what an oscilloscope recommended for a woman passionate about electronics?

[rstofer]

Charlotte,

You may find this interesting:

[CharlotteSwiss]

Now you're getting into Fourier Transforms - a mathematical representation of arbitrary signals.  The math gets deep - quick!

https://en.wikipedia.org/wiki/Fourier_transform

First the answer:  A square wave with 0 ns risetime is composed of sine waves of the fundamental frequency plus the sum of all the odd harmonics from DC way up to daylight (a really high frequency).  All of the odd harmonics - an infinite number of them.  Each harmonic (spike on graph) is at a decreasing amplitude so, for practical purposes, we might stop calculating at some reasonable frequency where the amplitude is getting pretty close to 0V.

You should see a spike at 1 kHz and then all of the odd harmonics 3 kHz, 5 kHz, 7kHz, etc out as far as the scope can go (or maybe it is limited by a maximum frequency setting).  When looking at a 1 kHz fundamental, it wouldn't make sense to go as far as 1 MHz and certainly not 50 MHz.  That would be the 50,000th harmonic!

You might also have a spike at 0 Hz if there is a DC component - a square wave from 0V to 3.3V.  This has a DC value of 1.65V and we talked about this weeks ago.  If the waveform is symmetric (AC coupled), the 0 Hz spike should disappear.

3blue1brown does a good job in this video

finally I have a few hours to dedicate to my oscilloscope, or rather to the FFT function.
I will go in small steps: I start with these considerations of yours and on that nice video where you switch from the classic intensity-time signal to an FFT graph through examples around a circle. For now I understand that if the signal is alternating, the graph should start from the center, while if we have a DC component it will start from the top. Then I realized that the signal oscillates around the zero of the graph, and has peaks (for now only upwards) when it reaches the signal frequency (if the signal is 3Hz, we will have peaks at 3, 6, 9, 12 Hz etc)
For now I have not yet considered what a harmonic represents (even, odd) and how it is represented, I'll get to it then I think ..
Ok now I see the next suggestions ..
:-)
thanks rstofer

[tautech]

A quick look at the SDS1104X-E FFT from May 2018 where since then the Markers have been added in later firmware and also to SDS1202X-E FFT.
Their FFT functionality is the same.

https://youtu.be/Cwbwq-AKbPc?t=406

[CharlotteSwiss]

Specifically, what you are seeing is the spikes at 0V, 1kHz, 3kHz, 5kHz...49999kHz - all of the odd harmonics up to 50 MHz.  You need to stop the upper frequency at around 9 kHz or 11 kHz (the odd 9th and 11th harmonics).

doing the practical example on my compensation signal (if I remember correctly coupled AC maybe, but it is not important ..)
I have reduced the x axis of FFt to 10Khz with 1Khz hz / div.
What can I understand from the 1Khz compensation signal?
The peaks in the FFT graph correspond to each ramp of the signal; I have 1 peak every signal period; in the FFt graph each peak occurs at 1Khz, then 3Khz, 5 Khz etc. etc. or at each multiple frequency of the original frequency, except for the positive frequencies; I can also see that each peak gradually decreases in value on the Y axis (0 / -10 / -18 / -20 etc ..)
Now I have to rearrange my ideas and understand what this teaches me!

(yes I saw the sum of signals in the video, now I'm analyzing only 1 signal, it is obvious that the FFt graph can also represent a sum of signals)

edit after 5 minutes of reasoning:
so from what you wrote (9Khz = ninth harmonic) a signal harmonic has a width x = signal frequency!
Different example: the signal was at 3Khz, in the FFT graph the ninth harmonic would have been at 27Khz in the x graph
maybe I'm starting to understand something .. 

