Octave cheatset

File opening

clear all;

File operations

To include a *.m file (like test.m) at the location in the file simply use the filename without *.m in the code. E.g. to include “test.m” simply put “test” into the code.

Matrices & Vectors

m x n = column x row = Zeile x Spalte

a = [1;2;3] # vector 3×1 (vertical)
b = [1,2,3] # 1×3 (horizontal)

a = [1;2;3] # vector 3×1 (vertical)
b = [1,2,3] # 1×3 (horizontal)

c = [

r3 = c(:3); # select 3rd row

Filter, find and concanate

b = find( c(:2)==8 ) # return all values from 2nd row of c where value is 8

C = [A,B] # horizontal_concanation
C = [A;B] # vertical concanation

for concanation can use:

horzcat (array1, array2, …, arrayN)
vertcat (array1, array2, …, arrayN)


fig1 = figure(1);
hold on;
title (“Titel”);
xlabel (“x-axis”);
ylabel (“y-axis”);
grid on;
grid minor on;
box on;

plot(x, y, “+”, “markersize”, 10, ‘color’, ‘red’); # markers only
# to add line connecting markers -> use linestyle

legend(‘S11′,’S22’, “location”, “southeast”)
hold off;

Vertical & Horizontal lines

plot([x,x],[0,8], “linestyle”, “–“); # vertical line at x
plot([0,8],[y,y], “linestyle”, “–“); # horizontal line a y

Plot to pdf export

print (fig1, “my_pdfname.pdf”, “-dpdflatexstandalone”);
system (“pdflatex my_pdfname”);
open my_pdfname.pdf


str_result = strcat(str1, str2);
str = num2str(my_number)

LinuxCNC and charge pump

In many cases of a CNC mill, the stepper motors are controlled using the parallel port of a computer (LPT port). The CNC software toggles the pins (step & direction) for each axis according to the needs of the desired toolpath (G-code). The LPT port solution is the most simple and cheap way. One problem is latency and jitter of the software pin toggle which must be performed in realtime (synchronizing of multiple axes). Usually, LinuxCNC will take care of this problem although the result is not optimal (performance problems etc.)

Another problem of the LPT port is the undefined state and behavior during the boot of the computer. If you switch on your CNC mill usually the stepper motor driver is immediately activated. During the boot sequence of the controlling computers, some LPT pins are toggled or are in an undefined state. This might result in undesired steps and thus undesired motion of the CNC mill. In order to prevent this behavior, some stepper motor controllers have a built-in charge pump.  This charge pump requires a  defined squarewave signal at a specific LPT pin to enable the stepper motor controller. If this charge pump signal is missing the stepper motor driver won’t perform any motion (steps). The signal is only generated when the CNC software (here LinuxCNC) is running properly and no emergency stop condition is met. During the boot of the operating system the LPT pins might toggle or be undefined but the condition for the charge pump good won’t be met and thus no steps will be performed.

I am using the “Tripple Beast” stepper motor controller by Benezan Electronics which has charge pump functionality but the information provided here applies analogous to other motor controllers, too. In order to use the charge pump (sometimes called watchdog) on the Tripple Beast jumper 2-1 needs to be removed. The square wave signal (10kHz … 100kHz) is expected on LPT pin 16. Please refer to the manual of your stepper motor driver for the exact specifications of your charge pump.

If you’re setting up LinuxCNC you probably will be using the “Stepconf Wizzard”. During setup, you can specify the output pin of the LPT port for the charge pump. In the drop-down menu of the pin (for me it’s pin 16) select “charge pump”. This will route the charge pump signal to the desired pin in the LinuxCNC HAL.

Unfortunately, some manual changes in the HAL file are required which can not be done in Stepconf Wizzard. Please note, that the following manual changes will be overwritten every time you perform Stepconf Wizzard! In general it’s strongly recommended to backup the settings files for each LinuxCNC profile before changes or Stepconf Wizzward. Probably a (local) git repository is a suitable solution (fast revert and good diffs due to text based settings).

  1. Navigate to the HAL file of your machine (*.hal) and open it with a text editor (e.g. “Mousepad” in LinuxCNC environment).
  2. Completely remove the line

net estop-out charge-pump.enable iocontrol.0.user-enable-out

  1. Add the following line instead

net estop-ext => charge-pump.enable

After that you should see a squarewave output on the desired pin (no emergency stop must be active in LinuxCNC). In my case (Tripple Beast stepper motor controller)  there is a “charge pump OK” LED which will light up green when a valid charge pump signal is detected.

