QQE of Parabolic-Weighted Velocity [Loxx]QQE of Parabolic-Weighted Velocity is a QQE indicator that takes as its input parabolic-weighted velocity calculation. This version can help in determining trend. Adjust the calculating period to your trading style: longer - to trend traders, shorter - for scalping.
What is Qualitative Quantitative Estimation (QQE)?
The Qualitative Quantitative Estimation (QQE) indicator works like a smoother version of the popular Relative Strength Index ( RSI ) indicator. QQE expands on RSI by adding two volatility based trailing stop lines. These trailing stop lines are composed of a fast and a slow moving Average True Range (ATR).
There are many indicators for many purposes. Some of them are complex and some are comparatively easy to handle. The QQE indicator is a really useful analytical tool and one of the most accurate indicators. It offers numerous strategies for using the buy and sell signals. Essentially, it can help detect trend reversal and enter the trade at the most optimal positions.
Included:
Loxx's Expanded Source Types
Alerts
Signals
Bar coloring
M-oscillator
J_TPO Velocity VariationThis one is a very random indicator but with an excellent concept. Unfortunately, I don't know much about the origin of this indicator or who made it. Still, the first appearance was around 2004 on a Meta Trader forum. There are a lot of variations of the J_TPO indicator. One of them is the J_TPO Velocity. The difference from the original version is that it uses the price range of the latest candles to change the magnitude of the indicator value, but the concept is the same.
More info here
In its original form, an oscillator between -1 and +1 is a nonparametric statistic quantifying how well the prices are ordered in consecutive ups (+1) or downs (-1), or intermediate cases. The velocity variation adds the price range, and this script variation adds a baseline as a filter for the indicator. This indicator will work as a confirmation indicator. Using it with the trend filter will work as an entry indicator.
Besides the columns representing the indicator's values, 2 more signals will be printed on the chart. One is the middle cross, the other the kicking middle cross. The first will print a signal when the J_TPO crosses the middle line (0) in favor of the trend. A diamond will be printed when the baseline is above 0, and the cross is upwards. The inverse for crosses downwards. The other signal is the Kicking middle cross which will appear when the cross comes after an opposite cross. This will give only one signal per cross in the same direction, which may help identify earlier the trend direction.
Autocorrelative Power Oscillator (APO) [SpiritualHealer117]This indicator is very strong in identifying short-term trends, and was made for trading stocks and commodities. When it is green, it indicates an uptrend, and red indicates a downtrend. The transparency of the columns illustrates the strength of the trend, with transparent columns indicating weakness, while solid columns indicate strength.
Basic Explanation of the Indicator
This indicator calculates an asset's Pearson's R coefficient when compared with several different lags of the stock's price. After that, the oscillator checks whether the indicator is in the green or red compared to those correlations, and takes the sum of the correlative periods to predict which direction the market should go based on the relationship of the current price with its past correlations.
MACD frontSide backSide + TTM Squeeze by bangkokskaterDark Mode is enabled by default for black theme
disable Dark Mode for white theme
MACD frontSide backSide
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an elegant, much better way to use MACD
for trend following momentum ( aka momo) style
MACD with default settings of 12/26 smoothing of 9
✔️ but without histogram
✔️ only has MACD and signal "lines"
green = frontSide momentum impulse
take longs only
red = backSide momentum impulse
take shorts only
black area = exit (once green or red is no longer showing)
or keep holding till next bigger TP
PS: credits to Warrior Trading Ross Cameron for this idea
youtu.be
TTM Squeeze
===================
white dots = incoming pump / dump (monitor for entry)
PS: credits to John Carter's TTM Squeeze & Greeny for PineScript adaptation
TheATR: Aroon Oscillator.Aroon Oscillator (AO).
The Aroon Oscillator, was developed by Tushar Chande, in 1995, to highlight the start of a new trend and to measure trend strength.
I re-branded a bit the whole thing, If you are familiar with how this Oscillator usually is, you are going to notice the differences.
Aroon Oscillator Components.
1 - Aroon Up -> Bullish Directional Component, highlighted in blue.
