The spectrogram was created using the standard MATLAB command specgram.m which produces an estimate of the short-term, time-localized frequency content of the signal. I used a 128 point windowed fourier transform which will produce 65 frequency bins. The original plan was to have only 64 bins, but MATLAB standard functions produced 65 bins. Since an extra bin won't significantly change the output, and since it was easier, and probably more reliable, the output was left at 65 . As a window, I used a 128-point Hanning function, or half cosine. The window was advanced by 8 samples leaving 120 points of overlap. My m.file assumes the incoming data is in the binary format, and was sampled at 50 megasamples per second. It also assumes that the senter frequency is 38 MHz. This is necessary to allow the m.file to appropriately label the frequency access. The spectrogram will be correct regardless of the actual center frequency, but will have an incorrectly labeled frequency access. The image.m function was used to graph the spectrogram. This requires that the the colormapping be scaled to data since there are around eight orders of magnitude between the smallest and largest values, and most of the data is concentrated in a smaller range of only several magnitudes. This scaling is accomplished by graphing the log base10 of the signal as well as setting the 'CDataMApping' property to 'scaled'. The image.m function also plots the Y-axis in the 'reverse' direction (from top to bottom - similar to a raster scan). Subsequently, the spectrogram 'YDir' property must be set to 'normal'. This process should provided a stardard spectrogram, and for our data, a chirped signal similar to this TATR signal.
The signal was pre-whitened to supress any carrier
frequencies that are present in the signal. This process involved
taking the top %50 of the frequency bins, based on power. This is
accomplished by determing the average power of each row. For each
row in the top %50, this average power is set to the median power of the
entire spectrogram. The spectrogram is now regraphed with the now
suppressed carriers. The following pre-whitened
signal should result.
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The signal experiences ionospheric dispersion which causes a recognizable "chirping" of the signal. In order to determine the power spectrum of the signal, it must be de-chirped, or straightened. With a straight spectrum, we can time-sum the energy at each frequency. Dechirping is almost a process of trial and error. We essientially guess at the value of ioniospheric dispersion by taking several guesses at the Total Electron Content and determine which of these guesses gives us the straightest de-chirped signal. We discriminate between different levels of "straightness" by creating a figure of merit. This is derived by taking the fourth power of the frequency-summed spectral intensity and then time-summing these values. Taking the taking the fourth power will nonlinearly reward the "right" TEC. Once the Figure of Merit is determined, the signal is group shifted by the function: