FIR filter with minimum phase - page 5
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build a bank of bandpass filters links to the author's work:
https://www.mql4.com/go?http://belisa.org.by/pdf/Publ/Art7_i17.pdf
https://www.mql4.com/go?http://belisa.org.by/pdf/Publ/Art4_i18.pdf
described in sufficient detail with examples of possible use, all seemed very logical, but the author himself, as I now think, somewhat miscalculated without stating a word about the delay, because if in the lowest frequency filter the central frequency of the filter is the order of 1/MN1 then the delay even in a few samples will be very large, so I think that determining when choosing a filter should be the minimum delay
Delay has nothing to do with it. Take a bank of bandpass filters with a delay and plot the price quotation by the sum of the outputs of those filters. Everything should work out without any artificial shifts on the time axis. The main thing is that the filters should overlap as Vadim described. Actually, this area of signal decomposition mathematics is well studied and called Discrete Wavelet Transform. Start reading it here and then go through the books:
https://ru.wikipedia.org/wiki/%D0%94%D0%B8%D1%81%D0%BA%D1%80%D0%B5%D1%82%D0%BD%D0%BE%D0%B5_%D0%B2%D0%B5%D0%B9%D0%B2%D0%BB%D0%B5%D1%82-%D0%BF%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
build a bank of bandpass filters links to the author's work:
https://www.mql4.com/go?http://belisa.org.by/pdf/Publ/Art7_i17.pdf
https://www.mql4.com/go?http://belisa.org.by/pdf/Publ/Art4_i18.pdf
described in details with examples of possible use, all seemed very logical, but the author himself, as I now think, somewhat miscalculated without stating a word about delay, because if in the lowest frequency filter the central frequency of the filter is about 1/MN1 then the delay even in several samples will be very large, so I think that the determining factor when choosing the filter should be the minimum delay
You didn't answer the question. What will you do with the filters?
I assumed in my work that any smooth line can be extrapolated with minimal distortion in the most primitive way over small distances. That is, the problem boils down to getting a collection of smooth and sinusoidal lines after decomposition. Then, extrapolate them into the future and stack them there. Question... What does the phase have to do with it? It is compensated for. It doesn't matter the phase and the delay.
This work is still incomplete.
======================
To solve this problem fast enough with FIR filters would require thousands of computers like yours.
Delay has nothing to do with it. You take a bank of delayed bandpass filters and spread the price quotation over the sum of the outputs of those filters. Everything should work out without any artificial shifts on the time axis. The main thing is that the filters should overlap as Vadim described. Actually, this area of signal decomposition mathematics is well studied and called Discrete Wavelet Transform. Start reading it here and then go through the books:
https://ru.wikipedia.org/wiki/%D0%94%D0%B8%D1%81%D0%BA%D1%80%D0%B5%D1%82%D0%BD%D0%BE%D0%B5_%D0%B2%D0%B5%D0%B9%D0%B2%D0%BB%D0%B5%D1%82-%D0%BF%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
Thank you. I'll look into it.
You didn't answer the question. What will you do with the filters?
I assumed in my work that any smooth line can be extrapolated with minimal distortion in the most primitive way over small distances. That is, the problem boils down to getting a collection of smooth and sinusoidal lines after decomposition. Then, extrapolate them into the future and stack them there. Question... What does the phase have to do with it? It is compensated for. It doesn't matter the phase and the delay.
This work is still incomplete.
======================
To solve this problem fast enough with FIR filters would require thousands of computers like yours.
Thanks, I'll look into it.
I like searching for patterns, i.e. let's say the mutual arrangement of decomposition lines now corresponds to the one that was observed many times before and the price from this position often increased, we act accordingly, as for the use of one or another type of filters in your problem, I think nobody knows it better than you.
A few months ago I created a single layer neural network with decompositions of a price quote as inputs, like F2, F4, F8, ... F512, where F stands for a filter output and the number for its period. That is the price was filtered by a binary derivative of 9 filters as described in your cited articles. I trained the network with built-in genetics tester. But it had no success. The net stores past patterns and slowly goes down on a forward one. In my personal opinion, trading based on such filters is the same as trading based on MACDs. IACDs alone are not enough to determine entry points. It is necessary to take into account all other information contained in a quote: the history of price movement, support and resistance levels, volatility, time of day, day of week, etc. It is very difficult to feed all this information to the net entries. Therefore we need to look for patterns with our eyes and simplify them. Instead of a bank of 9 filters, you may need only 2-3 filters and forget about decomposition as such.
