Fourier Transform of EEG

For an attempt to explaining what the Fourier transform is or how something looks in the frequency domain rather than in time domain please refer to the following euroelectron post.


Has this been done on EEGs?


Would it be useful?


How would the signal of an EEG sound like if we speed it up in time domain so that we can hear the low REM frequencies? This may be done by recording and then increasing the playback sampling rate.


Reference:


Waves - Berkley Physics Course

Fourier transform for stock exchange price charts

Has anyone made a Fourier transform of a stock price graph?


Would it be useful?


What is Fourier transform?


It is a mathematical operation, now performed easily using a computer, FFT, that converts time domain to frequency domain.


Stock prices are in time domain, as the x axis is time. The Fourier transform of this is price with respect to (the x axis now being) frequency. Equivalent information.


Peaks at high frequency for example would mean that the particular stock has a tendency to vary very quickly.


A better way to understand is in music.



A music signal is vibrations. We can readily feel these if we touch our laryng while singing. Low notes have a low frequency. High notes have a high frequency. If we look at the vibration as amplitude displacement with respect to time it looks like any quickly varying graph.


The Fourier transform of this is what notes are being played. What we might see watching a spectrum analyzer while singing.


Like the keyboard of a piano, left notes are vibrating at lower frequency than the next note on the right.


This is frequency domain.


Reference:


Waves - Berkley Physics Course

How balanced signal transfer operates

It is two conductors that carry the signal.


Example:


The two conductors connected to the voice coil output of a microphone.


At any instant when electron move to one direction on one conductor, say towards the preamp the electrons on the other conductor move away.


We must not forget it is not electrons that move from microphone to preamp.


They just oscillate about a point with a motion mimicking the vibration of music. Like dancing. The electrons on the other conductor do exactly the opposite as a mirror.


It is the electromagnetic wave (the cause of movement) that moves from mic to preamp at the speed of light in the material of the wires.


Same as on the sea waves. The water oscillates back and forth. It is not water that travels, it is the wave, by definition the transfer of energy. The water is not transferred from sea to shore. It stays where it is.


Back to balanced...


Electrons repel each other. The ones vibrating repel the nearby ones to vibrate too at the signal of music. The next ones near by vibrate too and so on. Until the cause (the wave) arrives at the input of the microphone preamplifier.


Electrons arriving at the live pin (2) have a mirror motion from those arriving at pin (3) of the XLR connector. If the signal goes to an input transformer when electrons on one side of the primary winding go in, electrons from the other side exit. So it is like moving a towel back and forth with our hands while drying out hair. The balanced motion aids the action.


But if there is an external interference signal arriving somewhere along the cable, it will be pickup up equally by both conductors which are next to each other. Electrons will have almost exactly the same motion, so whatever motion they have at any instant they will collide when they enter the input transformer. In fact if you think about it is the cause or 2 waves that collide.


So interference is out while music is in.


For obvious reasons the two wires are twisted, so hugging each other they have the same experience of the environment.


The shield is an extra precaution. It hugs them both. Apparently it reflects electromagnetic waves arriving externally. In reality what happens is that somewhere near or far electrons may oscillate with an unwanted noise interference signal. Jealous electrons at the screen do the same. And the electromagnetic wave is reflected like a sliver coated mirror does. Whatever happens jealous electrons do not see what happens outside. So they are not inflicted by the interference. And concentrate romantically dancing in a balanced way to music.


Reference:


Feynman Lectures in Physics


BBC notes on how balanced twisted pair signal transmition operates (exact title not recalled, internal instructions)

A cartoon with super market bags ??

AKG MI 201-100 microphone

Another great sounding microphone


Omnidirectional.


Some s problems. Later addition. Not sure if they come from the mic or the following amplifiers.


The microphone has 800Ω output impedance. Layer addition. It was measured to be 667Ω. After a few day it was measured again 830Ω. Possible aging electrolytic capacitor effects on the Escort LCR digital meter.


On the following setup, sound quality was greatly changed by connecting in either polarity. It seems to be an electrical effect than acoustic phase effect that needs to be explained. Late addition. Possibly just phase with respect to the phase of the monitoring headphones when monitoring in real time. A phase inverting adaptor solves the problem.


The Sotwer transformer used synergies very well as it goes very low in frequency and the microphone does not. So together they give a flat frequency responce from singer's vocal chords to listener's brain.


Setup, signal path:


(1-3inch) - (AKG MI 201 - 100) - Sowter 3104x (1:10), input inductance 3.9H - Pleiades V4 at 3.4volts - Realistic Disco Mixer mic mono input - HD580


Great sound when the mic is used very close, full body and detail. It sounds so natural like an acoustic transmission line.