2 - Aroon Down -> Bearish Directional Component, highlighted in purple.
We also have the Oscillators static thresholds, which are:
- 0 Line.
- 100 Line.
- Exit Signal Line Level.
How to read the Aroon Oscillator.
The AO main goal, is to identify the trend from its first stages, to then come up with how strong that trend is.
So, classic interpretation for the AO would be:
-Aroon Up>Aroon Down = Bull Scenario.
-Aroon Up<Aroon Down = Bear Scenario.
There's also a filter I added, called "Weak Spots Filter". It's purpose goes alongside with how the Aroon present its signals, which a big spike, that usually reaches the top range of the Oscillator, for both Long and Short cases.
So, if the momentum of the market fails to push the Aroon up to a specific level (Exit Signal Line Level), the Filter says market's not strong, and therefore signal is not valid.
The same level (Exit Signal Line Level) allows the user to set Exit Signals for the AO.
I found Exit Signal extremely powerful in this oscillator, as they way they're structured aims to capture the slow down of the trend, which may be followed by the market reversing.
TheATR Documentation regarding TheATR: Aroon Oscillator.
I pretty much already say what I love about the Aroon: It's Exit Signals.
Those are the most valuable part of the Oscillator, by far, in my opinion.
Also, I noticed it gives nice trend recognition when the lenght it's set to
big number (from 150 to 200, for ex).
But. I would never use JUST the Aroon, to decide when to enter and exit the market.
I think it may be an outstanding player if its in a team, where it should play a defensive role.
But that's just my way of using it. I wish you find profitable ways too!
Thanks for reading,
TheATR.
QG-Relative Strength Rank MTF DSL
Relative strength rank is a momentum indicator based on combination of short and long term strength combined with ATR to adjust for current volatility.
The Multi timeframe version long with signals only above or below +1 and -1 provide quite reliable signals and entries for pullback levels.
The RSR signal has been smoothed with EMA.
RSI TrendRSI Hull Trend is a hybrid indicator with RSI of HULL Signal. The Hull MA is combined with RSI to see if the Hull MA Buy/Sell Signal is in overbought or oversold condition. Buy Sell Signals are plotted based on settings of OB/OS or RSI. This indicator is very useful to see if the Trend is in Exhaustion or Beginning of a Trend. Entry and Exit conditions can be more precise based on OB/OS condition of price action. In addition normal RSI trend is plotted with trend color from Hull MA. Best Performance with Heiken Ashi Candles.
OB/OS Settings provided
Hull Buy/Sell Signals plotted
Double RSI FAST and DEFAULT signal with crossover
Bar Color applied based on Hull RSI Trend
Hull Trend + RSI + Price Action
TDI - Traders Dynamic Index [Goldminds] with DIV RSI AlertsOriginally from Goldminds. Later modified by Jakub a Babo. I just added RSI DIV alerts. You're welcome. :)
Instruction: once you have have this indicator and press Alt + A to create alert.
Tom Joseph MACD 5-35 for Elliot WavesThis oscillator for the Elliott Theory has been invented by Tom Joseph and it's useful to correctly count the impulsive and corrective waves.
Its difference compared to a simple MACD is the peculiarity to use the ratio between the Fast SMA (default period set to 5) and the Slow SMA (default period se to 35).
The used formula is as below:
( (fast_SMA / slow_SMA) -1 ) * 100
Hope you could find it useful! 😉
Currency Strength V2An update to my original Currency Strength script to include a 2nd timeframe for more market context.
Changed the formatting slightly for better aesthetics, as the extra column and colors became unsightly.
Also added a new setting for "Flat Color", which changes the value background to a simple green/red for above or below 50, rather than using the Color Scale that increases color intensity the further it gets from 50.
________________________________________________________________________________
This script measures the strength of the 6 major currencies USD, EUR, GBP, CAD, AUD and JPY.
Simply, it averages the RSI values of a currency vs the 5 other currencies in the basket, and displays each average RSI value in a table with color coding to quickly identify the strongest and weakest currencies over the past 14 bars (or user defined length).
