VLF MD with digital signal processing : Bee-Buzz 1

[Carl-NC]

[JoyJo]

Thank you, Carl! That's very kind of you!

[Olly]

This is exactly how the DFT algorithm works, but instead of correlating the input signal with the entire set of frequencies up to N/2, here it is only done with the frequencies of interest giving us the real and imaginary values of each very quickly without bothering about the other frequencies in the Fourier spectrum. Quite ingenious !!!

[Carl-NC]

Quite ingenious !!!

Since 1932, no less.

[Aziz]

Hi all,

I'm really sick of buggy publications. So be very careful if you are going to use some example codes or information resources from the internet publications.
This is a good source for digital Lock-in Amplifier:
https://www.zhinst.com/ch/en/resourc...k-in-detection

On Wikipedia, it is simply wrong for Y-component. The negative sign for Y is missing there, which is very important for correct phase calculations.
see https://en.wikipedia.org/wiki/Lock-in_amplifier

Same applies to Goertzel algorithms.
https://en.wikipedia.org/wiki/Goertzel_algorithm
On wikipedia, the scaling by 1/N (normalisation) is missing. Most implementations don't decode in complex form (I/Q with real/imag components). So they aren't interested in phase information. We are interested on both (magnitude and phase).

If you take care of all the details, there is no difference in making either FFT, Lock-in Amplifier or Goertzel decoding.
All three methods deliver same complex results within the numerical accuracy.

- FFT does require more DSP horse power and pre-calculated sine/cosine tables (slow and requires more memory).

- Lock-in amp does require pre-calculated reference sine/cosine tables for each frequency of interest if you take the internal reference base (fast, requires more memory and therefore not optimal for embedded projects).
If you have an external reference signal, you have to generate a 90 ° phase shifted signal of the external reference signal.

- Goertzel does only require one pair of sine/cosine value for each frequency of interest (low memory required, very fast and ideal for embedded projects).

My new USB Sound Blaster G3 will arrive today!

Cheers,
Aziz

[Aziz]

This is an example of a comparision in the complex frequency spectrum:
Note, that it shows the DC-Value (k=0), positive and negative frequency spectrum of the sample data.

=== FFT/Goertzel/Lockin-Test ===

Number of Samples N = 32
Samplerate = 48000 Hz
Bin-Resolution =  1500.000 Hz
k = 1
Frequency =  1500.000 Hz
Amplitude =     1.000
Phase = -12.345679
DC =  0.250

Sin/Cos-Table, Data (cos(x))-Table:
k=0 : sin=  0.000000000 cos=  1.000000000 Data=  1.226875426
k=1 : sin=  0.195090322 cos=  0.980785280 Data=  1.249817157
k=2 : sin=  0.382683432 cos=  0.923879533 Data=  1.234336475
k=3 : sin=  0.555570233 cos=  0.831469612 Data=  1.181028295
k=4 : sin=  0.707106781 cos=  0.707106781 Data=  1.091941220
k=5 : sin=  0.831469612 cos=  0.555570233 Data=  0.970498815
k=6 : sin=  0.923879533 cos=  0.382683432 Data=  0.821368045
k=7 : sin=  0.980785280 cos=  0.195090322 Data=  0.650279922
k=8 : sin=  1.000000000 cos=  0.000000000 Data=  0.463809265
k=9 : sin=  0.980785280 cos= -0.195090322 Data=  0.269122039
k=10: sin=  0.923879533 cos= -0.382683432 Data=  0.073699963
k=11: sin=  0.831469612 cos= -0.555570233 Data= -0.114947001
k=12: sin=  0.707106781 cos= -0.707106781 Data= -0.289569257
k=13: sin=  0.555570233 cos= -0.831469612 Data= -0.443456168
k=14: sin=  0.382683432 cos= -0.923879533 Data= -0.570693948
k=15: sin=  0.195090322 cos= -0.980785280 Data= -0.666392920
k=16: sin=  0.000000000 cos= -1.000000000 Data= -0.726875426
k=17: sin= -0.195090322 cos= -0.980785280 Data= -0.749817157
k=18: sin= -0.382683432 cos= -0.923879533 Data= -0.734336475
k=19: sin= -0.555570233 cos= -0.831469612 Data= -0.681028295
k=20: sin= -0.707106781 cos= -0.707106781 Data= -0.591941220
k=21: sin= -0.831469612 cos= -0.555570233 Data= -0.470498815
k=22: sin= -0.923879533 cos= -0.382683432 Data= -0.321368045
k=23: sin= -0.980785280 cos= -0.195090322 Data= -0.150279922
k=24: sin= -1.000000000 cos= -0.000000000 Data=  0.036190735
k=25: sin= -0.980785280 cos=  0.195090322 Data=  0.230877961
k=26: sin= -0.923879533 cos=  0.382683432 Data=  0.426300037
k=27: sin= -0.831469612 cos=  0.555570233 Data=  0.614947001
k=28: sin= -0.707106781 cos=  0.707106781 Data=  0.789569257
k=29: sin= -0.555570233 cos=  0.831469612 Data=  0.943456168
k=30: sin= -0.382683432 cos=  0.923879533 Data=  1.070693948
k=31: sin= -0.195090322 cos=  0.980785280 Data=  1.166392920