[CharlotteSwiss]

A quick look at the SDS1104X-E FFT from May 2018 where since then the Markers have been added in later firmware and also to SDS1202X-E FFT.
Their FFT functionality is the same.

https://youtu.be/Cwbwq-AKbPc?t=406

thanks taut, in the evening I also watch this video 

[borjam]

doing the practical example on my compensation signal (if I remember correctly coupled AC maybe, but it is not important ..)
I have reduced the x axis of FFt to 10Khz with 1Khz hz / div.
What can I understand from the 1Khz compensation signal?
The peaks in the FFT graph correspond to each ramp of the signal; I have 1 peak every signal period; in the FFt graph each peak occurs at 1Khz, then 3Khz, 5 Khz etc. etc. or at each multiple frequency of the original frequency, except for the positive frequencies; I can also see that each peak gradually decreases in value on the Y axis (0 / -10 / -18 / -20 etc ..)
Now I have to rearrange my ideas and understand what this teaches me!

(yes I saw the sum of signals in the video, now I'm analyzing only 1 signal, it is obvious that the FFt graph can also represent a sum of signals)

It's not difficult to understand, sometimes a bit more difficult to explain

The signals we see in the real world, and I mean not only electrical signals, but sounds, are complex. These "complex" signals can be represented like a sum of components, each component having the waveform of a sinusoid. You could call a sinusoid a "pure" signal.

So, let's say you are listening to music. You have an amplifier with the typical "bass" and "treble" tone controls. If you turn down the treble you will notice that the sound changes. You are reducing the level of the high frequency components.

For periodic signals you can still measure a frequency (for a music sound that would give you the note) which is the lowest frequency component. That's called the "fundamental". And most of the complex signals you will find (again, imagine the sound of a flute although some evil instruments such as bells are different) are a sum of a fundamental and a series of components that have a special property: their frequency is a multiple of that of the fundamental. They are called harmonics

So, if the fundamental (hence, the signal) has a frequency f, the harmonics will have frequencies 2*f,  3*f, 4*f, 5*f, etc.

The funny thing is, by summing those harmonics you don't perceive different signals being added together, but "sound texture" changes. Imagine a trumpet, a pipe organ and a flute playing the same note. The frequency is the same but the levels of the harmonics are different.

By decomposing a signal into its components you can find out a lot about it. First, many waveforms are quite similar despite having a very different sound. Decomposing the signal into its components makes it easier to study.

And that by examining the composition of the signal, which is called the spectrum, you can learn a lot about it and it can help you diagnose some faults. The Fourier transform is the mathematical method to obtain the spectrum of a signal, and the FFT (Fast Fourier Transform) is an especially optimized method to compute the Fourier transform so that it runs much faster, hence being more efficient.

Now you can see why the spectrum of the square wave in your calibration output looks like that. It is a sum of a signal at frequency f and harmonics with odd mutiple frequency (3*f, 5*f, 7*f, 9*f...) each with an amplitude 1/3, 1/5, 1/7, 1/9...

So it would be (WARNING, NOT CORRECT EQUATION BUT TRYING TO MAKE IT MORE INTUITIVE)

sin(f*t) + 1/3 sin (3f*t) + 1/5 sin(5f*t) + 1/7 sin(7f*t)...

You can try a function generator and compare the spectrums of square, sawtooth and triangular signals for example.

Also, do you know why telephone voice sounds so bad? Yes, the narrow bandwidth transmits very few of the signal components.

I forgot, for an intuitive treatment of the matter, especially good if you like music,

"The Science of Musical Sound" by John R Pierce.

And it's a really deep subject. It is also related to the amount of information you can send over a transmission channel, go figure!

[rstofer]

I have been trying to avoid the math, it gets out of hand pretty fast!

For a square wave:

Look at equation 7:  What this is saying is that the square wave is formed of some constant (4/pi) times the sum of the odd harmonics with amplitude of 1/n (the harmonic number).  The third harmonic will have an amplitude of 1/3 while the 5th has an amplitude of 1/5.  In other words, the amplitude of any harmonic is 1/harmonic number.  Higher harmonics contribute less and less.

n is the harmonic number and 1/n is the amplitude of that harmonic,

https://mathworld.wolfram.com/FourierSeriesSquareWave.html

Another way of writing it:

a square wave = sin(x) + sin(3x)/3 + sin(5x)/5 + ... (infinitely)

Here you can see how the amplitude and harmonic number are used to determine the contribution of each frequency. 5x is the 5th harmonic and its amplitude is 1/5

https://www.mathsisfun.com/calculus/fourier-series.html

The relationship between the edge transitions of the square wave and the frequency spikes is probably just a happenstance.  What you care about in the FFT is the amplitude of the various spikes and you can see that their amplitude is decreasing just like predicted from the stuff I wrote above.  You will notice that only odd harmonics are present and they are of diminishing amplitude.

