The Discrete Fourier Transform Indicator was written by John Ehlers and more details can be found at www.mesasoftware.com I have color coded everything as follows: blue line is the dominant cycle, orange line is the power converted to decibels, and I have marked the other line as red if you should sell or green if you should buy Let me know if you would like...

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This function implements the Goertzel algorithm (for integer N). The Goertzel algorithm is a technique in digital signal processing (DSP) for efficient evaluation of the individual terms of the discrete Fourier transform (DFT). In short, it measure the power of a specific frequency like one bin of a DFT, over a rolling window (N) of samples. Here you see an...

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Library "JohnEhlersFourierTransform" Fourier Transform for Traders By John Ehlers, slightly modified to allow to inspect other than the 8-50 frequency spectrum. reference: www.mesasoftware.com high_pass_filter(source) Detrended version of the data by High Pass Filtering with a 40 Period cutoff Parameters: source : float, data source. Returns:...

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Adaptive Moving Averages are nothing new, however most of them use EMA as their MA of choice once the preferred smoothing length is determined. I have decided to make an experiment and separate length generation from smoothing, offering multiple alternatives to be combined. Some of the combinations are widely known, some are not. This indicator is based on my...

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Level: 2 Background John F. Ehlers introuced his DFT-ADAPTED RELATIVE STRENGTH INDEX (RSI) in Jan, 2007. Function In "Fourier Transform For Traders" in Jan, 2007, John Ehlers presented an interesting technique of improving the resolution of spectral analysis that could be used to effectively measure market cycles. Better resolution is obtained by a...

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Level: 2 Background John F. Ehlers introduced DFT Spectral Estimate in his "Cycle Analytics for Traders" chapter 9 on 2013. Function The DFT is accomplished by correlating the data with the cosine and sine of each period of interest over the selected window period. The sum of the squares of each of these correlated values represents the relative power at each...

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Collection of Dominant Cycle estimators. Length adaptation used in the Adaptive Moving Averages and the Adaptive Oscillators try to follow price movements and accelerate/decelerate accordingly (usually quite rapidly with a huge range). Cycle estimators, on the other hand, try to measure the cycle period of the current market, which does not reflect price movement...

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A complimentary indicator to my Adaptive MA constructor. It calculates the difference between the two MA lines (inspired by the Moving Average Difference (MAD) indicator by John F. Ehlers). You can then further smooth the resulting curve. The parameters and options are explained here: The difference is normalized by dividing the difference by twice its Root mean...

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Adaptive Oscillators use the same principle as Adaptive Moving Averages. This is an experiment to separate length generation from oscillators, offering multiple alternatives to be combined. Some of the combinations are widely known, some are not. Note that all Oscillators here are normalized to -1..1 range. This indicator is based on my previously published public...

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As a longtime fan of ADX, looking at Vortex Indicator I often wondered, where is the third line. I have rarely seen that anybody is calculating it. So, here it is: Average Vortex Index - an ADX calculated from Vortex Indicator. I interpret it similarly to the ADX indicator: higher values show stronger trend. If you discover other interpretation or have...

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Library "MathSpecialFunctionsDiscreteFourierTransform" Method for Complex Discrete Fourier Transform (DFT). dft(inputs, inverse) Complex Discrete Fourier Transform (DFT). Parameters: inputs : float array, pseudo complex array of paired values . inverse : bool, invert the transformation. Returns: float array, pseudo complex array of paired values .

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In digital signal processing knowing how a system interact with the frequency content of an input signal is extremely important, the mathematical tool that give you this information is called "frequency response". The frequency response regroup two elements, the amplitude response, and the phase response. The amplitude response tells you how the system modify the...

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This is the translation of discret cosine tranform (DCT) usage by John Ehler for finding dominant cycle period (DC). The price is first filtered to remove aliasing noise(bellow 8 bars) and trend informations(above 50 bars), then the power is computed. The trick here is to use a normalisation against the maximum power in order to get a good frequency...

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