The arrow in the current RSI column shows the difference in average RSI value between current and X bars back (user defined), telling you whether the combined RSI value has gone up or down in the last X bars.
Using the average RSI allows us to get a sense of the currency strength vs an equally weighted basket of the other majors, as opposed to using Indexes which are heavily weighted to 1 or 2 currencies.
The additional security calls for the extra timeframe make this slower to load than the original, but this was a user request so hopefully it will prove worthwhile for some people.
Those who find the loading too slow when switching between charts may be better off still using the original, which is why this is posted as a separate script and not an update to the original.
This is the table with Flat Color option enabled.
GDM Price Power & Under CurrentPrice Power & Under Current.
This is an updated version of the script I had shared earlier namely 'GDM Power Cross'
I have added under current and have removed upper an lower bands.
How to Trade:
Similar to various Moving Average cross over strategies; this indicator can be used to trade crossovers of Price Powers.
Lengths I have used as default are 7, 9 and 21. So when smaller Power Crosses above the Higher Powers; it is a Bullish Crossover and vice versa.
It is observed that most times we do get opportunity to enter in the price range of the candle where cross over has taken place.
Under Current: These are moving averages of above mention Price Powers. it is found that cross overs of Power lines work better when under currents are already in Bullish or Bearish mode. e.g. Bullish Cross Over of Power Lines will work better when Under Current lines are already Bullish or say Smaller Length Under Current is already above the Higher Length Under Current.
Indicator works better for bigger time frames... recommended time frame is 1 day.
Please feel free to Post your views.
Best Regards
Girish Mane
Re-Lions Trading Academy
+91 8080755813
Revolver Oscillator Strategy 1.2 (RSI+UO+MFI)ROS (Revolver Oscillator Strategy)
Version 1.2
Description
This script combines three popular oscillators (RSI, Ultimate Oscillator and MFI) to accurately determine the price momentum of an asset.
Context
- RSI (Relative Strength Index) is a momentum oscillator that measures the speed and change of price movements over a period of time (14).
- Ultimate Oscillator uses three different periods (7, 14, and 28) to represent short, medium, and long-term market trends.
- Money Flow Index (MFI) is a momentum indicator that measures the flow of money into and out over a period of time. It is related to the Relative Strength Index (RSI) but incorporates volume, whereas the RSI only considers price
How does it work?
When a RED bar appears, it means that the three oscillators have exceeded the set thresholds, and it is a SELL signal.
When a GREEN bar appears, it means that the three oscillators are below the set thresholds, and it is a BUY signal.
I recommend leaving the default settings.
Rsi/W%R/Stoch/Mfi: HTF overlay mini-plotsOverlay mini-plots for various indicators. Shows current timeframe; and option to plot 2x higher timeframes (i.e. 15min and 60min on the 5min chart above).
The idea is to de-clutter chart when you just want real-time snippets for an indicator.
Useful for gauging overbought/oversold, across timeframes, at a glance.
~~Indicators~~
~RSI: Relative strength index
~W%R: Williams percent range
~Stochastic
~MFI: Money flow index
~~Inputs~~
~indicator length (NB default is set to 12, NOT the standard 14)
~choose 2x HTFs, show/hide HTF plots
~choose number of bars to show (current timeframe only; HTF plots show only 6 bars)
~horizontal position: offset (bars); shift plots right or left. Can be negative
~vertical position: top/middle/bottom
~other formatting options (color, line thickness, show/hide labels, 70/30 lines, 80/20 lines)
~~tips~~
~should be relatively easy to add further indicators, so long as they are 0-100 based; by editing lines 9 and 11
~change the vertical compression of the plots by playing around with the numbers (+100, -400, etc) in lines 24 and 25
MFI StrategyThis indicator is based on MFI25 and EMA55 and optimized for 1 day graph and slow swing trading to show large moves and tops and bottoms.
You can change the MFI and EMA settings according to your style of trading.
The change from green to red and visa versa are the buying and selling moments.
The yellow line indicates that a change is possibly comming or not really sollid, so with yellow it's your own feeling that is leading.
Always combine this graph with others. F.i. a RSI14 to look for divergenses.