This is truly an advanced topic so it may take a while to sink in.  As I said earlier, I think it was a 3rd year topic.

When you look at a signal on a scope, you are looking at its amplitude as a function of time.  You are working in the 'time domain' where time is on the X axis.  When you look at an FFT of that signal, it is frequency along the X axis and you are viewing the signal in the frequency domain (what frequencies does it contain and at what amplitude).  Time and frequency are inverses of each other.  1/frequency = time per cycle.  Of course it does:  cycles per second (frequency) is the inverse of seconds per cycle (period).

As you can see from the linked article, the math gets pretty ugly.  And that is for a simple waveform like a square wave.

[CharlotteSwiss]

thanks borjam and rstofer, tonight I read your contributions well, for sure they will help me a lot, then I'll let you know
 

[CharlotteSwiss]

When we take the FFT of a signal, we are trying to find out what frequencies are present and their amplitude.  The grass at the bottom of the trace is the noise floor.  We usually ignore it.

We want to see the frequency of each significant spike and the amplitude.

Khan Academy (world famous for Saul Khan's mathematics series) also has a series on Electrical Engineering.  Here is a link to the beginning of the Fourier Series topic:

https://www.khanacademy.org/science/electrical-engineering/ee-signals/ee-fourier-series

Here is a link to the beginning of the EE program:

https://www.khanacademy.org/science/electrical-engineering

I'm not trying to push the AWG issue again but the Siglents allow you to create a fundamental sine wave and then add in a number of odd or even harmonics at adjustable amplitudes.  In the Fourier program above, Saul is creating a more-or-less square wave out of the fundamental, 3rd, 5th and 7th harmonics at declining amplitude.  You can see how, with an increasing number of harmonics, the waveform gets more and more 'square'.  You can do this with the Siglent SDG 1032X.  You can pick a fundamental frequency and then keep adding harmonics while watching the waveform on your scope.  Not all AWGs have this capability so make sure you read the datasheets.  That Valentine's Day Heart is a terrific example of using harmonics with appropriate phase and amplitude values to create a really strange waveform.  Note that it really IS a waveform.  It has a beginning and end as well as continuous values over the range.  Mathematically, it would just be considered magic.

And that is how you learn what the FFT, indeed the entire topic of Fourier Analysis, is all about.  We can hand wave and watch videos until the cows come home but the real learning happens on the bench.

This topic of Fourier Analysis is the basis for all signal processing.  It is terribly important but it takes time to come to grips with it.

Khan Academy for math and the EE track at Khan Academy are my two favorite resources.  3blue1brown is also a great resource.  If I were in college, or even high school, I would want to know about desmos.com for graphing and symbolab.com for solving.  Great resources!

i watched khan academy videos, but they are not very easy for beginners to understand, i understand better the one of 3blue.
While the video posted later (arduino and basic oscilloscope), I understood almost everything as by studying the manual I had already learned those things.
 

[CharlotteSwiss]

For giggles, I created the attached image which uses a 1 kHz fundamental sine wave at 1Vpp plus 3 kHz at 0.33Vpp plus 5 kHz at 0.2Vpp (voltages aren't the exact coefficients but close enough for a demonstration).

You can see where the sine waves have added together in such a way that they begin to look like a square wave.  This stuff is MAGIC of the highest order!

The FFT is scaled at 2kHz/div so the first spike is at 1 kHz, the next at 3 kHz and finally one at 5 kHz. Note that there is no DC spike, the waveform is symmetric about 0V.  You can see the decreasing amplitude of each harmonic.
(Attachment Link)

so in this example we have three sine waves that add up, and the FFT graph shows us the 3 peaks that correspond to the frequency of each summed wave (1-3-5 khz) 

[CharlotteSwiss]

It's not difficult to understand, sometimes a bit more difficult to explain

The signals we see in the real world, and I mean not only electrical signals, but sounds, are complex. These "complex" signals can be represented like a sum of components, each component having the waveform of a sinusoid. You could call a sinusoid a "pure" signal.

