: In equation 4, ( ) f t is nonlinear functions, 0 f is the initial output frequency; t is continuous time。In discrete time domain, there is relation formula: f is the initial output frequency; n is a sampling site.
For nonlinear (Nonlinear) chirp functions, it is actually the quadratic function of the instantaneous frequency of signals, which can be expressed as a function: frequency, 2 f is the Doppler frequency, and 3 f is the conversion rate. When 3 f is 0, secondary FM signals are degraded into linear FM signals, so the sine and cosine signals and linear FM signals are the specials cases of secondary FM signals.

Simulation analysis
After the simulation in Matlab/Simulink is ensured to be correct, the chirp signal model is transformed into VHDL language document using the Signal Compiler in DSP Builder so that it can be realized in FPGA. Figure 8 shows the result of the timing sequence simulation conducted in QuartusII. Figure 9 shows the waves tested by embedded logic analyzer. It indicates that its waves are similar to the simulation waves of Matlab/Simulink and it confirms the correctness of the design.

Experimental Result
After the system is set up, the pin of FGPA is configured. Then it is translated and edited and the engineer document downloads the document •sof to the FPGA chips in the experiment box through the download cable. In this way, the Chirp signal generator is designed. The output side of the generator is tested with the Oscilloscope. Part of its waves are shown in figure 10. From the figure 10 we can find that the frequencies of the Chirp signals designed in the way change obviously with the time, are considerably controllable and has good continuity in phases. Their functions and indicators are: 1) they can be used to generate sine waves with fixed frequencies and used in nonlinear FM; 2) the word length of the accumulator is 30, the output of the phase accumulator used to search ROM is 10 and the output word length of ROM is 8.

Conclusion
The paper studies the design plan of nonlinear FM pulse signals based on the technique DSP-Builder. It has simple system circuit, is extremely controllable and can be programmed repeatedly. Meanwhile, the design based on FPGA is highly readable and portable; therefore, it has good application prospect.