![\"\"](\"https:\/\/aerospaceresearch.net\/wp-content\/uploads\/2020\/08\/workflow.png\")
<\/figure><\/div>\n\n\n\nThis project aims to have a universal tracker for sporadic and continuous type signals. This requires the above workflow. Overall there are three main stages of processing before we arrive at our final track. Every stage has its own function and uses a particular algorithm.\u00a0<\/p>\n\n\n\n
- Stage 1: Pre-Processing<\/li>
- Stage 2: Decision Making<\/li>
- Stage 3: Tracking <\/li><\/ul>\n\n\n\n
Waterfall<\/h2>\n\n\n\n
![\"\"](\"https:\/\/aerospaceresearch.net\/wp-content\/uploads\/2020\/08\/waterfall_multi_plot-2.png\")
<\/figure><\/div>\n\n\n\nBefore the pre-processing stage, it\u2019s important that we have our signal in the frequency domain, by taking the Fourier Transform. So, the program performs the FFT in chunks to improve memory performance and runtime. It then selects the desired channels of a specific bandwidth, as per the user\u2019s requirement. <\/p>\n\n\n\n
Signal Detection<\/h2>\n\n\n\n
FFT Averaging <\/h3>\n\n\n\n
Before we make a decision, whether a certain FFT frame has the signal or not, we need to remove some consistent artefacts present throughout the duration of the recording.\u00a0<\/p>\n\n\n\n
The basic idea of averaging for spectral noise reduction is the same as arithmetic averaging to find a mean value. This operation is a type of low-pass filtering that can reduce high-frequency noise.<\/p>\n\n\n\n
![\"\"](\"https:\/\/aerospaceresearch.net\/wp-content\/uploads\/2020\/08\/iss-aprs-9.png\")
APRS signal example<\/figcaption><\/figure><\/div>\n\n\n\n Calculating an average spectrum involves averaging across common frequencies in multiple spectra. So we subtract an average spectral frame from the sample frame in question. This improves measurement accuracy and also helps to compensate for a low signal-to-noise ratio.
<\/p>\n\n\n\nDecision <\/h3>\n\n\n\n
The decision of whether a signal exists in a given FFT frame is done by checking the neighbouring frequency bins of a sample bin (n) that all have bin magnitudes greater than that of a dynamic threshold. <\/p>\n\n\n\n
![\"\"](\"https:\/\/aerospaceresearch.net\/wp-content\/uploads\/2020\/08\/decision-making.jpg\")
an illustration of the decision making<\/figcaption><\/figure>\n\n\n\n This threshold is calculated as follows:
Threshold = Mean + SD + safety gap<\/em><\/p>\n\n\n\n![\"\"](\"https:\/\/aerospaceresearch.net\/wp-content\/uploads\/2020\/08\/noaa-2019521-spectra-plt-1.jpg\")
Black indicates selected bins <\/figcaption><\/figure><\/div>\n\n\n\n ![\"\"](\"https:\/\/aerospaceresearch.net\/wp-content\/uploads\/2020\/08\/noaa-2019521-spectra-plt-3.png\")
A NOAA signal’s full spectra; green(channel selected)<\/figcaption><\/figure><\/div>\n\n\n\n <\/p>\n\n\n\n
Tracking <\/h2>\n\n\n\n
Finding the center<\/font><\/font><\/h3>\n\n\n\n
Once the signal is found in a particular FFT frame, it is a matter of finding the centre of the geometric signal. To cover most signal types a generic approach has to be taken. This is why a <\/font><\/font>spectral centroid<\/font><\/font><\/em> is a good enough representation of the signal center.\u00a0<\/font><\/font> A spectral centroid analogous to geometric center and refers to the balance point of the signal. <\/p>\n\n\n\n
x(n) represents the weighted frequency value, or magnitude, of bin number n, and f(n) represents the center frequency of that bin.<\/figcaption><\/figure>\n\n\n\n ![\"\"](\"https:\/\/aerospaceresearch.net\/wp-content\/uploads\/2020\/08\/noaa-2019521-spectra-plt-2.png\")
<\/figure><\/div>\n\n\n\nTrack <\/font><\/font>S<\/strong>moothing<\/strong><\/h3>\n\n\n\n
The frequency track of the signal through the recording is curve fitted with a polynomial function of order 3. It is also important to remove outliers before fitting the data. <\/p>\n\n\n\n
![\"Waterfall](\"https:\/\/i.imgur.com\/7YUSvKv.jpg\")
NOAA Waterfall Signal Track<\/em> (white-raw track, black-filtered track)<\/figcaption><\/figure><\/div>\n\n\n\n ![\"\"](\"https:\/\/i.imgur.com\/EVdrp5m.png\")
APRS Waterfall Signal Track – (white- raw track, black – fitted track)<\/figcaption><\/figure>\n\n\n\n ![\"\"](\"https:\/\/i.imgur.com\/n1DcUQQ.png\")
APRS Waterfall Signal Track (BW-10kHz) – (white- raw track, black – fitted track)<\/em> <\/figcaption><\/figure>\n\n\n\n Outputs<\/h1>\n\n\n\n
The program can output spectral frame and waterfall plots of multi-channels and bandwidths specified by the user. The frequency track of the signal from the specified channels, when found, is finally stored in a JSON file.\u00a0 <\/p>\n\n\n\n
![\"\"\/](\"https:\/\/lh4.googleusercontent.com\/hLZN7jpmONIszFIKbqXUxhSjcbaVrups_tIa6FMteUI-qJxVI3Nrno8WYJh2w59ppQxmxLM7a_ZRt2KYkCVcmsCSraRzbB6x0LbschKG-lHTrrND5PJ8M0gDoXO9vaGpbEXBnmGj\")
![waterfall <\/a><\/td>](\"https:\/\/i.imgur.com\/CTGxOq3.png\"){kind=link}