So, let's say you are listening to music. You have an amplifier with the typical "bass" and "treble" tone controls. If you turn down the treble you will notice that the sound changes. You are reducing the level of the high frequency components.

For periodic signals you can still measure a frequency (for a music sound that would give you the note) which is the lowest frequency component. That's called the "fundamental". And most of the complex signals you will find (again, imagine the sound of a flute although some evil instruments such as bells are different) are a sum of a fundamental and a series of components that have a special property: their frequency is a multiple of that of the fundamental. They are called harmonics

So, if the fundamental (hence, the signal) has a frequency f, the harmonics will have frequencies 2*f,  3*f, 4*f, 5*f, etc.

The funny thing is, by summing those harmonics you don't perceive different signals being added together, but "sound texture" changes. Imagine a trumpet, a pipe organ and a flute playing the same note. The frequency is the same but the levels of the harmonics are different.

By decomposing a signal into its components you can find out a lot about it. First, many waveforms are quite similar despite having a very different sound. Decomposing the signal into its components makes it easier to study.

And that by examining the composition of the signal, which is called the spectrum, you can learn a lot about it and it can help you diagnose some faults. The Fourier transform is the mathematical method to obtain the spectrum of a signal, and the FFT (Fast Fourier Transform) is an especially optimized method to compute the Fourier transform so that it runs much faster, hence being more efficient.

Now you can see why the spectrum of the square wave in your calibration output looks like that. It is a sum of a signal at frequency f and harmonics with odd mutiple frequency (3*f, 5*f, 7*f, 9*f...) each with an amplitude 1/3, 1/5, 1/7, 1/9...

So it would be (WARNING, NOT CORRECT EQUATION BUT TRYING TO MAKE IT MORE INTUITIVE)

sin(f*t) + 1/3 sin (3f*t) + 1/5 sin(5f*t) + 1/7 sin(7f*t)...

You can try a function generator and compare the spectrums of square, sawtooth and triangular signals for example.

Also, do you know why telephone voice sounds so bad? Yes, the narrow bandwidth transmits very few of the signal components.

I forgot, for an intuitive treatment of the matter, especially good if you like music,

"The Science of Musical Sound" by John R Pierce.

And it's a really deep subject. It is also related to the amount of information you can send over a transmission channel, go figure!

you explained very well, let's see what I understood and what is still not clear in my head.
A complex signal is composed of several components, the component with the lowest frequency is called "the fundamental"; the other components are called harmonics.
Harmonics have a frequency which is a multiple of the fundamental frequency.
So if the fundamental has frequency f, the first harmonic will have frequency fx2, the second fx3, etc.
The FFT function is basically the mathematical function of the signal spectrum, and it helps to examine the components of a signal.
In my image of the compensation signal FFT, we can therefore say that the frequency of the square wave is 1Khz, and this frequency represents the fundamental. Then there are the harmonics represented by the peaks going to the right at 3Khz, 5Khz, 7Khz etc.
But the question comes naturally to me: why are the harmonics of the signal only the odd ones? (3xf- 5xf etc)?
the even harmonics (2xf- 4xf etc.) are not contained in this signal?
thank you

[CharlotteSwiss]

I have been trying to avoid the math, it gets out of hand pretty fast!

