--- title: "High-Pass Filter: Formula, Meaning" description: "A high-pass filter removes slow components such as trend and passes short-period fluctuations. In John Ehlers' trading filters it is usually a two-pole..." canonical: https://www.getswoopr.com/indicators/cycle-and-signal-processing/high-pass-filter/ source: "Swoopr Investment: https://www.getswoopr.com" --- ## Direct Answer > A high-pass filter removes slow components such as trend and passes short-period fluctuations. In John Ehlers' trading filters it is usually a two-pole recursive design where a cutoff period sets the point at which longer cycles start to be attenuated. Output oscillates around zero and retains movements shorter than the cutoff. # High-Pass Filter: Formula, Meaning, Signals, Examples and How to Use It ## How Is High-Pass Filter Calculated? A high-pass filter removes slow components such as trend and passes short-period fluctuations. In John Ehlers' trading filters it is usually a two-pole recursive design where a cutoff period sets the point at which longer cycles start to be attenuated. **Formula:** `alpha = (cos(0.707*2*pi/P) + sin(0.707*2*pi/P) - 1) / cos(0.707*2*pi/P); HP = (1 - alpha/2)^2 * (price - 2*price[1] + price[2]) + 2*(1 - alpha)*HP[1] - (1 - alpha)^2 * HP[2]` **Inputs:** - Close prices - Cutoff period P in bars (for example 48) **Worked example.** A cutoff period of 48 bars gives a smoothing coefficient alpha of 0.0885. The inputs are illustrative numbers, not market data. **Reading it.** Output oscillates around zero and retains movements shorter than the cutoff. It is a detrending step used before measuring cycles, and a positive reading means price is above the filter's moving baseline. **Limits.** The cutoff is a judgment and the filter responds slowly after large jumps. The output has the units of price and its size depends on the volatility of the instrument. ## What is High-Pass Filter? A high-pass filter removes slow components such as trend and passes short-period fluctuations. In John Ehlers' trading filters it is usually a two-pole recursive design where a cutoff period sets the point at which longer cycles start to be attenuated. ## How to use High-Pass Filter Output oscillates around zero and retains movements shorter than the cutoff. It is a detrending step used before measuring cycles, and a positive reading means price is above the filter's moving baseline. A reading alone is never a buy or sell signal; it needs context from price structure, volume, volatility and the broader market regime. ## Strengths - The two-pole design removes slow components with a sharper cutoff than a one-pole filter, leaving oscillation around a zero baseline. - Its single parameter, the cutoff period, maps directly to bars, so the user states in plain units which cycle lengths are being removed. - Reproducible when the formula and data convention are fixed. ## Weaknesses and limitations - A recursive high-pass rings after a step in price, so a single jump produces oscillation in the output for several bars. - The 0.707 damping term in alpha is a fixed design choice that sets a particular overshoot behavior, which cannot be changed without altering the formula. - Correlated indicators can create false confidence by repeating the same underlying information. ## Editorial and risk note This page is educational content, not individualized investment advice. It should not imply guaranteed prediction, accuracy or outperformance. ## Frequently Asked Questions Is High-Pass Filter a buy or sell signal? No. Output oscillates around zero and retains movements shorter than the cutoff. The cutoff is a judgment and the filter responds slowly after large jumps. A trade built on it still needs a trigger, an invalidation rule, a position size and realistic execution assumptions. What is the best setting for High-Pass Filter? High-Pass Filter takes these inputs: close prices; cutoff period P in bars (for example 48). There is no universal best setting for the tunable ones, so test them across instruments, regimes and out-of-sample periods and favor stable parameter regions over one historical winner. Can High-Pass Filter be used by itself? The cutoff is a judgment and the filter responds slowly after large jumps. The output has the units of price and its size depends on the volatility of the instrument. For that reason it is read next to measures of direction, participation, valuation, liquidity and risk, not alone. Does High-Pass Filter work on every timeframe? The calculation (alpha = (cos(0.707*2*pi/P) + sin(0.707*2*pi/P) - 1) / cos(0.707*2*pi/P); HP = (1 - alpha/2)^2 * (price - 2*price[1] + price[2]) + 2*(1 - alpha)*HP[1] - (1 - alpha)^2 * HP[2]) can be run on any bar size, but behavior is not portable: a reading on a five-minute chart describes a very different market window from the same reading on a daily chart. Validate the exact timeframe before relying on it. Why does High-Pass Filter give false signals? A recursive high-pass rings after a step in price, so a single jump produces oscillation in the output for several bars. The 0.707 damping term in alpha is a fixed design choice that sets a particular overshoot behavior, which cannot be changed without altering the formula. Lag, noise and regime changes add to this, because market participants react to new information after the reading is calculated. How should High-Pass Filter be backtested? Rebuild High-Pass Filter from close prices using point-in-time data, write the rules before testing, include delisted securities where relevant, model realistic fills and costs, reserve a validation sample and compare with a simpler baseline. S Swoopr Editorial Team The Swoopr Editorial Team produces independent investment education, research, and tools for understanding markets, evaluating opportunities, and managing risk. All content is educational only and does not constitute personalized investment advice. See our [editorial policy](https://www.getswoopr.com/legal/editorial-policy/) and [corrections policy](https://www.getswoopr.com/legal/corrections-policy/).