You can, of course, do it another way. Decompose the price precisely into N smooth filters and, instead of identifying patterns, extrapolate each of those filters into the future and see how their sum (price) behaves as Vadim suggests. But I don't believe in that. Judge for yourself: we don't know the future price and it can go up or down with equal probability. With these two different outcomes there should be two different extrapolations of past prices. Right? But when Vadim talks about extrapolation, he means one extrapolation for each filter, not several. This creates a paradox. In order to describe different futures, there must be different extrapolations. And we choose only one. Why do we think that this particular extrapolation option is correct?
A few months ago I created a single-layer neural network with decompositions of a price quote as inputs, like F2, F4, F8, ... F512, where F stands for a filter output and the number for its period. That is the price was filtered by a binary derivative of 9 filters as described in your cited articles. I trained the network with built-in genetics tester. But it had no success. The net stores past patterns and slowly goes down on a forward one. In my personal opinion, trading based on such filters is the same as trading based on MACDs. IACDs alone are not enough to determine entry points. It is necessary to take into account all other information contained in a quote: the history of price movement, support and resistance levels, volatility, time of day, day of week, etc. It is very difficult to feed all this information to the net entries. Therefore we need to look for patterns with our eyes and simplify them. Instead of a bank of 9 filters, you may need only 2-3 filters and forget about decomposition as such.
You can, of course, do it another way. Decompose the price precisely into N smooth filters and, instead of identifying patterns, extrapolate each of those filters into the future and see how their sum (price) behaves as Vadim suggests. But I don't believe in that. Judge for yourself: we don't know the future price and it can go up or down with equal probability. With these two different outcomes there should be two different extrapolations of past prices. Right? But when Vadim talks about extrapolation, he means one extrapolation for each filter, not several. This creates a paradox. In order to describe different futures, there must be different extrapolations. And we choose only one. Why do we think that this particular extrapolation option is correct?
The idea of decomposing a problem into its components is universal in science and is widely used.
For this idea there is a well-known constraint called "reversibility" without which the decomposition cannot be recognised as such - it is the sum of the parts into which the problem is decomposed must give that problem. In the case of harmonics, this means that the sum of the harmonics into which the quotient is decomposed must give the original quotient.
As far as I remember Fourier. Any signal can be represented absolutely precisely if the number of harmonics equals the number of observations. This is the condition for reversibility. Otherwise there is some error in the representation of the original signal. In DSP it doesn't matter much because there the signal is extracted and the noise is got rid of.
In a cotier there is no signal. And it is generally accepted that analysis of the residual from decomposition of the original quotient is important. It is the residual that dictates the future forecast, not the set of smooth curves that we have extracted from the quotient.
require no mental effort .....
We could, of course, do it differently. Get an accurate decomposition of price into N smooth filters and, instead of identifying patterns, extrapolate each of these filters into the future and see how their sum (price) behaves as Vadim suggests. But I don't believe in that. Judge for yourself: we don't know the future price and it can go up or down with equal probability. With these two different outcomes there should be two different extrapolations of past prices. Right? But when Vadim talks about extrapolation, he means one extrapolation for each filter, not several. This creates a paradox. In order to describe different futures, there must be different extrapolations. But we choose only one. Why do we think that this particular extrapolation option is correct?
The idea of decomposing a problem into its components is universal in science and is widely used.
For this idea there is a well-known constraint, called "reversibility", without which the decomposition cannot be recognised as such - it is the sum of the parts into which the problem is decomposed must give that problem. In the case of harmonics, this means that the sum of the harmonics into which the quotient is decomposed must give the original quotient.
As far as I remember Fourier. Any signal can be represented absolutely precisely if the number of harmonics equals the number of observations. This is the condition for reversibility. Otherwise there is some error in the representation of the original signal. In DSP it doesn't matter much because there the signal is extracted and the noise is got rid of.
In a cotier there is no signal. And it is generally accepted that analysis of the residual from decomposition of the original quotient is important. It is the residual that dictates the future forecast, not the set of smooth curves we have extracted from the quotient.
One does not contradict the other. I have the original series restored.
This last point is very true of extrapolation. The extrapolation itself, although highly accurate, is not absolute. If we consider that there are a lot of such lines (perhaps several tens of thousands), the accumulated error will also affect the forecast. So, Vladimir, there is no paradox here.
I took out matcad and this is what I got after applying the algorithm:
was LPF became LPF
FF is now FF.
the result of applying the original filters on p4
the result of the modified filters below is simply summed up the signal from the filter outputs (red line) without any shift
Thank you all the topic can be closed