Ps. I'm not a professional or very experienced trader, but this indicator works perfect for me.
Succes.
Squeeze Momentum Indicator [LazyBear] added Alerting + webhookA modified version of Squeeze Momentum Indicator visualizing on Price Chart.
author: @LazyBear, modified by @KivancOzbilgic, and by @dgtrd
I took in all of the information as the script below is based on the V2 Script that @LazyBear posted and then added Alerting based on the math and the conditions that @dgtrd added.
Per the description here:
The Squeeze Indicator measures the relationship between Bollinger Bands and Keltner's Channels to help identify consolidations and signal when prices are likely to break out (whether up or down).
The Squeeze Indicator finds sections of the Bollinger Bands which fall inside the Keltner's Channels, and in this case, the market is said to be in a squeeze (indicator turns off, displayed with grey diamond shapes in this study).
When the volatility increases, so does the distance between the bands. Conversely, when the volatility declines, the distance also decreases, and in such cases, the squeeze is said to be released (indicator turns on, displayed with triangle up or triangle down shapes)
Taking the above information and what was in the script was able to base the alert conditions:
So when the condition:
Squeeze On or No Squeeze = In Squeeze
Squeeze Off = Squeeze Release Long or Squeeze Release Long based off conditions.
There are 2 separate alert Types.
1. App, Pop-up, eMail, play sound and Send email to SMS
2. It Is dedicated to Webhook for your various applications.
Alerting Options
i.imgur.com
App Notification
i.imgur.com
i.imgur.com
Webhook test into Discord
i.imgur.com
Polynomial Regression Derivatives [Loxx]Polynomial Regression Derivatives is an indicator that explores the different derivatives of polynomial position. This indicator also includes a signal line. In a later release, alerts with signal markings will be added.
Polynomial Derivatives are as follows
1rst Derivative - Velocity: Velocity is the directional speed of a object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. 60 km/h northbound). Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies.
2nd Derivative - Acceleration: In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the orientation of the net force acting on that object.
3rd Derivative - Jerk: In physics, jerk or jolt is the rate at which an object's acceleration changes with respect to time. It is a vector quantity (having both magnitude and direction). Jerk is most commonly denoted by the symbol j and expressed in m/s3 (SI units) or standard gravities per second (g0/s).
4th Derivative - Snap: Snap, or jounce, is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. Equivalently, it is the second derivative of acceleration or the third derivative of velocity.
5th Derivative - Crackle: The fifth derivative of the position vector with respect to time is sometimes referred to as crackle. It is the rate of change of snap with respect to time.
6nd Derivative - Pop: The sixth derivative of the position vector with respect to time is sometimes referred to as pop. It is the rate of change of crackle with respect to time.
Included:
Loxx's Expanded Source Types
Loxx's Moving Averages
Williams % Range overlay mini plotPlots Williams Percent Range over bought/oversold indicator as a small overlay in top right corner.
De-clutter chart when all you're interested in is the real-time W%R to 'give permission' to enter a trade.
i.e. to remove the Williams %R lower pane from the above chart completely.
~~User Inputs~~
~W%R length
~Number of bars to show (default is last 6 bars)
~Plot offset (horizontal position of the plot; can be negative)
~Line color and thickness
~Show/hide plot title
~~tips~~
~in line 26, edit the multiplier (3*), to compress/expand the vertical size of the plot
Defu_DivergenceThis is a composite indicator, a collection of multiple indicators
It includes the following:
1. the gray background has a huge trading volume ,
2. the market cost deviates, and the relationship between the closing price of the black line, the red line and the blue line and the short-term, medium-term and long-term average. Compare the difference after mutual subtraction.
3. blue orange column fund flow indicator MFI , color transparency indicates the value
4. the Bollinger belt signals with a short deviation rate, which is the Bollinger belt with a black line.
======================The above translation is from Google
这是一个复合指标，集合了多种指标
包括以下：
1.灰色背景成交量巨大，
2.市场成本乖离 ，黑色线、红色线、蓝色线收盘价与 短期 、中期、长期三条均线之间的关系。互减后比较差值。
3.蓝橙柱 资金流量指标MFI,颜色的透明度表示值的大小
4.布林带 以短期乖离率信号，就是黑色线的布林带。
TheATR: Fisher Oscillator.Fisher Oscillator(FO).