The Beyer M55, at close distance vocals needs an input transformer of only about 400mH input inductance to sound correct to listener's brain as the 400mH introduces the desired low cut together with the mics 500Ω output impedance. (Later addition, more than 400mH, ie of the order of 1.7H may be needed. The transformer measured exhibits a much higher inductance at low frequencies due to the magnetic material used, see other posts.) It then sounds amazing.  No sibilant problem. Many commercial inline low to hi Z transformers already have this order of inductance. A Pleiades transformer can be made using relatively few turns with a Magnetec Nanoperm Nanocrystalinne tape wound ring core.


The AKG MI sounded fantastic on piano.


Just by being placed on top of an upright piano with its tiny plastic support stand.


Setup:


L channel - Beyer M55 -

                                             - Sony TCD5 Pro II - HD580

R channel - AKG MI 201-100 -


The piano was played softly.


So expression was captured and the sustain and clarity of high notes was a joy to listen to.


Later addition 18101218


It sounds very natural just connected to the amazing Uher 4200 report portable reel to reel. See a forward in time euroelectron post.


It sounds great directly connected to Sony TC-D5 Pro, the Sony used in real time as a mic amp and headphone drive amp.

Proximity effect compensation or parametric EQing using 2 microphones

At your own risk.


Both mics can be literally connected in series and one mic is connected out of phase.


We sing to one of the mics and the distance of the other is varied.


It worked great on the following setup using the omnis MD21 HL. It may be possible with directional mics and by connecting to an adding (mixing) desk. On the omni mics although there is no proximity effect the bass was reduced to restore flat frequency responce from vocal chords of singer to brain of listener.


(The live output of one mic was connected to the live of the other, (for phase difference) the 2 remaining pins were the output of the combined mic and were connected to the live, return input of an XLR).


Setup:


+MD21 in series with (-MD21) - Canford input transformer - Pleiades V4, 3.4volt - Realistic Disco Mixer mic mono input - Sennheiser HD580


When two mics were connected in phase it is also very interesting as now the combination appears as a mic quite a few times as strong and noise quiet compared to a single mic and the impedance becomes 400Ω!


There must be comb filtering at play too and it can be used constructively to get the desired sound by varying the distance of the far from source mic.

How to balanced connect the MD421 HL HN MD21 HL HN M55 HL HN

All these microphones are balanced too.


They have an autotransformer to step up the impedance if needed but this does not change much.


If one looks at the schematic or measures the pins with an LCR impedance meter:


The voice coil (low impedance) is directly connected to 2 of the pins. So there are balanced as a voice coil is by definition balanced.


The high impedance part of the autotransformer (full coil) is also connected to 2 pins so it is balanced too as it is a coil too, (the only difference being it is a coil of more turns outside of the microphone voice coil).


In the above situations a pin is common to avoid the use of 4 pins. So everything is done on a Tuchel 3 pin or DIN 3 pin in the case of the M55. Same reasoning applies to the Grundig GDM311.


To summarize:


An autotransformer has 3 terminals.


The first two terminals are connected to the voice coil and the 2 output pins.


The end of the winding hi Z terminal is connected to the other pin.


It follows the other side of the auto winding is common. This is by manufacturer convention connected to the central pin of the output connector.


It follows the other pins are low Z and high Z.


The metal part of the microphone is not internally connected to any of these pins and this is good news for maintaining balanced output.


To summarize again:


There are 2 output options. The voice coil itself and the full autotransformer winding. Both are floating windings so they are balanced.


The fact that the voice coil is also connected in parallel with the low Z part of the autotransformer is not bad too as the latter acts as a Pleiades filter cutting some low end and making the microphone closer to flat (to listener's brain) frequency responce when singing is performed for example. It also electromagnetically damps the membrane making an effective pop filter.


From the above it follows:


To connect as low Z to XLR:


The central Tuchel pin is connected to either pin 2 or 3 of the XLR.


The other (low Z) terminal of the Tuchel connector is connected to either pin 3 or 2.


There is a fourth cable or connection. This is the metal part of the microphone and it is naturally connected to pin 1 of the XLR.


A very easy way to remember the XLR protocol is to remember 1,2,3 equals X,L,R, equals Xternal, Live, Return. So pin 1 is shield and the other pins are the signal pins, 2 being the live pin. When we design and make our own preamplifiers the chassis female XLR pin 1 must be connected to the 4th (nearest pin) which is the metal part of the chassis. In this way the microphone metal part is connected to the metal chassis through the cable shield. So everything is shielded and quiet. More information on the Jensen transformers website pin 1 literature. The chassis of equipment must be earthed for safety too.


You may experiment with swapping pins 2 and 3. It changes absolute phase but on some mics and preamp configurations it also may change the sound dramatically. A way to hear the difference is singing directly close to the microphone.