Please note that the frequency of the charge pump signal (“charge-pump.out”) is the frequency of the LinuxCNC base thread. If the frequency is too high to meet the specifications of your charge pump you can use a divided by 2 (“charge-pump.out-2”) or divided by 4 (“charge-pump.out-4”) signal. (See LinuxCNC documentation). Frequencies higher than those of the base thread of course can not be achived.

rfft and irfft for Octave / Matlab

One-dimensional Discrete Fourier Transform (DFT) for real input.

function rfft = rfft(a)
ffta = fft(a);
rfft = ffta(1:(floor(length(ffta)/2)+1));

Inverse of the Discrete Fourier Transform (DFT) for real input.

function irfft = irfft(x,even=true)
n = 0; % the output length
s = 0; % the variable that will hold the index of the highest
% frequency below N/2, s = floor((n+1)/2)
if (even)
n = 2 * (length(x) – 1 );
s = length(x) – 1;
n = 2 * (length(x) – 1 )+1;
s = length(x);
xn = zeros(1,n);
xn(1:length(x)) = x;
xn(length(x)+1:n) = conj(x(s:-1:2));
irfft = ifft(xn);


GPS ceramic patch antenna (Aliexpress) S11

Some time ago I ordered a lot of (cheap) and small GPS patch antenna from Aliexpress.


I was very interested in the resonant frequency so I decided to connect it to my HP8753C to evaluate the match.


    • Minimum S11 -13.4 dB (VSWR: 1.544:1, reflection coefficient gamma: 0.214) at approx. 1070 MHz
    • Antenna resonant peak far off GPS L1 center frequency (nominal 1575.42 MHz). Usually, a sufficient ground plane is required for patch antennas, but these usually shift the resonant frequency to lower values.
    • Nevertheless the match looks better than 10dB at the 1575.42 MHz which is sufficient

Side Note: A good match does not necessarily lead to a “good antenna”. Although a good match is a basic requirement for all energy being transported from (and to) the antenna it is not guaranteed that the energy will be radiated in an effective way. S11 (or VSWR) only quantifies the amount of energy being reflected back from the antenna into the transmitter. It is up to the antenna (material and geometry) to efficiently radiate the delivered energy. Just think of a dummy load as an extreme of this phenomena: Nearly all energy is transferred (very good match, S11 minus many dB) but nearly nothing is radiated. Beside impedance mismatch losses, ohmic conduction losses (copper etc.) and mostly dielectric losses of surrounding material (like FR4 etc.) massively degrade antenna efficiency. The belonging measure is called “antenna efficiency” mostly given in %. (For RX operation the same applies analogous due to the antenna reciprocity theorem).


    • HEWLETT PACKARD 8753C, SW: 4.02
    • APC-7 – SMA (f)
    • SMA (f) – U.FL (m) MULTICOMP MC000984
    • RG 58A/U 0,5m SMA (m) – SMA (m)
    • Kirkby Microwave 85033, ‘50Ω SMA Calibration & verification kit’

Touchstone file (*.S1P)



Self-sustaining circuit using P-channel MOSFET

The circuit below shows a simple but effective way to power activate a (DC) device by pressing a button. The device can be completly switched of electronically (e.g. by a microcontroller). (Switch SW2 if only shown to demonstrate the operation principle of the circuit.)

Depending on the selected P-channel MOSFET T13 the circuit can handle voltages bigger of more than 60V and currents of several tens of amperes.

The same functionality could be achieved by a relay at the expense of volume (relay is much bigger) and power consumption (~100mW or more). Especially in a battery powered portable application, there is no way for a relay.

Circuit description

Power enters the schematic at the PWR_IN port (top left). In OFF-state the MOSFET handling the power (T13) is blocking current from its source to drain. Please note the body diode of the MOSFET is in reverse to the current flowing from PWR_IN to PWR_OUT when MOSFET is conducting. In the OFF-State the gate of T13 is pulled to the PWR_IN voltage level via pull-up resistor R294 thus keeping the MOSFET not conducting. The value of R294 is selected to keep safe operation at minimal losses when the gate is pulled low.

