Add more ideas.

doc/erko_teaser_talks.txt

 Teaser talk topic ideas
 
+0) Teaser talk: Introduction to Geometric Algebra (18 Jan 2022)
 1) Teaser talk: Quantization in LOFAR2.0 Station Firmware
 2) Teaser talk: Subbands, beamlets and channels
 3) Teaser talk: Signal statistics, correlation and beamforming
 
 
+0) Introduction to Geometric Algebra (18 Jan 2022)
+
+Abstract:
+
+For my hobby I wanted to calculate the positioning of a robot arm. I did that using rotation
+matrices, like I learned from Linear Algebra. Instead of using matrices I wanted to use
+quarternions. In short quarternions are in 3-D what complex numbers are in 2-D, so they
+represent rotations. Therefore I started googling to learn more about it and that is how I came
+across Geometric Algebra, which is the topic of this talk. For me Geometric Algebra is the most
+interesting topic that I have ever studied. I enjoy it very much, because it generalizes Linear
+Algebra, complex numbers, quarternions, Pauli matrices, and much more in a coherent way.
+Geometric Algebra can also be applied with Calculus and then it appears that for example
+Maxwell's 4 equations for electromagnetism can be written as one equation. I will present an
+introduction to Geometric Algebra and also explain why we did not learn about it at school and
+at university.
+
+
+
 1) Teaser talk: Quantization in LOFAR2.0 Station Firmware
 
-* floating point - fixed point - integer (two complement, so range e.g. -8 to +7 for 4 bit value)
+* floating point - fixed point - integer
   . 2**+127 -------------------------- 1. ------------------ 2**-127
                               <n bit int>
                                         .   <n bit fxp>           fraction only
                                     <n bit fxp>                   with fraction
                      <n bit fxp>        .                         scaled
+
+  . two complement, so range e.g. -8 to +7 for 4 bit value
   . format:
     - unsigned : u(w, p)
     - signed : s(w, p)
@@ -39,7 +60,8 @@ Teaser talk topic ideas
     . dBFS
     . SNR, P_quant
     . processing gain log2(sqrt(N_fft)) = 5b, log2(sqrt(N_ant)) = 3.3b for N_ant = 96
-    . coherent input (sine), incoherent input (sky noise, weak astronomical signal burried in noise)
+    . coherent input (sine), incoherent input (sky noise, weak astronomical signal burried in
+      noise)
 
 * Implementation details
   - Use separate function to do DFT for two real ADC inputs with complex FFT
@@ -50,8 +72,9 @@ Teaser talk topic ideas
   - Interally extra LSbit inside PFB and before applying the weights, see try_round_weight.py
 
 * Conclusion:
-  - Fixed point arithmetic uses less FPGA resources (multipliers, RAM, logic) than floating point,
-    but requires carefull bookkeeping or the fixed point position in the FW implementation.
+  - Fixed point arithmetic uses less FPGA resources (multipliers, RAM, logic) than floating
+    point, but requires carefull bookkeeping or the fixed point position in the FW
+    implementation.
 
 * References:
   [] SDP FW design, https://support.astron.nl/confluence/display/L2M/L4+SDP+Firmware+Design+Document
@@ -63,41 +86,61 @@ Teaser talk topic ideas
 
