FIR filters - page 7
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Let's start with a libretto.
1. How does look like a sine wave spectrum ?
Like this.
All the energy of the signal is gathered at a single frequency. In the example 10 Hz, the amplitude is 5.
Now let's input this algorithm not with a sine wave whose spectrum is known and we have checked that the algorithm calculates it correctly, but with bar claws.
The result.
We see that at zero frequency the maximum of energy has gathered. It is not present in the figure above (see previous page).
Let's reset it to A(0)=0 in order to avoid observation of other components of the spectrum. Let's take a look.
We can see that low-frequency components of the spectrum prevail over the rest. This is understandable. This will always be the case whether you take clones of minutes, hours or days.
Now compare it with the spectrum above (previous page). Where is the zero frequency component? And it's always there (it's the equivalent of a dash, averaged over 256 bars).
Where is the maximum energy located ?
And then, when you will have figured it out, where did Kravchuk's cycles come from?
For those who want to check all my constructions given here I attach the files of Matcad version 14 and the archive of quotations.
to Prival
в школу. или в институт. попытайтеь хотя бы тройку получить по этому предмету. Так может утверждать только человек который сам никогда этот спектр не строил.
Relax, you don't understand a damn thing. Apparently you never got beyond Fourier. And you still haven't learned about the existence of parametric methods based on autoregressive model. It's you who should study before making such statements as "The spectrum looks quite different!!!".
to begemot61
It might be a spectrum, only there are no periodic components in it that are worthy of attention.
Please draw the amplitude on a logarithmic scale. Frequency preferably too.
And don't tell me that 3dB signal/noise is enough to claim anything when using FFT.
The calculation error is much larger.
What is wrong with you colleague? What does FFT have to do with anything? Do you even read what the author uses or just write? What do you mean "Please draw the amplitude" why the hell should I draw it for you if you don't even know what you're talking about.
to neoclassic
Thank you, something has cleared up! I'll deal with the library, now I need to figure out how to calculate the spectrum. If I'm not mistaken, the spectrum in our case is the amplitude-period relation. First of all it is not clear, in what units is amplitude measured in GCM? Secondly, I have spectrum taken with finware "Spectrum Analyzer" program that I've heard good reviews about, we get completely different results, although the algorithm is the same (MESA).
There's nothing wrong with not getting very similar results. There are several modifications of the methodot, besides all fineness in determining the parameter (the method is parametric) of the order of the model (number of ACF samples that will be used in the calculation of the spectrum). So, everything is perfectly normal, and there are always subtleties with these prameters - related to the identification of the model. By the way, some people don't understand that in order to calculate the spectrum you have to rely on some model, and in this case the author uses the specific model you wrote about.
Let the education begin.
...One more post like this, I'll spit on the ban and call you just a fool.
Study...
Now let's input this algorithm not with a sine wave whose spectrum is known and we have checked that the algorithm calculates it correctly, but with bar claws.
The result.
We see that at the zero frequency the maximum of energy has gathered. And it is not present in the figure above (see previous page).
Let's reset it to A(0)=0 so it will not interfere with other components of the spectrum. Let's take a look.
We can see that low frequency components of the spectrum prevail over the rest. This is understandable. This will always be the case whether you take clones of minutes, hours or days.
Now compare it with the spectrum above (previous page). Where is the zero frequency component? It's always there (it's the equivalent of a dash, averaged over 256 bars).
Where is the maximum energy located ?
And then, when you will have figured it out, where did Kravchuk's cycles come from?
For those who want to check all my constructions presented here I attach Matcad`s files (version 14) and the archive of quotations.
You're talking ligbez, smart-ass. For random series, the spectrum of a discrete signal is the Fourier transform of its correlation function (Wiener-Hinchin theorem), and what you have shown here makes no sense for the signals you are considering. The application of parametric methods is justified as well but not Fourier - it cannot be applied, the application is meaningless. This "spectrum" shown by you says nothing for these series.
PS: To be absolutely clear - there is no maximum energy in your spectrum, for the reason that this spectrum does not reflect reality in any way, it is completely random, which is proved. For such series only power spectrum as F-transformation from its ACF makes sense (with respect to the Fourier transform).
You can see that the low-frequency components of the spectrum dominate the rest. This is understandable. This will always be the case whether you take clones of minutes, hours or days.
Now compare it with the spectrum above (previous page). Where is the zero frequency component? And it's always there (it's the equivalent of a dash, averaged over 256 bars).
You made a mistake due to your lack of attention))))
Now look at your charts along the X axis and look at the X axis chart in the program
you have the frequency and the program has the wave (i.e.1/f)
so there's not even a constant component there
left to right X axis starts with a high frequency component equal to infinity in frequency and ends at a low frequency of 1/150
You got in a hurry by not paying attention and got it all upside down ))))
now look at your graphs on the x-axis and look at the graph on the x-axis in the program
you have the frequency and the program has the wave (i.e.1/f)
so there is no constant component
the x-axis on the right begins with a high-frequency component equal to infinity in frequency and ends with a low frequency of 1/150
This is right-to-left in MQL. The higher the frequency the further up the x-axis it goes.
In MQL the counting is from right to left. It's different in matcadec, as it is in mathematics. the higher the frequency, the further along the x-axis it is.
It's not about the direction, it's about the spectrum of waves, not frequencies
It's more convenient for estimating a discrete signal and calculating filter coefficients
no one would ever calculate the filter for frequencies close to zero. for such a filter, no quotes history from the History-center would be enough
you're overreacting )
To sab1uk
The spectrum is the frequency distribution of the signal energy.
The frequency is related to the wavelength by a single-digit transformation (through the speed of light). Therefore it is possible to plot as a function of wavelength and frequency, the nature of the graph will not change. sab1uk you have fooled yourself with these octaves and you are confusing others.
"...because no one would think of calculating a filter for a frequency close to zero... " it's in front of your eyes A(0) filter is set to frequency = zero. What you're talking about I understand, it's about FIR filter and methods of their construction, then yes it can't be built. But the fact that it cannot be practically implemented is not a proof that there is no constant component in the spectrum. Try to understand what I mean.
Fourier transform
https://ru.wikipedia.org/wiki/%D0%9F%D1%80%D0%B5%D0%BE%D0%B1%D1%80%D0%B0%D0%B7%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5_%D0%A4%D1%83%D1%80%D1%8C%D0%B5
"In terms of signal processing, the transform takes the time series representation of a signal function and maps it into a frequency spectrum, where ω is the angular frequency. That is, it turns a time function into a frequency function; it is a decomposition of the function into harmonic components at various frequencies.
When the function f is a function of time and represents a physical signal, the transformation has a standard interpretation as a spectrum of the signal. The absolute value of the resulting complex function F represents the amplitudes of the corresponding frequencies(ω), while the phase shifts are obtained as an argument of this complex function."
For grasn
Don't confuse God's gift with the egg.
Read them at your leisure. You will like it.
not only because they sell matched filters, but also because they have cracked a free software and put their interface on it (if i'm not mistaken)
i don't know about the gimmick, i didn't need to investigate it. let them sell it to sloths. at least it's kind of adaptive.
You shouldn't stigmatize them like that.
If you want it, buy it. If you don't want it, don't buy it.
But they do have a great free subscription to the lykbase.
I've got two issues of it - excellent and understandable material, at good scientific level.
Just the right thing for people who haven't dealt with signal filtering.