The Fisher Oscillator is inspired by John Ehlers "Fisher Transform".
The oscillator highlights when prices have moved to an extreme, based on recent prices.
The FO may help in spotting turning points, in the short-medium trends of an asset, also, it helps in recognizing the asset's trends themselves, giving a picture of mkt conditions affected by less noise.
Fisher Oscillator Components.
Fisher V1 -> Main FO.
Fisher V2 -> Past Candle FO.
0-line threshold -> Directional Component.
How to read the Fisher Oscillator.
The FO is super easy to read by itself.. also, I coded some features which make it even easier to read.
It's suggestions, which we can call "Signals", come from 2 different sources, accessible thanks to the variable "Signals Type".
- 0-Line Crosses:
When the "Fisher V1" upcrosses the oscillator 0-line, the oscillator suggests a Long scenario.
When the "Fisher V1" downcrosses the oscillator 0-line, the oscillator suggests a Short scenario.
- Classic Lines Crosses:
When the "Fisher V1" upcrosses the "Fisher V2", the oscillator suggests a Long scenario.
When the "Fisher V1" downcrosses the "Fisher V2", the oscillator suggests a Short scenario.
Users will be able to recognise these Signals visually, thanks to some color customisation to the "Fisher V1" line, and thanks to the ability of the oscillator of plotting Signals.
TheATR Documentation regarding TheATR: Fisher Oscillator.
Researching and backtesting the FO, I noticed it's skill of being able to dynamically identify trend reversals with a nice degree of reliability.
Also, the FO's able to keep up with trends up to their tops/bottoms, as it's very responsive.
This makes the FO a trend-following oscillator in my personal view, because its nature of being very fast in detecting reversals will lead to many false reversals as well.
On the other face of this coin, if we look at the FO as a source for confirmations for a trend-following strategy, may be very useful.
To conclude, I would use the FO as a confirmation oscillator, in a trend-following strategy that needs to have other components.
Thanks for reading,
TheATR.
Ultimate Oscillator + DivergencesUltimate Oscillator (UO) + Divergences + Alerts + Lookback periods.
This version of the Ultimate Oscillator adds the following 3 additional features to the stock UO by Tradingview:
- Optional divergence lines drawn directly onto the oscillator.
- Configurable alerts to notify you when divergences occur.
- Configurable lookback periods to fine tune the divergences drawn in order to suit different trading styles and timeframes.
This indicator adds additional features onto the stock Ultimate Oscillator by Tradingview, whose core calculations remain unchanged. Namely the configurable option to automatically, quickly and clearly draw divergence lines onto the oscillator for you as they occur, with minimal delay. It also has the addition of unique alerts, so you can be notified when divergences occur without spending all day watching the charts. Furthermore, this version of the Ultimate Oscillator comes with configurable lookback periods, which can be configured in order to adjust the sensitivity of the divergences, in order to suit shorter or higher timeframe trading approaches.
The Ultimate Oscillator
Tradingview describes the Ultimate Oscillator as follows:
“The Ultimate Oscillator indicator (UO) indicator is a technical analysis tool used to measure momentum across three varying timeframes. The problem with many momentum oscillators is that after a rapid advance or decline in price, they can form false divergence trading signals. For example, after a rapid rise in price, a bearish divergence signal may present itself, however price continues to rise. The ultimate Oscillator attempts to correct this by using multiple timeframes in its calculation as opposed to just one timeframe which is what is used in most other momentum oscillators.”
More information on the history, use cases and calculations of the Ultimate Oscillator can be found here: www.tradingview.com
What are divergences?
Divergence is when the price of an asset is moving in the opposite direction of a technical indicator, such as an oscillator, or is moving contrary to other data. Divergence warns that the current price trend may be weakening, and in some cases may lead to the price changing direction.
There are 4 main types of divergence, which are split into 2 categories;
regular divergences and hidden divergences . Regular divergences indicate possible trend reversals, and hidden divergences indicate possible trend continuation.