To activate the device the user will press the activation switch S3 which closes the contacts A-B and pulling the gate of T13 to GND. As soon as the gate-source voltage at the gate of the MOSFET drops below Vgs_th (threshold voltage see the datasheet of your preferred MOSFET) T13 will start conducting. As current flows from PWR_IN to PWR_OUT a microcontroller connected to PWR_EN can boot and then control the bipolar NPN transistor T12 which will pull the gate towards GND, too. As the microcontroller starts to work it immediately needs to output high level (3,3V or 5V) to T12. After this, the button can be released by the user. The sequence to power a microcontroller should take less than 1ms.

Remaining components are mostly protecting the MOSFET and the microcontroller pin. One big problem with this kind of circuit is the limited gate-source voltage of most modern MOSFET. The majority of them will take permanent damage if the gate-source voltage (Vgs) is bigger than (-)20V. If you want to use this circuit in a 24V or even 48V environment Vgs needs to be limited. This is done by the zener diode D111. Across D111 there is a constant voltage drop of the zener voltage (chosen to be 10V here). At this voltage, Vgs is big enough to keep T13 fully conducting. D111 forms a voltage divider in conjunction with R295. TVS diodes D110 and D112 further protect T13 against voltage transients and act as a basic over voltage circuit (requiring a fuse elsewhere before this circuit!). D113 is used to protect the bipolar NPN transistor T12 in the case of an overvoltage event. R296 acts as current limiting resistor into T12 in order to limit the current out of the microcontroller pin. For T12 any NPN (e.g. BC817, BC547, BC548, …) should be fine. TVS diode D114 limits the current in case of a failure at the MOSFET (low impedance failure MOSFET conducting input voltage to its gate).

In order to switch the device OFF the microcontroller needs to deactivate its output pin (switch to lo-state). As a consequence, T12 stops pulling the gate of T13 to GND. The gate is charged again to input-level voltage (via pull-up resistor R294). T13 stops conducting, the circuit’s power supply is cut off and so is the microcontroller. Nearly no current is consumed by this circuit in OFF-state.

Simplification for lower voltage

If you have a supply voltage which is lower than the maximum gate-source voltage (Vgs_max) of your selected MOSFET (T13 above) there is no need for the MOSFET driver (T12), the voltage divider and zener diodes. This might be useful at USB designs etc.

As you can see on the left side of the circuit above the self-sustaining circuit only consists of MOSFET T1, pull-up resistor R43 (and R18). R18 is not necessary but can protect the microcontroller pin connected to EN_MOSFET in the case of an overvoltage event.


Si(x) / Ci(x) (Sine integral function / Cosine integral function) in Python

The Si(x)-function (integral of the sine) in Python requires the usage of the scipy-package!


import scipy
from scipy.special import*

(si,ci) = sici(X)

Now si and ci hold the results of the sine / cosine integral.

Make sure not to confuse the Si(x)-function with si(x) = sin(x)/x = sinc(x), the cardinal sine function. Especially German literatur often uses the expression si(x) instead of sinc(x).

Flight Computer for Hang Gliders

This project was my master’s thesis back in 2016/2017. It is based on the i.MX6 quad Linux board from http://wandboard.org

The PCB contains multiple buttons and rotary knobs for intuitive handling of the XCsoar flight software. A STM32F4 microcontroller additionally handles the signal processing of the sensors on the PCB (GPS, 9 DOF IMU, 2x absolute pressure sensor + 2x differential pressure sensors for pitot tube, lightning detection).

A high brightness (1000 nt) display is selected for proper visibility in heavy sunlight conditions. 1 nt= 1 Nit = 1 cd/m2


Activating UART2 on Wandboard Quad / Dual (iMX6 / Kernel 3.0.35 up)

The Wandboard (linux board) Quad, Dual and Singe have several UART interfaces (3.3V, not 5V tolerant) available. The official images from http://www.wandboard.org/ have UART1 activated by default because it allows you to manipulate the bootloader and to have a simple terminal access. On the wandboard baseboard UART is converted to RS232 and can be accessed via a null modem cable as shown here. Unfortunately you will get a constant output of kernel messages on this stream which might interfere with your application. However if you want to use a UART interface in your application you should either disable the kernel output on UART1 or activate and use another UART interface (like UART2). I would highly recommend you to choose the latter way since you will definitely need the kernel / boot output messages in order to make your system boot.

So here’s the deal: If you need to activate UART2 you’ll need to apply changes to the kernel & device tree and recompile it. If you want to know if activation is necessary on your system simply check if you can find a device called mxcfb2 in your /dev folder. NXP (former Freescale) decided to name the UARTs of the i.MX6 this way. The kernel output mxcfb1 (UART1), mxcfb2 = UART2, mxcfb3 (UART3, Bluetooth module connected there).

cd /dev && ls -l

If you can find mxcfb2 there your UART2 is already activated. If not you need to activate it according to this post.