FFT:
k=0  f=    0.000 Hz Re= 0.249999999999999970000 Im= 0.000000000000000000000 Mag= 0.249999999999999970000, Phase= 0.000000
k=1  f= 1500.000 Hz Re= 0.488437713033456510000 Im=-0.106904632671585720000 Mag= 0.499999999999999890000, Phase=-12.345679
k=2  f= 3000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=3  f= 4500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=4  f= 6000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=5  f= 7500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=6  f= 9000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=7  f=10500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=8  f=12000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=9  f=13500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=10 f=15000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=11 f=16500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=12 f=18000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=13 f=19500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=14 f=21000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=15 f=22500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=16 f=24000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=17 f=25500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=18 f=27000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=19 f=28500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=20 f=30000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=21 f=31500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=22 f=33000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=23 f=34500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=24 f=36000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=25 f=37500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=26 f=39000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=27 f=40500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=28 f=42000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=29 f=43500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=30 f=45000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=31 f=46500.000 Hz Re= 0.488437713033456620000 Im= 0.106904632671585540000 Mag= 0.499999999999999940000, Phase=12.345679

Lock-in Amplifier:
k=0 : f=    0.000 Hz Re= 0.249999999999999940000 Im= 0.000000000000000000000 Mag= 0.249999999999999940000, Phase= 0.000000
k=1 : f= 1500.000 Hz Re= 0.488437713033456510000 Im=-0.106904632671585650000 Mag= 0.499999999999999830000, Phase=-12.345679
k=2 : f= 3000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=3 : f= 4500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=4 : f= 6000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=5 : f= 7500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=6 : f= 9000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=7 : f=10500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=8 : f=12000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=9 : f=13500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=10: f=15000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=11: f=16500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=12: f=18000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=13: f=19500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=14: f=21000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=15: f=22500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=16: f=24000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=17: f=25500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=18: f=27000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=19: f=28500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=20: f=30000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=21: f=31500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=22: f=33000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=23: f=34500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=24: f=36000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=25: f=37500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=26: f=39000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=27: f=40500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=28: f=42000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=29: f=43500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=30: f=45000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=31: f=46500.000 Hz Re= 0.488437713033457070000 Im= 0.106904632671585340000 Mag= 0.500000000000000330000, Phase=12.345679