 2) Teaser talk: Subbands, beamlets and channels
 
-* Implement delays by phase rotation
+* Implement delays by phase rotation:
   - sinus --> phase exactly reprensent delay
-  - narrow band --> phase is only exact at center of band, approximate towards the edges
+  - narrow band --> phase is only exact at one frequency (typically the center frequency) in the
+    band, approximate towards the band edges
 * f_sub
-  - coherence bandwidth T_sub >> B diameter of a Station antenna field
+  - coherence bandwidth of a staion requires T_sub >> B / c, where B is the diameter of a Station
+    antenna field and c = 3e8 m/s the speed of light in free space.
   - distributed processing of N_pn processing nodes f_sub = RF_BW / N_pn / N_sub_per_pn
 * PFB to separate ADC sampled signal into frequency bands
   - FFT bin has sync bandpass, PFB has narrow band bandpass --> bins are called subbands
   - Repeat FFT per N_fft samples in time yields bin coefficients per T_sub
   - Bin is complex value, because it has to represent phase and gain of the bin
-    . complex /= difficult --> complex = aggregate number of two parts: re and im or gain and phase A*exp(phi)
+    . complex /= difficult --> complex = aggregate number of two parts: re and im or gain and
+      phase A*exp(phi)
   - For CW in center of bin the subband the subband value is a constant phase
   - For CW left or right of center the phasor rotates left or right
-  - Narrow band noise in subband is a noisy CW at RF_sub = n * f_sub, so can be delayed using phase rotation
-    . plot fft(noise) --> keep only subband bin n, make other bins zero --> ifft() --> noisy CW at RF_sub
-  - subband = Narrow band frequency signal from PFB output. Also called coarse channel in other radio telescopes
+  - Narrow band noise in subband is a noisy CW at RF_sub = n * f_sub, so can be delayed using
+    phase rotation
+    . plot fft(noise) --> keep only subband bin n, make other bins zero --> ifft() --> noisy CW
+      at RF_sub
+  - subband = Narrow band frequency signal from PFB output. Also called coarse channel in other
+    radio telescopes.
 * BF
   - weight and summate subbands from all antenna signal inputs that are part of the beam
-  - BF weights are complex values, the phase points the beam by compensating for the geometrical delay and the gain shapes the beam
-    . Jones matrix, cross pol weights are not used (kept 0), because the dual pol antenna are all aligned in the field
-  - Update rate
+  - BF weights are complex values, the phase points the beam by compensating for the geometrical
+    delay and the gain shapes the beam
+    . Jones matrix, cross pol weights are not used (kept 0), because the dual pol antenna are all
+      aligned in the field
+  - BF weights update rate:
     . depends of f_RF and B
     . applied when written (no need for double buffer like in LOFAR1)
   - beamlet = beamformed subband. A station beam of one subband.
 * Subband equalizer
-  - weights the subbands to fine adjust for cable delays and fine adjust for frontend gain differences
-    . coarse delays are compensated by a sample input delay buffer in the SDPFW at the ADC input
-    . coarse gains are compensated by an attenuator in the RCU2 in steps of 1 dB = factor 1.26 in power
-  - in LOFAR1 subband weights were incoporated into the BF weights, in LOFAR2 they are separate CP
-  - the subband weights can also be used to compensate for the bandpass shape of the RCU2 and antenna, to
-    keep the dynamic range of the subbands signals within the lowest bits. This then can be used to
-    have beamlets of 4 bits instead of 8 bit (default).
+  - Weights the subbands to fine adjust for cable delays and fine adjust for frontend gain
+    differences between receiver inputs:
+    . coarse delays are compensated by a sample input delay buffer in the SDPFW at the ADC
+      input
+    . coarse gains are compensated by an attenuator in the RCU2 in steps of 1 dB = factor
+      1.26 in power
+  - In LOFAR1 subband weights were incoporated into the BF weights, in LOFAR2 they are separate CP
+  - The subband weights can also be used to compensate for the bandpass shape of the RCU2 and
+    antenna, to keep the dynamic range of the subbands signals within the lowest bits. This then
+    can be used to have beamlets of 4 bits instead of 8 bit (default).
 * CEP correlator and beamformer
-  - operate on channels that are narrow band frequency signals within a beamlet, so from a PFB at CEP.
-  -
+  - Operate on channels that are narrow band frequency signals within a beamlet, so from a PFB at
+    CEP.
+  - Also called fine channels in other radio telescopes.
+  - Coarse geometrical delay differences between stations can be compensated by beamlet sample
+    delays of T_sub, so in steps of T_sub * c = 5.12us * 3e8 m/s = 1536 m. So for stations that
+    are 1000 km apart this implies coarse delays of ~1000 beamlet samples.
+  - The remaining fine geometrical delay differences within ~1500 m can be compensated using
+    phase rotation of the fine channels. The coherence bandwidth of whole LOFAR requires
+    T_chan >> T_sub, so typically more than 10 channels per beamlet. In fact CEP uses N_chan =
+    64 - 512 for for coirrealtor pipeline and N_chan = 256 for tied array BF pipeline.
+
 
 * References:
   [] https://support.astron.nl/confluence/pages/viewpage.action?spaceKey=L2M&title=Temporary+storage+of+documents+and+papers