For a square wave:

Look at equation 7:  What this is saying is that the square wave is formed of some constant (4/pi) times the sum of the odd harmonics with amplitude of 1/n (the harmonic number).  The third harmonic will have an amplitude of 1/3 while the 5th has an amplitude of 1/5.  In other words, the amplitude of any harmonic is 1/harmonic number.  Higher harmonics contribute less and less.

n is the harmonic number and 1/n is the amplitude of that harmonic,

https://mathworld.wolfram.com/FourierSeriesSquareWave.html

Another way of writing it:

a square wave = sin(x) + sin(3x)/3 + sin(5x)/5 + ... (infinitely)

Here you can see how the amplitude and harmonic number are used to determine the contribution of each frequency. 5x is the 5th harmonic and its amplitude is 1/5

https://www.mathsisfun.com/calculus/fourier-series.html

The relationship between the edge transitions of the square wave and the frequency spikes is probably just a happenstance.  What you care about in the FFT is the amplitude of the various spikes and you can see that their amplitude is decreasing just like predicted from the stuff I wrote above.  You will notice that only odd harmonics are present and they are of diminishing amplitude.

This is truly an advanced topic so it may take a while to sink in.  As I said earlier, I think it was a 3rd year topic.

When you look at a signal on a scope, you are looking at its amplitude as a function of time.  You are working in the 'time domain' where time is on the X axis.  When you look at an FFT of that signal, it is frequency along the X axis and you are viewing the signal in the frequency domain (what frequencies does it contain and at what amplitude).  Time and frequency are inverses of each other.  1/frequency = time per cycle.  Of course it does:  cycles per second (frequency) is the inverse of seconds per cycle (period).

As you can see from the linked article, the math gets pretty ugly.  And that is for a simple waveform like a square wave.

thanks for the explanation, no math at the moment it is better to leave it aside; for now I just need to understand the basics, or what that FFT chart can tell me.
As you wrote, with FFt we are interested in seeing the amplitude of the harmonics and that it is decreasing (1 / 3- 1/5 etc ..); in fact in my image the harmonics (represented by the peaks at 1- 3- 5-7-9 etc. of frequency), you can clearly see that the peak is decreasing. But if we want to give a value to these amplitudes that degrade, we must look at the y axis: it may therefore be reasonable to state that the first harmonic has an f 1Khz and an amplitude 0db, the third harmonic has f3khz and an amplitude -10db, the fifth harmonic has f5khz and amplitude -17db and so on to infinity?
I then quote your sentence: You will notice that only odd harmonics are present and they are of diminishing amplitude.
Yes I noticed, but as I asked above, are positive harmonics not present in the signal?
 

[borjam]

you explained very well, let's see what I understood and what is still not clear in my head.
A complex signal is composed of several components, the component with the lowest frequency is called "the fundamental"; the other components are called harmonics.
Harmonics have a frequency which is a multiple of the fundamental frequency.

Yes, those components are called harmonics because their frequency is a multiple of the fundamental.

Why the "harmonics" name? It comes from music. In music, when you raise a tone by an octave you are actually doubling frequency. And if you play together two notes in different octaves (try on a piano, for example to play two Cs together) you will perceive it as a single note. +

The FFT function is basically the mathematical function of the signal spectrum, and it helps to examine the components of a signal.
In my image of the compensation signal FFT, we can therefore say that the frequency of the square wave is 1Khz, and this frequency represents the fundamental. Then there are the harmonics represented by the peaks going to the right at 3Khz, 5Khz, 7Khz etc.
But the question comes naturally to me: why are the harmonics of the signal only the odd ones? (3xf- 5xf etc)?
the even harmonics (2xf- 4xf etc.) are not contained in this signal?

Well, that signal is square because if you add a series like that, a fundamental with odd harmonics and with those amplitudes, you obtain a square signal.

But for example, a sawtooth contains both odd and even harmonics.

https://en.wikipedia.org/wiki/Sawtooth_wave

[rstofer]

We usually start discussing FFT with a square wave because it has a simple Fourier Series expansion.  The sum of the ODD harmonics from the fundamental all the way out to infinity.  A square wave has only odd harmonics and all of the harmonics are in phase  Other signals may have both odd and even frequencies (not necessarily harmonics of the fundamental) with arbitrary amplitude and phase.  The thing is, the math gets too complex to deal with unless you are really up to speed with the process.

In engineering, we need to be aware of the underlying math but we don't need to specialize in it.  We only want to use the tool (FFT in this case), we don't need to reinvent it.

