I have a little question about the spectrograms plotted on the Colab Notebook. It is stated that the IQ matrix has a shape of 128x32, being 128 the doppler ranges and 32 time units. The FFT is applied over the axis 0 of the matrix. In other words, it is applied to the 128 doppler ranges of a time unit. My question is, what does the resulting spectrogram represents when we do this? Isn't more usual to apply the FFT along the 32 time units to obtain a set of frequencies that correlate to the speed of the tracked human/animal? This Wikipedia article describes what I mean: https://en.wikipedia.org/wiki/Pulse-Doppler_signal_processing. Could someone cast light on this? Thank you in advance.Posted by: Galeros93 @ July 16, 2020, 4:53 p.m.
The IQ matrix contains 128 x 32 elements being 128 I/Q time data samples within a single radar processing time frame and 32 consecutive such time units. The reason FFT is performed on the ‘fast time’ axis (i.e. 128 samples) rather than on the ‘slow time’ axis (i.e. 32 samples) is a matter of scale. An underlying assumption for an effective FFT analysis is that ‘acceleration’ during the time frame represented by the data is very low. Given the type of motion presented by humans and animals only the ‘fast time’ axis comply with this assumption.
Therefore, FFT processing should be applied over the dimension of 128 I/Q time samples to get the frequency content of the returned radar signal at each time frame. A spectrogram (as shown in the samples) is generated by attaching together 32 consecutive FFT results (please note that besides FFT processing some additional manipulation is required to properly display a spectrogram – like taking a LOG of the absolute value and passing a threshold – this is well detailed in the ‘Processing’ section of the competition notebook). Therefore, a spectrogram would eventually provide a display of how the frequency content of the returned signal is changing along time.
(MAFAT Challenge Team)
I'm confused regarding the dimensions of the matrix. If it represents 32 consecutive time units of 128 I/Q time data samples, can't it be viewed as a single vector of 4096 I/Q time data samples with time continuity?
Or is the time continuity non existent between consecutive vectors?
You are not confused at all, the data can be seen as a single continuous time vector. Nevertheless, each column might have a different phase or amplitude when you move from one column to another.
Note that after performing FFT you can no longer view the data as a continuous time vector as the Y-axis is transformed to a frequency domain.
(MAFAT Challenge team)