FFT and Spectrum Analyzer

How to use an oscilloscope as Spectrum analyzer...

I start to love my oscilloscope. I honestly can't say I have used something that works so well.

I have just finished to add the FFT functionality... and I was amazed with the results, accuracy and speed!

I'm sampling only @100MSPS , 2K buffer. 

1 MHz Sine wave

By applying 1 MHz sinewave, as you can see the spectrum analyzer is correctly indication 1 MHz. The smae indication you can get with the time cursor, but is not so funny with it. 

 after I have applied 1 MHz, I have then applied 2 MHz, 3MHz, and so  up to 40 MHz.
and the spectrum analyzer always gives the correct results:

2MHz sine wave

4 MHz sine wave

 10 MHz Sine wave

20 MHz Sine 

30 MHz sine

Square wave!

The square wave is the most interesting to watch from a spectrum point of view. As you probably know the square wave has got only odd harmonics, e.g. the 1st, 3rd , 5th etc.

Let see the spectrum on a 1 MHz and a 10 MHz square wave:

1 MHz Squarewave

As you can see, the spectrum analyzer correctly report the 1st, 3rf, 5th, 7th, etc. 

10 MHz Square-wave

a 10 MHz square-wave, and we can still see  all the odd harmonics! the Oscilloscope works very well!

 100 KHz Square-wave

100 KHz the spectrum analyzer still works OK, but the resolution is poor. the is due to the fact that with 2048 bytes of buffer, the minimum resolution I can get by sampling at 100 MHz is 100MHz/2048 = 48.8 KHz (approx)... so I was thinking that in the next prototype I will probably add more ram.... maybe changing the FPGA or adding extra ram on the board..

Vertical and Horizontal cursors

Adding more functionality on the Oscilloscope

Horizontal and vertical cursors

Designing a digital oscilloscope that is actually useful for a designer seems to be an hard task today for many company. Probably one reason is that the person who write the specs... most of the time.... is not a designer... It could be a very clever chap but sometime  doesn't use the oscilloscope very often.

For example one of the most useful function on a modern oscilloscope is to be able  to make horizontal and vertical measurement. Now while most oscilloscope have this functionality, a functionality very useful is to bring an horizontal cursor back to the screen, without the need to turn 100 times the knob, or without the need to zoom out, then bring the cursor in the middle, then zoom in, and so on.

I have added a simple button that does that for me! 

In many oscilloscope, for some reason the cursors interface is quite a mess, you need to press a button to switch between he cursor and when you press one more time you need to do again and again...

why make the life difficult?

see the GUI below and you immediately understand how it works.

Se you at next time.

AN oscilloscope that I would use in the lab

Getting better and better

The Oscilloscope it start to be good enough to bring it in the lab with me.

On the screen the user has all the information he needs.

I have slightly changed the look as well. 

I'm so happy to have started this project! I still can't believe I have done this!

Next time... I will:
adding the menu for Cursors, Measure, Math (with the FFT).

a working USB Occilloscope

The oscilloscope SW is very fast!

Last week end I finally found  a working solution for the interpolation algorithmic and tonight I decided to work on the SW side to make the SW very responsive. I'm very impressed how the GUI react with the commands considering the amount of work is doing to calculate the interpolation of a waveform.
I'm also impressed with the linearity displayed from the sinc(x) exp(-x^2/3) algorithm.
So now my task for the next day is to assemble the second channel on the PCB and to finish the SW.

The Oscilloscope is growing up

More waveform

I made a bit more work on the interpolation algorithm, I haven't finished yet... but for the time being I will stop for now to work on the interpolation algorithm as I have achieved some good result today.

So the Oscilloscope is still sampling only at 100 MHz! (200 MHz next week end I guess).

Let see some waveform:

 

1 MHz Sinewave

Not too bad I think... it is still possible to see some issues due to common mode noise that probably goes inside the input ( 1MHz) of the oscilloscope and is displayed, as at moment the oscilloscope is still not isolated from the PC I must leave with it until I isolate it.

 1 MHz squarewave

Not too bad I think, considering that the square wave is the function with lots of  harmonics   .