The most popular method for calculating the Fourier Transform is the Cooley-Tukey approach.

https://en.wikipedia.org/wiki/Cooley%E2%80%93Tukey_FFT_algorithm

That paper gives a clean example of why this is a 3rd year topic.  I have used the FFT exactly once in the 30 years I worked in electrical engineering after undergrad.  It was interesting but once was enough.


More often than not, we're just curious about the spectrum and not necessaryily the series expansion itself.

Here is a fairly simple explanation of the Fourier Series for a square wave.  Note how it is symmetric around the X axis (+ and - amplitudes).  This is done to make the math simpler.  Each step in creating the series is shown.  All of the cos() terms drop out as do all of the sin(x) where x is an even harmonic.

https://www.mathsisfun.com/calculus/fourier-series.html

This is about as easy an explanation as there can be for the Fourier Series expansion of a square wave.

Under "Finding the Coefficients" there is a complete expression for the general Fourier Series.  This is a general expansion for any complex waveform, it remains an exercise to determine the values of the coefficients.  For a square wave, there are no cos() terms so all 'a' terms drop out and only the odd terms exist for the sin().  Other waveforms will not have so many terms drop out.  And, remember, the series usually has an infinite number of terms.  That's why the sums are taken from n=1 to n=infinity (which it never can, there is always 1 more term).

[CharlotteSwiss]

Yes, those components are called harmonics because their frequency is a multiple of the fundamental.

Why the "harmonics" name? It comes from music. In music, when you raise a tone by an octave you are actually doubling frequency. And if you play together two notes in different octaves (try on a piano, for example to play two Cs together) you will perceive it as a single note. +

Well, that signal is square because if you add a series like that, a fundamental with odd harmonics and with those amplitudes, you obtain a square signal.

But for example, a sawtooth contains both odd and even harmonics.

https://en.wikipedia.org/wiki/Sawtooth_wave

I begin to understand better now.
I have reported below the FFT image of the sawtooth signal:
The fundamental as they say is at 220Hz, and therefore is the first peak that I marked in red: we can say that in a signal, the fundamental is the harmonic with the lowest frequency and with the greatest amplitude. We can indicate the fundamental with f1 (first odd harmonic), followed by f2 (first even harmonic), f3 (second odd harmonic) etc. etc.
In the specific case, since the fundamental is 220Hz, we will have the first harmonic equal to 440Hz, the second odd harmonic to 660Hz .......
At the same time the amplitude is decreasing: second harmonic will be f/2, third harmonic will be f /3 etc.
A signal like this in music will make us hear mainly the sound of the fundamental, while the downward harmonics will be less and less audible.
We can also affirm that every harmonic in practice is a sinusoid, and the sum of the sinusoids then makes us a signal displayed on the oscilloscope that is not necessarily sinusoidal (such as a square wave).
I have two points that are still unclear:
1) in the FFt graph we said that the x axis represents the frequency ok; the y axis represents the amplitude, I don't understand the unit of measurement though? why not turn? why dbv? and we have a standard reference of db? in the example below the first harmonic I see that it has a value of about 200db, what does it mean? why does it have that value?
2) in the FFT spectrum do we focus only on the upward peaks? the downward ones have no significance / meaning?

thank you 

[CharlotteSwiss]

We usually start discussing FFT with a square wave because it has a simple Fourier Series expansion.  The sum of the ODD harmonics from the fundamental all the way out to infinity.  A square wave has only odd harmonics and all of the harmonics are in phase  Other signals may have both odd and even frequencies (not necessarily harmonics of the fundamental) with arbitrary amplitude and phase.  The thing is, the math gets too complex to deal with unless you are really up to speed with the process.

In engineering, we need to be aware of the underlying math but we don't need to specialize in it.  We only want to use the tool (FFT in this case), we don't need to reinvent it.

The most popular method for calculating the Fourier Transform is the Cooley-Tukey approach.

https://en.wikipedia.org/wiki/Cooley%E2%80%93Tukey_FFT_algorithm

That paper gives a clean example of why this is a 3rd year topic.  I have used the FFT exactly once in the 30 years I worked in electrical engineering after undergrad.  It was interesting but once was enough.


