MATLAB Waveform Analysis Validation

Before any practical measurements were done, had the MATLAB analyzing software to be tested for its waveform computability. Thus to insure that the waveform could be analyzed properly with the available PC. Correspondingly were the FFT power estimation and spectrogram algorithms tested and optimized for the preprogrammed waveform.

Firstly had a theoretical FMCW waveform generator to be implemented. A set of complex FMCW signals were therefore implemented in accordance with the displayed waveforms in section 2.2, so different FMCW modulations could be studied on selec- tion. Appendix B.1.1 shows the waveform.m-function, which takes the amplitude, chirp bandwidth, desired signal length, number of periods, desired waveform and sampling frequency parameters. The function then returns the complex time signal, its time vector and the used sampling frequency. By selection would the five different types of FMCW signals be generated as symmetric LFM waveforms.

In the case of the preprogrammed waveform analysis, did the string WF5 generate a similar waveform with up-chirp, CW hold-period, and down-chirp. However dis the theoretical signal differ from the preprogrammed with a hold-period equal to the chirp- period. Nevertheless was this seen as an advantage in the MATLAB testing, since it would test a longer signal than the preprogrammed, thereby insuring computability for even longer signals. In addition was this preferable, since the real waveform generation and oscilloscope sampling would not be synchronized. Hence was a longer acquisition time in oscilloscope sampling needed, to insure that the full waveform could be captured. Thus was the long theoretical signal in MATLAB be perfered to insure handling of long measurement vectors.

Secondly was the signal analyzing code written. Appendix B.1.2 show the theoreti- cal.m-script that set the FMCW parameters for the signal generation and call the wave- form.m-function to obtain the wanted waveform. The FMCW parameters were set in accordance with a down-converted Ku-band LO-board output, to a 100 MHz IF. A

amplitude was then set from a theoretical output power of +0 dBm to insure amplitude similarity. Further were a chirp period of 40 ms and a 188.762 MHz bandwidth set similar to the theoretical output. The sampling frequency were then implemented as 1.5-Nyquist of maximal beat frequency to insure a good power estimate and tested of long measurement vector handling. However were the modulation only applied for one period. This was done, since a pre-tests of the measurement setup revealed that the memory depth of the available oscilloscope were limited to 20.5 Mpts. This meant that the real measurements could not obtain more than one period or parts of one waveform, for analy- sis. Already at this point it was obvious that a full waveform capture was impossible since

Lsignal= tm· fs = 50 ms · (3 · 266.814 M Hz) = 43.3M samples

Even with sampling at 1-Nyquist, would the number of samples be 29 Msamples. Hence were the waveform-acquiring-setup designed for both IF offsets at 1 MHz, 50 MHz and 100 MHz.

Nevertheless were the theoretical test, performed with full signal length to see the full signal appearance and MATLAB computabilliy.

The general theoretical analysis were then further performed in three steps, as intended for the real measurement. Hence time-signal analysis, FFT-spectrum analysis and spec- trogram analysis. The time-signal were plotted to study possible time-signal anomalies, which could help to identify and isolated the chirp in time. Then the FFT power spec- trum [17] were derived and plotted to study the resemblance to spectrum analyzer output. Furthermore were the MATLAB-provided, spectrogram-function [18], applied for 3D- and 2D- captures of the waveform in respectively power, time and frequency. The spec- trogram is a algorithm that uses the Short-Time Fourier Transform (STFT) to generate a spectral estimation in relation to time. This algorithm uses segmented DFT estimation, to obtain 3D-measurement data. Although this algorithm is normally fast, had the extremely long signal vector (Lsignal = 104M samples, tm = 120 ms) to separated in three further

segments. Hence to reduce the spectrogram computing time to belove one hour. Such signal segmenting would normally give an error to the frequency spectrum estimate. However dis the large number of samples reduce the error to a minimum. Further were the spectrogram parameters, then tuned for optimal performance and computing time. After optimalization of the analyzing parameters, were simulated test results were ob- tained, shown in appendix B.2.1. Figure B.2 show the optimal, real part FFT spectrum. Figure B.3 present the 2D-spectrogram in the combined time-frequency-doiman. Hence showing the typical linear FMCW characteristics of the full waveform. In figure B.4 was the up-chirp part of the waveform, isolated as a shorter time vector (40 ms) of the total waveform. Thus revealing more details in the plot and how the distribution of power was descending out from each frequency segment in waveform.

To conclude did the trial for real signal analysis reveal that the MATLAB software in combination with the available PC, were well suited for large measurement data wave- form analysis both in time, frequency and combined spectrum.

5.1. Obtaining Waveform Spectrogram 71