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Damped Sine Wave Weighted Filter

Introduction
Remember that we can make filters by using convolution, that is summing the product between the input and the filter coefficients, the set of filter coefficients is sometime denoted "kernel", those coefficients can be a same value (simple moving average), a linear function (linearly weighted moving average), a gaussian function (gaussian filter), a polynomial function (lsma of degree p with p = order of the polynomial), you can make many types of kernels, note however that it is easy to fall into the redundancy trap.
Today a low-lag filter who weight the price with a damped sine wave is proposed, the filter characteristics are discussed below.
A Damped Sine Wave
A damped sine wave is a like a sine wave with the difference that the sine wave peak amplitude decay over time.

A damped sine wave
Used Kernel
We use a damped sine wave of period length as kernel.

The coefficients underweight older values which allow the filter to reduce lag.
Step Response

Because the filter has overshoot in the step response we can conclude that there are frequencies amplified in the passband, we could have reached to this conclusion by simply seeing the negative values in the kernel or the "zero-lag" effect on the closing price.
Enough ! We Want To See The Filter !
I should indeed stop bothering you with transient responses but its always good to see how the filter act on simpler signals before seeing it on the closing price. The filter has low-lag and can be used as input for other indicators

Filter with length = 100 as input for the rsi.

The bands trailing stop utility using rolling squared mean average error with length 500 using the filter of length 500 as input.
Approximating A Least Squares Moving Average
A least squares moving average has a linear kernel with certain values under 0, a lsma of length k can be approximated using the proposed filter using period p where p = k + k/4.

Proposed filter (red) with length = 250 and lsma (blue) with length = 200.
Conclusions
The use of damping in filter design can provide extremely useful filters, in fact the ideal kernel, the sinc function, is also a damped sine wave.
Remember that we can make filters by using convolution, that is summing the product between the input and the filter coefficients, the set of filter coefficients is sometime denoted "kernel", those coefficients can be a same value (simple moving average), a linear function (linearly weighted moving average), a gaussian function (gaussian filter), a polynomial function (lsma of degree p with p = order of the polynomial), you can make many types of kernels, note however that it is easy to fall into the redundancy trap.
Today a low-lag filter who weight the price with a damped sine wave is proposed, the filter characteristics are discussed below.
A Damped Sine Wave
A damped sine wave is a like a sine wave with the difference that the sine wave peak amplitude decay over time.
A damped sine wave
Used Kernel
We use a damped sine wave of period length as kernel.
The coefficients underweight older values which allow the filter to reduce lag.
Step Response
Because the filter has overshoot in the step response we can conclude that there are frequencies amplified in the passband, we could have reached to this conclusion by simply seeing the negative values in the kernel or the "zero-lag" effect on the closing price.
Enough ! We Want To See The Filter !
I should indeed stop bothering you with transient responses but its always good to see how the filter act on simpler signals before seeing it on the closing price. The filter has low-lag and can be used as input for other indicators
Filter with length = 100 as input for the rsi.
The bands trailing stop utility using rolling squared mean average error with length 500 using the filter of length 500 as input.
Approximating A Least Squares Moving Average
A least squares moving average has a linear kernel with certain values under 0, a lsma of length k can be approximated using the proposed filter using period p where p = k + k/4.
Proposed filter (red) with length = 250 and lsma (blue) with length = 200.
Conclusions
The use of damping in filter design can provide extremely useful filters, in fact the ideal kernel, the sinc function, is also a damped sine wave.
Mã nguồn mở
Theo đúng tinh thần TradingView, người tạo ra tập lệnh này đã biến tập lệnh thành mã nguồn mở để các nhà giao dịch có thể xem xét và xác minh công năng. Xin dành lời khen tặng cho tác giả! Mặc dù bạn có thể sử dụng miễn phí, nhưng lưu ý nếu đăng lại mã, bạn phải tuân theo Quy tắc nội bộ của chúng tôi.
Check out the indicators we are making at luxalgo: tradingview.com/u/LuxAlgo/
"My heart is so loud that I can't hear the fireworks"
"My heart is so loud that I can't hear the fireworks"
Thông báo miễn trừ trách nhiệm
Thông tin và ấn phẩm không có nghĩa là và không cấu thành, tài chính, đầu tư, kinh doanh, hoặc các loại lời khuyên hoặc khuyến nghị khác được cung cấp hoặc xác nhận bởi TradingView. Đọc thêm trong Điều khoản sử dụng.
Mã nguồn mở
Theo đúng tinh thần TradingView, người tạo ra tập lệnh này đã biến tập lệnh thành mã nguồn mở để các nhà giao dịch có thể xem xét và xác minh công năng. Xin dành lời khen tặng cho tác giả! Mặc dù bạn có thể sử dụng miễn phí, nhưng lưu ý nếu đăng lại mã, bạn phải tuân theo Quy tắc nội bộ của chúng tôi.
Check out the indicators we are making at luxalgo: tradingview.com/u/LuxAlgo/
"My heart is so loud that I can't hear the fireworks"
"My heart is so loud that I can't hear the fireworks"
Thông báo miễn trừ trách nhiệm
Thông tin và ấn phẩm không có nghĩa là và không cấu thành, tài chính, đầu tư, kinh doanh, hoặc các loại lời khuyên hoặc khuyến nghị khác được cung cấp hoặc xác nhận bởi TradingView. Đọc thêm trong Điều khoản sử dụng.