More often than not, we're just curious about the spectrum and not necessaryily the series expansion itself.

Here is a fairly simple explanation of the Fourier Series for a square wave.  Note how it is symmetric around the X axis (+ and - amplitudes).  This is done to make the math simpler.  Each step in creating the series is shown.  All of the cos() terms drop out as do all of the sin(x) where x is an even harmonic.

https://www.mathsisfun.com/calculus/fourier-series.html

This is about as easy an explanation as there can be for the Fourier Series expansion of a square wave.

Under "Finding the Coefficients" there is a complete expression for the general Fourier Series.  This is a general expansion for any complex waveform, it remains an exercise to determine the values of the coefficients.  For a square wave, there are no cos() terms so all 'a' terms drop out and only the odd terms exist for the sin().  Other waveforms will not have so many terms drop out.  And, remember, the series usually has an infinite number of terms.  That's why the sums are taken from n=1 to n=infinity (which it never can, there is always 1 more term).

rstofer I admit that the math chapter (therefore also FFT), up to now is perhaps the most complex part that I have studied in the manual, for this I have some difficulties, but now I already have a freer mind ...

Ok I understand, a square wave signal, if we break it down we will have a fundamental and an infinite series of only dispai harmonics: all harmonics are in phase!
If we had a signal that contains odd and even even harmonics, the even ones would not be in phase with the odd ones (indeed perhaps the same even harmonics are not in phase with each other)

I agree that I don't want to go into Fourier mathematics, but I just need to have the basics to understand what I'm seeing in the FFT spectrum of a signal, and maybe be able to understand if everything is fine in that signal or we have something unusual, that's all.

looking at the link of the mathsisfun site, it is quite clear how a square wave is composed, that is, it should have a sinusoidal fundamental with 1 cycle per period, then the next harmonic is a sinusoidal with 3 cycles per period, then 5 cycles per period and so on. .. at about 99 cycles ... adding all the previous harmonics up to now, the signal on the display increasingly assumes the classic square wave shape!

Adesso forse ho capito meglio lo spettro FFT, almeno quando lo guardo adesso so cosa cerca di suggerirmi..
Poi avrò modo di capire magari come può aiutarmi, nel mio piccolo, a verificare un segnale.

Now maybe I understand the FFT spectrum better, at least when I look at it now I know what it tries to suggest to me ..
Then I will have the opportunity to understand maybe how it can help me, in my small way, to verify a signal.
My example on the compensation signal, we have only one square wave signal from the ch1 probe; i guess if i had two different signals (ch1 and ch2), the FFT spectrum represents both of them i think, i have to check ...

very thanks 

[CharlotteSwiss]

I tried with other signals (using an online generator for now ..), just to change frequency or type of wave, just to better understand:
800Hz sine wave.
Being a perfect sine wave, the FFT graph shows us its fundamental peak at 800Hz .. and then no other harmonic evident .. but a falling linear graph

[CharlotteSwiss]

again square wave, but with 800Hz frequency: we have the fundamental at 800Hz and then a series of odd harmonics (2400hz, 4000hz ...) of decreasing amplitude

[CharlotteSwiss]

800Hz sawtooth wave: we can appreciate the fundamental at 800Hz, and then all the harmonics both even and odd (first equal to 1600hz, second odd at 2400hz, etc.)

Instructive

[borjam]

The FFT has a limited accuracy, so the spectrum of a signal will never look like a set of vertical bars,
but more like vertical peaks with a broader base.

There are several parameters you can adjust if you need more accuracy in the time or frequency domain,
but if I were you I would wait before diving into there at least for now

[CharlotteSwiss]

The FFT has a limited accuracy, so the spectrum of a signal will never look like a set of vertical bars,
but more like vertical peaks with a broader base.

There are several parameters you can adjust if you need more accuracy in the time or frequency domain,
but if I were you I would wait before diving into there at least for now

thanks, yes for now I am satisfied to understand what the FFT spectrum shows me ... and I have understood this by now, except for a few things.
Then understand when it might be useful to view a signal with FFT (for example if there are harmonics that disturb the signal it could be a good reason, I would probably see a harmonic with a non-decreasing amplitude but with an anomalous peak ..)
 