Regular bullish divergence: An indication of a potential trend reversal, from the current downtrend, to an uptrend.
Regular bearish divergence: An indication of a potential trend reversal, from the current uptrend, to a downtrend.
Hidden bullish divergence: An indication of a potential uptrend continuation.
Hidden bearish divergence: An indication of a potential downtrend continuation.
Setting alerts.
With this indicator you can set alerts to notify you when any/all of the above types of divergences occur, on any chart timeframe you choose.
Configurable lookback values.
You can adjust the default lookback values to suit your prefered trading style and timeframe. If you like to trade a shorter time frame, lowering the default lookback values will make the divergences drawn more sensitive to short term price action.
How do traders use divergences in their trading?
A divergence is considered a leading indicator in technical analysis, meaning it has the ability to indicate a potential price move in the short term future.
Hidden bullish and hidden bearish divergences, which indicate a potential continuation of the current trend are sometimes considered a good place for traders to begin, since trend continuation occurs more frequently than reversals, or trend changes.
When trading regular bullish divergences and regular bearish divergences, which are indications of a trend reversal, the probability of it doing so may increase when these occur at a strong support or resistance level. A common mistake new traders make is to get into a regular divergence trade too early, assuming it will immediately reverse, but these can continue to form for some time before the trend eventually changes, by using forms of support or resistance as an added confluence, such as when price reaches a moving average, the success rate when trading these patterns may increase.
Typically, traders will manually draw lines across the swing highs and swing lows of both the price chart and the oscillator to see whether they appear to present a divergence, this indicator will draw them for you, quickly and clearly, and can notify you when they occur.
Disclaimer : This script includes code from the stock UO by Tradingview as well as the RSI divergence indicator.
Aroon Oscillator [bkeevil]The Aroon Oscillator is intended to highlight short-term trend changes by comparing the number of periods since the last high with the number of periods since the last low.
Since the crossover rules for this oscillator frequently give false signals, I have opted for a more general approach: When the oscillator passes above the 50 line, the background of the indicator will turn green, indicating a general short term buy condition. When the oscillator passes below the -50 line, the background of the indicator will turn red, indicating a general short term sell condition. Use this indicator in combination with other indicators and price signals to identify short term trend changes.
This version improves on existing versions by:
Adding background colors to indicate general buy/sell conditions
More visually appealing
Uses the latest version 5 features
Well documented source code that conforms to the style guide
Dap's Oscillator- Short Term Momentum and Trend. BINANCE:BTCUSDT BYBIT:BTCUSDT BYBIT:ETHUSDT BINANCE:ETHUSDT
DAP's OSCILLATOR:
WHAT IS IT?
This Oscillator was created to inspire confidence in the short-term trend of traders. This will work very well with a volatility metric (I recommend BBWP by @The_Caretaker)
WHAT IS IT MADE OF?
1. Consists of a series of equations (mainly the difference between simple to exponential moving averages) and Standard deviations of these moving average differences (length equivalent to the length of sampled ma's)
2. These equations are then boiled down through an averaging process array, after averaging the covariants are equated against the variants of the positive side of the array. This is what is presented as the aqua line.
3. The RC average (yellow) is the sma following the DAP'S Oscillator at a specified length
4. The most important part of this indicator is simply the momentum oscillator represented as a green or red line based on the value relative to the Oscillators.
HOW DO I USE THIS?
As I mentioned before mixed with a volatility metric, it should set you up for a good decision based on short-term trends. I would say to be careful for periods of consolidation, with the consolidation the momentum often meets hands with DAP's Oscillator and can cause fake-outs. You want to spot divergences from the price to the momentum difference, as well as room to work down or upward to secure a good entry on a position.
CHEAT CODE'S NOTES:
I appreciate everyone who has boosted my previous scripts, it means a lot. If you want to translate words to pine script onto a chart, feel free to PM me. I would be happy to help bring an indicator to life. I may take a quick break but will be back shortly to help create more cheat codes for yall. Thanks!