5 MHz sine wave 

not too bad I think

5 MHz square wave

Not too bad considering I'm sampling at 100 MHz!

10 MHz sine wave

pretty good!

10 MHz square wave

Not too bad  considering that the input is a 10 MHz square wave and I've got only 10 samples to rebuilds.

I wish to thanks all the person  that are following this blog  for the excellent suggestions on how to design the interpolation algorithm. When you buy an oscilloscope and you read sinc(x) interpolation. Don't believe it  without a good windowing you have overshoot all over the place. in my case I'm using a sin(x)e(-x^2/3) interpolation, the Gaussian works pretty well in reducing the overshoot. 

What to do now?

1) improve the SW

2) finish to design the isolator ( the noise should further reduce)

3) sample at 200 MSPS ( so far I haven't done because of a mistake of mine in choosing the clock pin of the FPGA)

Still problems on the interpolation

I love DSP but I'm bad at it!

It looks like I'm a bad SW designer... 

I'm still not sure I understood how to interpolate a raw data from the FPGA buffer to the screen.

In the picture below I have in yellow the raw data from the FPGA, and in red the interpolated data using the sinc(x) algorithm.

Now how you can see, there is nothing that suggest why I should have all that ringing.

In order to show the problem even better I have zoomed the image(see below): in red I still have the interpolated data, while in yellow I have the raw data.

From the raw data, I can see some small ringing that for some reason get amplified in red when I interpolate .

For example if you look at that negative edge... it doesn't look right isn't it? 

the above GUI is written using Lazarus . The function that create the interpolated data is :


function sinc_interpolation(buff: TCH_BUFF; Fsample: float; t: float): float;
var
  i: integer;
  sum: float = 0;
  x_nt: float;
  Ts: float = 0;

begin

 {
  x(t) = sum [ Xn sinc(pi/T(t-nT))] sum all the n...
  }

  Ts := 1 / FSample;  // sample time
  sum := 0;
  for i := 1 to BUF_SIZE - 2 do // remember to fix the bug inside the FPGA
  begin
    x_nt := buff[i] * sinc((t - i * Ts) / Ts);
    sum := sum + x_nt;
  end;
  Result := Sum;

end;  
When I call that function I set:
 Fsample = 100000000.0; (100 MHz)
t = time I want to diplay on the screen ( I start to calculate t  starting from the middle of the buffer)
and buff is the buffer from the FPGA

Do you think the code  above is correct?
any comment is welcome.

improving the sinc(x) interpolation

I need to improve the interpolation algorithm

I'm working on the sinc(x)/x algorithm... and I'm having some trouble understanding some effect I can see on the scope.

in the picture below I'm displaying on CH1 the interpolated signal, while on CH2 I'm displaying the FPGA buffer

the first  picture is is a sinewave 1 MHz  as you can see the sinewave is a bit wobbly...  the problem is that if I use a linear interpolation to display CH1... then it looks not too bad ( see old post)

The wobbly effect is more evident when I use a triangle wave... as you can see... I do have some problem...

now I'm running out of idea... any suggestion is really welcome!

Oscilloscope specifications

Oscilloscope DSO-2-200-B

Characteristics

Characteristics	DSO-2-200-B
Bandwidth	20 MHz
Channels	2
Sample Rate on Each channel	200 MS/s
Record Length	3K points at all time base on all mode
Vertical resolution	8
Vertical sensitivity	5mV/div to 5 V/div on all modes
DC Vertical accuracy	3.00%
Vertical Zoom	Vertically expand or compress a live or stopped waveform
Maximum input voltage	100 Vrms derated at 20 dB/decade above 50 Khz
Position range	5mV to 500 mV/div (1:1 probe) 50 mV to 5V/div (1:10 probe)
Input coupling	AC, DC
Input impedence	1 Mohm, in parallel with 20pF
Time Base Range	20 ns to 5 s/div
TimeBase accuracy	50 ppm
Horizontal Zoom	Horizontally expand or compress a live or stopped waveform

Acquisition mode

Mode	Description
Peak Detect	Capture Glitches as narrow as 30 ns at all base setting
Sample	Raw data
Average	Waveform avareged, selectable 4,16
Single sequence	To capture a single event
Roll	At acquisition time > 100 ms/div