Goertzel:
k=0 : f=    0.000 Hz Re= 0.250000000000003550000 Im= 0.000000000000000000000 Mag= 0.250000000000003550000, Phase= 0.000000
k=1 : f= 1500.000 Hz Re= 0.488437713033456840000 Im=-0.106904632671585060000 Mag= 0.500000000000000000000, Phase=-12.345679
k=2 : f= 3000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=3 : f= 4500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=4 : f= 6000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=5 : f= 7500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=6 : f= 9000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=7 : f=10500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=8 : f=12000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=9 : f=13500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=10: f=15000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=11: f=16500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=12: f=18000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=13: f=19500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=14: f=21000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=15: f=22500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=16: f=24000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=17: f=25500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=18: f=27000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=19: f=28500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=20: f=30000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=21: f=31500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=22: f=33000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=23: f=34500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=24: f=36000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=25: f=37500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=26: f=39000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=27: f=40500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=28: f=42000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=29: f=43500.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=30: f=45000.000 Hz Re= 0.000000000000000000000 Im= 0.000000000000000000000 Mag= 0.000000000000000000000, Phase= 0.000000
k=31: f=46500.000 Hz Re= 0.488437713033460060000 Im= 0.106904632671580390000 Mag= 0.500000000000002220000, Phase=12.345679
End.

[Aziz]

Sound Blaster G3
It isn't the money worth!
Payed 35 bucks (+5 shipping), it is only 10 bucks worth!
The best part: USB-C to USB-A converter.

Creative, go to the hell!

[moodz]

Buy a 24 bit eval board ...or make ur own. Soundblaster have not made a good card for years.

[Aziz]

Buy a 24 bit eval board ...or make ur own. Soundblaster have not made a good card for years.

But the former models performed really very well (10 - 15 years ago however). I have boughts several models the last 20 years.

But the G3 is no good. It is band limitted to 22 kHz. SNR is bad too. Anyway, there are some other USB sound cards to test yet.
Did I say Creative go to the hell? I have to write a bad rewiew on Amazon yet.

G6 can be used for high frequency dual VLF/LF detector. And it has huge power to the TX coil.

[Aziz]

Btw guys,

the Goertzel and Lock-in Amplifier decoding can even be realised in the interrupt service routine (ISR) sample-by-sample. So you don't need DMA for block processing for embedded projects. Lock-in is optimal for the MAC operation (multiply and accumulate). You need two MAC's for each sample. After getting all the samples, the result must be calculated (scaling, sqrt, atan2). Sqrt and atan2 can be realised via pre-calculated tables of course, if you don't have much horse power in the embedded project.

I will provide you with C sample source code soon so you can see how it really works. Including FFT code to make some comparisons.

Cheers
Aziz

[Aziz]

Hi all,

haven't been able to work on the project yet due to lack of time. I'm still coding the c-modules so you can make use of the simple & correct demodulators. With example coding of course.

The memory management for internal buffers (sin/cos-tables) will be left to the caller (except fft). Two implementation types: block-processing and sample-by-sample processing for Goertzel and Lock-in Amplifier.

The interface API forces you to use demodulation frequencies multiple of bin frequency width so you don't have any leakage effect and don't need any windowing of the samples.

And I have found some new candidates for testing USB sound cards.

Aziz

[Aziz]

Look, what I have found!
http://www.dicks-website.eu/low_nois...rt1/part1.html
6 parts
Someone has tested more transistors for us.
The 0.2 nV/sqrt(Hz) voltage noise density is near.

An interesting reading.

[Carl-NC]

The 0.2 nV/sqrt(Hz) voltage noise density is near.

? I see 0.2uv rms

[Aziz]

? I see 0.2uv rms

See page 3. The ZTX 851, 853 and 857 comes very close to the level. With gain of 60 dB (1000 x).
Paralleling two or three of them and you are save below 0.2 nV/sqrt(Hz).
The amplifier on page 3 is the same topology I use in my preamp.
He takes 10 mA collector current. And 1 Ohm gain defining resistor. I didn't go as much (2 mA I think and 4.7 Ohm).
So we have some nice low noise transistor choises.

[Detectorist#1]

And how this old information for low noise amplifiers with input power transistor and ultra low source impedance is connected to real metal detector's schematic?