-Cheat Code
Normalized, Variety, Fast Fourier Transform Explorer [Loxx]Normalized, Variety, Fast Fourier Transform Explorer demonstrates Real, Cosine, and Sine Fast Fourier Transform algorithms. This indicator can be used as a rule of thumb but shouldn't be used in trading.
What is the Discrete Fourier Transform?
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies. It has the same sample-values as the original input sequence. The DFT is therefore said to be a frequency domain representation of the original input sequence. If the original sequence spans all the non-zero values of a function, its DTFT is continuous (and periodic), and the DFT provides discrete samples of one cycle. If the original sequence is one cycle of a periodic function, the DFT provides all the non-zero values of one DTFT cycle.
What is the Complex Fast Fourier Transform?
The complex Fast Fourier Transform algorithm transforms N real or complex numbers into another N complex numbers. The complex FFT transforms a real or complex signal x in the time domain into a complex two-sided spectrum X in the frequency domain. You must remember that zero frequency corresponds to n = 0, positive frequencies 0 < f < f_c correspond to values 1 ≤ n ≤ N/2 −1, while negative frequencies −fc < f < 0 correspond to N/2 +1 ≤ n ≤ N −1. The value n = N/2 corresponds to both f = f_c and f = −f_c. f_c is the critical or Nyquist frequency with f_c = 1/(2*T) or half the sampling frequency. The first harmonic X corresponds to the frequency 1/(N*T).
The complex FFT requires the list of values (resolution, or N) to be a power 2. If the input size if not a power of 2, then the input data will be padded with zeros to fit the size of the closest power of 2 upward.
What is Real-Fast Fourier Transform?
Has conditions similar to the complex Fast Fourier Transform value, except that the input data must be purely real. If the time series data has the basic type complex64, only the real parts of the complex numbers are used for the calculation. The imaginary parts are silently discarded.
What is the Real-Fast Fourier Transform?
In many applications, the input data for the DFT are purely real, in which case the outputs satisfy the symmetry
X(N-k)=X(k)
and efficient FFT algorithms have been designed for this situation (see e.g. Sorensen, 1987). One approach consists of taking an ordinary algorithm (e.g. Cooley–Tukey) and removing the redundant parts of the computation, saving roughly a factor of two in time and memory. Alternatively, it is possible to express an even-length real-input DFT as a complex DFT of half the length (whose real and imaginary parts are the even/odd elements of the original real data), followed by O(N) post-processing operations.
It was once believed that real-input DFTs could be more efficiently computed by means of the discrete Hartley transform (DHT), but it was subsequently argued that a specialized real-input DFT algorithm (FFT) can typically be found that requires fewer operations than the corresponding DHT algorithm (FHT) for the same number of inputs. Bruun's algorithm (above) is another method that was initially proposed to take advantage of real inputs, but it has not proved popular.
There are further FFT specializations for the cases of real data that have even/odd symmetry, in which case one can gain another factor of roughly two in time and memory and the DFT becomes the discrete cosine/sine transform(s) (DCT/DST). Instead of directly modifying an FFT algorithm for these cases, DCTs/DSTs can also be computed via FFTs of real data combined with O(N) pre- and post-processing.
What is the Discrete Cosine Transform?
A discrete cosine transform ( DCT ) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. The DCT , first proposed by Nasir Ahmed in 1972, is a widely used transformation technique in signal processing and data compression. It is used in most digital media, including digital images (such as JPEG and HEIF, where small high-frequency components can be discarded), digital video (such as MPEG and H.26x), digital audio (such as Dolby Digital, MP3 and AAC ), digital television (such as SDTV, HDTV and VOD ), digital radio (such as AAC+ and DAB+), and speech coding (such as AAC-LD, Siren and Opus). DCTs are also important to numerous other applications in science and engineering, such as digital signal processing, telecommunication devices, reducing network bandwidth usage, and spectral methods for the numerical solution of partial differential equations.