Trigger Types

Trigger	Description
Edge (rising, falling)	Positive or negative slope on any channel, coupling selection AC, DC
Pulse width	Trigger on a pulse width less than, greater than, equal to, or not equal to, a selectable time limit from 30 ns to 1 sec

Trigger source

CH1, CH2

Cursors

Characteristic	Description
Types	Amplitude, Time
Measurement	t1-t2,Freq, V1-V2

Automatic waveform measurement

+Width, -Width, Rise time, Fall time, Max, Min, Peak-Peak, RMS

Waveform Math

Characteristic	Description
Operators	+ , - , * , FFT
FFT	Hanning, 2048 sample points
Sources	CH1, CH2 of any combination above

Connection to a PC

Characteristic	Description
Connection to a PC	USB. Default, option Ethernet
OS supported	Windows7, Windows8

10 MHz Input square wave

Time to play!

I'm still sampling at 100 MHz! the input signal is a 10 MHz square wave.

CH1 shows the actual square wave, while CH2 at moment shows the FPGA raw buffer.

I'm using the sinc(x) interpolation to rebuild the original wave form, and I've learnt 2 things.

1. From a spectrum point of view the beginning of the raw data is seen as a step  gradient, which goes against the hypothesis of  the Shannon theorem. That explain the first "distortion" of the CH1. 

So it's easy to fix.

2. Now the second point is that the square wave is a little wavelike on the top  and bottom... that I guess is because I haven't fixed the problem of the floor noise completely yet!

Therefore I'm going to work on that now.

1. by fixing the noise floor I think the square wave will look even better.

2. I could further improve the waveform by play with the delay in the DLL, so I could create an equivalent sample of 1 GSPS  and therefore the waveform should look very squared. ( Now I understand why so many USB oscilloscope use the ETS)

Any suggestion is welcome. 

First experiment with the sinc(x) interpolation

Sinc(x) interpolation

The Shannon Theorem states that given a signal  limited in bandwidth with the maximum harmonic fc <= 1/2 Fsample you can rebuild the original signal by interpolating :

I am applying on CH1 and CH2 a constant signal, and I'm plotting CH2 with a linear interpolation and CH1 with a Sinc(x) interpolation... unfortunately it looks like I'm a bad DSP designer as CH1 is the sinc itself! :-)
I wanted to write it  down because I found the CH1 waveform funny.  Its actually pretty!
So... last week I made lot's of progress, I'm now sampling at 100 MSPS... on the above picture the horizontal resolution is 20 nsec/div...
I will post again once I fixed the sinc(x) problem!

Another little step

Getting better

Yesterday night  I promised myself to work on the SW side as I knew the noise issue was easy to fix... But as hardware engineer I wanted to fix it.
As you can see, the Oscilloscope it start to be useful! The next 2 pictures are showing a sine wave and a square wave of 2.31 Vpp , 500 KHz. Please notice that the X, Y scale is still not working!

The first waveform

It start to work!!

This is my first waveform! the X and Y scaling are still not working...
I am applying an input signal of only  280 mVpp, 50 KHz sine wave .  How you can see below at moment the scope has a floor noise of 4 - 5 mV which I believe I can fix.
The noise floor is due to the FTDI chip .
Unfortunately the FTDI USB chip (at moment) is not isolated from my Scope, and this seems causing some noise issues. My plan is to insert a galvanic insulation between the scope and the FTDI, and I guess the Noise floor should improve.

My plan for next week:
work on the SW side only, so the scope start to behave like a proper scope.
maybe (if I've got time ) solder the channel 2 .

API building

I started designing the API to communicate with the oscilloscope

When I run the SW and you press the connect button the SW check how many oscilloscopes are connected if more than one, then you need to select one. So... in theory you can connect as many oscilloscope you want on a PC.
then check for the Device ID and the revision. it depend from the device ID, the behavior of the SW will be different.
I can now control the AC/DC  coupling, and control the overall GAIN and attenuation of the input stage amplifier!
See you soon!