Again this is only for kernel versions 3.0.53 and higher. The 3.0.53 kernel is the first to have a device tree. If you’re using a lower version of the kernel (e.g. “out of the box images” Wandboard Ubuntu 12.04) there is no device tree. If you‘re trying to work on this kernel you’ll need to apply changes to different C code source files. Anyway – if you’re using 3.0.53 and up your absolutely right here.

First step is to get the kernel sources. We will work on kernel version 3.10.53. So let’s check out the correct branch from the official Wandboard GIT repo:

git clone https://github.com/wandboard-org/linux.git -b wandboard_imx_3.10.53_1.1.0_ga

Then we can edit the device tree. I would recommend you to add a new set of pins to the file. This “pins pack” will define a set of pins which are used for UART2 communication. It is useful to define the pins RTS and CTS for hardware flow control as well. You do not need to use them but they are routed to EDM connector of the Wandboard aswell. Edit the imx6qdl.dtsi file with your favorite text editor.

 nano arch/arm/boot/dts/imx6qdl.dtsi

Add the following lines indicated with a “+” (patch style)

MX6QDL _ PAD _ EIM _ D29 __ UART2 _ DTE _ RTS _ B 0x1b0b1
+ pinctrl _ uart2 _ 3: uart2grp-3 {
+    fsl,pins = <
+         MX6QDL _ PAD _ SD4 _ DAT4 __ UART2 _ RX _ DATA 0x1b0b1
+         MX6QDL _ PAD _ SD4 _ DAT5 __ UART2 _ RTS _ B 0x1b0b1
+         MX6QDL _ PAD _ SD4 _ DAT6 __ UART2 _ CTS _ B 0x1b0b1
+         MX6QDL _ PAD _ SD4 _ DAT7 __ UART2 _ TX _ DATA 0x1b0b1
+    >;
+ };
uart3 {

This section simply defines pins of the i.MX6 processor to have UART2 alternate function. (Pins of large, complex or BGA style ICs are often called “pads”.)

Next we want to make use of the new pin set. Edit the file

nano arch/arm/boot/dts/imx6qdl-wandboard.dtsi

Again – add the lines indicated with a “+”. Other lines are only presented to enable navigation within the source code.

 status = "okay";
+ &uart2 {
+          pinctrl-names = "default";
+          pinctrl-0 = <&pinctrl _ uart2 _ 3>;
+          status = "okay";
+ };
&usbh1 {
 status = "okay";

After these simple steps your are ready to compile the kernel and device tree. Having finished compilation you should be able to find mxcfb2 in the /dev folder of your system.

Using terminal programmes like minicom you can simply test your UART interface.

sudo apt-get install minicom

sudo minicom -s

LVDS color problems / dimmed gray screen (Wandboard, iMX6, Ubuntu 12.04)

Enabling LVDS on my Wandboard Quad on Ubuntu 12.04 (see my blog entry here), I encountered two problems with my LVDS display.

Problem 1: Basically the settings seemed right, but there were some wrong colors everywhere (see image below).

LVDS color errorThus I decided to go for Test Card. It is freely available from Wikipedia in the linke above. Below you can see a photo of my LCD screen (upper image) and the original image as it should be (lower image).


Test Card Image courtesy of Wikipedia.

Obviously the red channel is missing so I decided to check the LVDS connector and found a loose contact on my LVDS cable.

Lesson learned: Always double check your connections (e.g. using a continuity tester / multimeter). When using continuity tester make sure not to connect ground of multimeter and LCD since the testing voltage of the tester could potentially destroy the LVDS input pin and the measurement result would be wrong!

Problem 2: The screen seemed very dark and white did not represent the maximum brightness of the screen. Since I definitely knew that the backlight was at full power (no PWM activated) the problem had to be caused by the display. At this moment I had the LVDS color mode set to RGB18 (see here) which was wrong for my LCD. After setting to RGB24 the problem was solved.

Lesson learned: The LCD might work even when the LVDS color mode is set wrong. When setting RGB18 (3×6 bit) obviously the two MSB of a 24bit (3×8 bit) LVDS transmission are omitted, the display sets them to  zero. Correct settings to RGB24 resolves the issue.