[borjam]

thanks, yes for now I am satisfied to understand what the FFT spectrum shows me ... and I have understood this by now, except for a few things.
Then understand when it might be useful to view a signal with FFT (for example if there are harmonics that disturb the signal it could be a good reason, I would probably see a harmonic with a non-decreasing amplitude but with an anomalous peak ..)
 

There are many possible reasons to check the signal spectrum with a FFT.

- You might want to check the frequency response of a circuit

- You might want to look at the spectrum of a distorted signal in order to check whether it matches what you expected.

- In a circuit that, for example, produces a dirty signal (imagine a switch mode power supply) you can find out whether it can be easy to filter out the unintended signal components.


... And so on, whenever you wonder "what's the spectrum of this signal?"

[CharlotteSwiss]

it is always useful to know how to understand an FFT spectrum, so I wanted to understand how it works, at least the basic things.
I imagine that harmonics can be a source of disturbance in many signals
 

[rstofer]

I have reported below the FFT image of the sawtooth signal:
The fundamental as they say is at 220Hz, and therefore is the first peak that I marked in red: we can say that in a signal, the fundamental is the harmonic with the lowest frequency and with the greatest amplitude. We can indicate the fundamental with f1 (first odd harmonic), followed by f2 (first even harmonic), f3 (second odd harmonic) etc. etc.
In the specific case, since the fundamental is 220Hz, we will have the first harmonic equal to 440Hz, the second odd harmonic to 660Hz .......

By convention, the first harmonic IS the fundamental, 220 Hz.  The second harmonic is 440 Hz, etc.

At the same time the amplitude is decreasing: second harmonic will be f/2, third harmonic will be f /3 etc.

Those coefficients are correct (after scaling) for a square wave but may not be anywhere close for some other waveform.  Here is a video discussing the FFT of a sawtooth.  Note that it has both even and odd terms for the sin() while the cos() terms drop out.

A signal like this in music will make us hear mainly the sound of the fundamental, while the downward harmonics will be less and less audible.
We can also affirm that every harmonic in practice is a sinusoid, and the sum of the sinusoids then makes us a signal displayed on the oscilloscope that is not necessarily sinusoidal (such as a square wave).
I have two points that are still unclear:
1) in the FFt graph we said that the x axis represents the frequency ok; the y axis represents the amplitude, I don't understand the unit of measurement though? why not turn? why dbv? and we have a standard reference of db? in the example below the first harmonic I see that it has a value of about 200db, what does it mean? why does it have that value?

Engineers are a lazy bunch and they don't like carrying a lot of digits.  Assuming a voltage ratio, the dB value is 20 log (voltage divided by reference).  Let's assume a reference of 1V.  In this case, if the voltage is 10V, the db is 20 log 10 or 20 dB.  If the voltage is 100 the dB is 20 log 100 or 40 dB.  200 dB is a HUGE number:  200 = 20 log (V) so V is 10 to the 10th or 10_000_000_000 or 10 billion.  I'm not sure what the scale is all about on that FFT but it probably isn't voltage.  A sound level makes more sense. We can get 175 dB from a gunshot of a rifle or pistol.

Here is a table of sound levels.  I jet engine at 25 meters is about 150 db

https://www.iacacoustics.com/blog-full/comparative-examples-of-noise-levels.html

Logarithms are also used because many of our physical responses are non-linear.  By log(), I mean log base 10 of some value.  The 'common' logarithm, not the natural logarithm which is base e.

2) in the FFT spectrum do we focus only on the upward peaks? the downward ones have no significance / meaning?

thank you 

Since the spike on the FFT shows the amplitude at a frequency, I'm not sure they can be negative.  I certainly haven't see a series that has that result but it would take more math than I'm up for to prove it one way or another.

[tautech]

FFT pro tip for Siglents: use a slower timebase setting to get many cycles of the waveform on the display then enter a new world of FFT results.