Time Domain and Frequency Domain Displays
Correcting Doppler-Induced Frequency Drift
Additional Information about CoolEdit 2000
CoolEdit 2000 opens a data file in the time-domain display mode (which displays signal intensity on the y-axis vs. time on the x-axis). The lower right corner has a table that shows the beginning and ending times of the displayed view, and of any selections made with the mouse. This table also shows the time duration of the view and any selection made. The lower left corner of the display has the recording and playing controls, as well as buttons to zoom in or out of the view.
The spectrogram view is more useful for detecting unusual signals. The spectrogram view can be selected by clicking on the View menu. There is also a button on the toolbar that toggles between the time-domain and frequency-domain data displays. The spectrogram view is really a 3-D view, with signal intensity on the z-axis (represented by color), frequency on the y-axis, and time on the x axis. The color / signal intensity code is based on the spectrum, with black being the lowest intensity and white being the highest. In between black and white, the color changes from violet to red as the signal (or noise) intensity increases. In contrast to Goldwave, CoolEdit displays the entire spectrogram at once, without requiring the user to scroll through the spectrogram in pseudoreal time. This is a major advantage of CoolEdit, and is especially valuable with one-hour data files. This data file appears as a routine spectrogram with no unusual signals.
The spectrogram of this data file reveals the presence of small signals in the data. Of course, faint lines can be easily integrated by a computer to increase their strength, and lines that you see in our files are more likely to be locally generated interference dismissed using the Known Interferences Log. We are most interested in having students look for complex patterns that would not integrate over time into a stronger signal. The rotation of the earth creates a steady drift in any signals from space through the changing Doppler shift. Signals with no drift at all (i.e., the line has slope = 0) have no Doppler acceleration, and the signal source is therefore likely fixed in position with respect to the radiotelescope dish. The Doppler shift change for our radiotelescope dish in its typical orientation, and pointed at a stationary object in space, is slightly over 6 Hz per minute. Of course, any motion of the distant source would also create a Doppler shift of unknown direction and magnitude. For this reason, it is logical to expect Doppler shifts to appear at least over a range from +13 to -13 Hz/min.
The Frequency Analysis function enables users to more precisely display signal intensity and frequency. The frequency analysis function in CoolEdit is more precise than the frequency vs. intensity display in Goldwave. Frequency Analysis in CoolEdit is initiated by clicking on Analyze / Frequency Analysis, or by pressing Alt-Z.
A new window opens and displays the FFT of the data of a set number of cells (65536 in this figure) at the cursor position. The number of cells integrated in the FFT is set in the box called FFT Size at the lower left of the analysis window. In general, this is set as large as possible to increase S/N. Ideally, the length of the FFT should exactly match the length of the signal. Doppler shifting of the signal puts an upper limit on the effective duration of the signal, however. The faster the signal drift, the shorter the FFT that can be used to still recover a signal. The apodization function is set in a box to the right of the FFT Size. In general, Welch (Gaussian) apodization seems to recover the microwave signals best.
As mentioned above, longer FFTs improve S/N as long as the frequency shifting of the signal is minimal. Using the cursor in conjunction with the Analysis window permits users to take arbitrarily long FFTs (much longer than the maximum size in the FFT Size box). To set the limits on signal integration with the cursor, left -click in the main screen on the left side of the signal that you want to examine (the starting time). Then right-click on the ending time. The selected signal region will then be highlighted in the main window. Push the Scan button on the Analysis window to take the FFT of the entire highlighted region. Note that the Analysis window reports the cursor coordinates in Hz and dB in the Cursor box (the x and y axes, respectively), and the Frequency box reports the frequency of the largest peak in the spectrum. (Note also the presence of small "birdie" signals that appear in the longer FFT integration on this data file. These signals were not visible in the simple integration of 65536 cells because signal adds as n while noise adds as the square root of n, so longer integrations bring out otherwise invisible signals.)
A steady 1301 Hz signal at 3% of the peak-to-peak (p-p) noise level is just large enough to be visible in the main spectrogram. However, if such a signal is given a 10 Hz / minute drift, such as might be caused by Doppler shifting from a distant rotating planet, the signal is virtually invisible even on a Scan-extended one-minute FFT integration.
Fortunately, CoolEdit provides a means for shifting the pitch of signals (although it is a means with somewhat limited frequency resolution). There are multiple reasons why we make use of this function in CoolEdit. First, of course, is the fact that applying an inverse Doppler shift may enable signals to be integrated long enough to become visible. In addition, the inverse Doppler shift reduces birdies and other constant interferences because these interferences are constant in the original data, and so become shifting signals after the inverse shift is applied.
To access the data frequency shifting function, click on Transform and then Time/Pitch, and then Stretch ... This brings up a Stretch dialog box containing index tabs labeled Constant Stretch and Gliding Stretch. If you use this function, don't forget to start each drift correction on a fresh copy of the file (you can use the Undo command or Open a fresh copy each time). Otherwise it will soon become difficult to tell exactly what correction has been applied, and this information is important to post if you detect something in a file. Remember, our data collection software performs dechirping and signal integration automatically. We are most interested in having students look for complex patterns that would not integrate over time into a stronger signal.
The example shows application of the Gliding Stretch. In the Gliding Stretch the user is able to shift both the Initial Pitch and the Final Pitch of the data. It is usually best to just shift one or the other, though. Users can correct Doppler drifts of the entire data file, or just a selected portion of it (using the mouse to make the selections). Given the antenna beamwidth, for 5-minute or 15-minute long files you should simply correct the entire file.
The 1301 Hz signal with an intensity equal to 3% of the p-p noise level reappears when an appropriate inverse frequency shift is applied. The intensity of the system "birdies" decreases at the same time. A better recovery of the signal could be obtained if more resolution were available in the CoolEdit transform, because the frequency drift must match the frequency correction for minimum band broadening and maximum signal recovery.
Data analysts who use CoolEdit can apply a range of frequency drift corrections on every data file because any real signals from space will almost certainly show a Doppler frequency drift of unknown magnitude, and CoolEdit has the capability to perform corrections and integrate long signals in its FFTs. A major advantage of this approach is the reduction of terrestrial-interference signal artifacts always present at low levels in the files. For example, one could do +12%, 11, 10, 9, 8, ... 2, 1, 0, -1, -2, ...-12% drift corrections, and check each complete spectrogram for signals. To maximize signal-to-noise ratio (S/N), one should then integrate each separate inverse shift in 15 minute blocks (which is the approximate antenna beamwidth in terms of transit time) and see if any signals appear. The best S/N enhancement seems to be obtained when the drift correction precision is 0.05% or better, although this places quite a burden on the analyst in terms of time spent on each file. You can manually type decimal % corrections (like 110.8) in the Gliding Stretch box that you cannot get with the slider.
You can make the process of dechirping easier by using a script to automate part of the process. Click on the link above for more details and scripts.
On very weak signals, the accuracy of the Gliding Stretch drift correction may not be high enough over several minutes to avoid spreading the center frequency of a signal enough to make it undetectable. The spectrogram view, with reverse colors, and zooming on the time and frequency axes, might provide the most sensitive signal detection. Reversing the color order in the Spectral Options box, or just by selecting a block of the file, allows users to see weak signals against the blue background. More fine-tuning tips are given in:
A very sensitive example analysis in which interference signals are analyzed in CoolEdit.
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