Apply Butterworth Highpass Filter to Signal

This function applies a highpass Butterworth filter to a signal using forward-backward filtering (filtfilt) to achieve zero phase distortion. The Butterworth filter is maximally flat in the passband, making it ideal for many signal processing applications.

Usage

filter_highpass(
  x,
  cutoff_freq,
  sampling_rate,
  order = 4,
  na_action = c("linear", "spline", "stine", "locf", "value", "error"),
  keep_na = TRUE,
  ...
)

Arguments

x

Numeric vector containing the signal to be filtered

cutoff_freq

Cutoff frequency in Hz. Frequencies above this value are passed, while frequencies below are attenuated. Should be between 0 and sampling_rate/2.

sampling_rate

Sampling rate of the signal in Hz. Must be at least twice the highest frequency component in the signal (Nyquist criterion).

order

Filter order (default = 4). Controls the steepness of frequency rolloff:

• Higher orders give sharper cutoffs but may introduce more ringing

• Lower orders give smoother transitions but less steep rolloff

• Common values in practice are 2-8

• Values above 8 are rarely used due to numerical instability

na_action

Method used to fill NA values before filtering, so the filter sees a complete series. One of "linear" (default), "spline", "stine", "locf", "value", or "error" to abort when NAs are present. Filling is internal: whether the filled values reach the output is controlled by keep_na.

keep_na

Logical. If TRUE (default), positions that were NA in the input are NA in the output — gaps stay gaps. If FALSE, the values used to fill those gaps are kept, so the output has fewer NAs than the input and genuinely-missing stretches come back as interpolated estimates.

...

Additional arguments passed to replace_na_with(). Common options include:

• value: Numeric value for replacement when na_action = "value"

• min_gap: Minimum gap size to interpolate/fill

• max_gap: Maximum gap size to interpolate/fill

Value

Numeric vector containing the filtered signal

Details

The Butterworth filter response falls off at -6*order dB/octave. The cutoff frequency corresponds to the -3dB point of the filter's magnitude response.

Common Applications:

• Removing baseline drift: Use low cutoff (0.1-1 Hz)

• EMG analysis: Use moderate cutoff (10-20 Hz)

• Motion artifact removal: Use application-specific cutoff

Parameter Selection Guidelines:

• cutoff_freq: Choose based on the lowest frequency you want to preserve

• order: Same guidelines as lowpass_filter

Common values by field:

• ECG processing: order=2, cutoff=0.5 Hz

• EEG analysis: order=4, cutoff=1 Hz

• Mechanical vibrations: order=2, cutoff application-specific

Missing Value Handling: The function uses replace_na_with() internally for handling missing values. See ?replace_na_with for detailed information about each method and its parameters. NAs can optionally be restored to their original positions after filtering using keep_na = TRUE.

References

Butterworth, S. (1930). On the Theory of Filter Amplifiers. Wireless Engineer, 7, 536-541.

See also

replace_na_with() for details on NA handling methods filter_lowpass for low-pass filtering

Examples

# Generate example signal with drift
t <- seq(0, 1, by = 0.001)
drift <- 0.5 * t  # Linear drift
signal <- sin(2*pi*10*t)  # 10 Hz signal
x <- signal + drift

# Add some NAs
x[sample(length(x), 10)] <- NA

# Basic filtering with linear interpolation for NAs
filtered <- filter_highpass(x, cutoff_freq = 2, sampling_rate = 1000)

# Using spline interpolation with max gap constraint
filtered <- filter_highpass(x, cutoff_freq = 2, sampling_rate = 1000,
                           na_action = "spline", max_gap = 3)

# Replace NAs with zeros before filtering
filtered <- filter_highpass(x, cutoff_freq = 2, sampling_rate = 1000,
                           na_action = "value", value = 0)

# Filter but keep NAs in their original positions
filtered <- filter_highpass(x, cutoff_freq = 2, sampling_rate = 1000,
                           na_action = "linear", keep_na = TRUE)