The use of cosine rather than sine functions is critical for compression, since it turns out (as described below) that fewer cosine functions are needed to approximate a typical signal, whereas for differential equations the cosines express a particular choice of boundary conditions. In particular, a DCT is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. The DCTs are generally related to Fourier Series coefficients of a periodically and symmetrically extended sequence whereas DFTs are related to Fourier Series coefficients of only periodically extended sequences. DCTs are equivalent to DFTs of roughly twice the length, operating on real data with even symmetry (since the Fourier transform of a real and even function is real and even), whereas in some variants the input and/or output data are shifted by half a sample. There are eight standard DCT variants, of which four are common.
The most common variant of discrete cosine transform is the type-II DCT , which is often called simply "the DCT". This was the original DCT as first proposed by Ahmed. Its inverse, the type-III DCT , is correspondingly often called simply "the inverse DCT" or "the IDCT". Two related transforms are the discrete sine transform ( DST ), which is equivalent to a DFT of real and odd functions, and the modified discrete cosine transform (MDCT), which is based on a DCT of overlapping data. Multidimensional DCTs ( MD DCTs) are developed to extend the concept of DCT to MD signals. There are several algorithms to compute MD DCT . A variety of fast algorithms have been developed to reduce the computational complexity of implementing DCT . One of these is the integer DCT (IntDCT), an integer approximation of the standard DCT ,: ix, xiii, 1, 141–304 used in several ISO /IEC and ITU-T international standards.
What is the Discrete Sine Transform?
In mathematics, the discrete sine transform (DST) is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using a purely real matrix. It is equivalent to the imaginary parts of a DFT of roughly twice the length, operating on real data with odd symmetry (since the Fourier transform of a real and odd function is imaginary and odd), where in some variants the input and/or output data are shifted by half a sample.
A family of transforms composed of sine and sine hyperbolic functions exists. These transforms are made based on the natural vibration of thin square plates with different boundary conditions.
The DST is related to the discrete cosine transform (DCT), which is equivalent to a DFT of real and even functions. See the DCT article for a general discussion of how the boundary conditions relate the various DCT and DST types. Generally, the DST is derived from the DCT by replacing the Neumann condition at x=0 with a Dirichlet condition. Both the DCT and the DST were described by Nasir Ahmed T. Natarajan and K.R. Rao in 1974. The type-I DST (DST-I) was later described by Anil K. Jain in 1976, and the type-II DST (DST-II) was then described by H.B. Kekra and J.K. Solanka in 1978.
Notable settings
windowper = period for calculation, restricted to powers of 2: "16", "32", "64", "128", "256", "512", "1024", "2048", this reason for this is FFT is an algorithm that computes DFT (Discrete Fourier Transform) in a fast way, generally in 𝑂(𝑁⋅log2(𝑁)) instead of 𝑂(𝑁2). To achieve this the input matrix has to be a power of 2 but many FFT algorithm can handle any size of input since the matrix can be zero-padded. For our purposes here, we stick to powers of 2 to keep this fast and neat. read more about this here: Cooley–Tukey FFT algorithm
SS = smoothing count, this smoothing happens after the first FCT regular pass. this zeros out frequencies from the previously calculated values above SS count. the lower this number, the smoother the output, it works opposite from other smoothing periods
Fmin1 = zeroes out frequencies not passing this test for min value
Fmax1 = zeroes out frequencies not passing this test for max value
barsback = moves the window backward
Inverse = whether or not you wish to invert the FFT after first pass calculation
Related indicators
Real-Fast Fourier Transform of Price Oscillator
STD-Stepped Fast Cosine Transform Moving Average
Real-Fast Fourier Transform of Price w/ Linear Regression
Variety RSI of Fast Discrete Cosine Transform
Additional reading
A Fast Computational Algorithm for the Discrete Cosine Transform by Chen et al.
Practical Fast 1-D DCT Algorithms With 11 Multiplications by Loeffler et al.
Cooley–Tukey FFT algorithm
Ahmed, Nasir (January 1991). "How I Came Up With the Discrete Cosine Transform". Digital Signal Processing. 1 (1): 4–5. doi:10.1016/1051-2004(91)90086-Z.
DCT-History - How I Came Up With The Discrete Cosine Transform
Comparative Analysis for Discrete Sine Transform as a suitable method for noise estimation
