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Apply FFT-based Highpass Filter to Signal

Source: R/filter_bandwidth_fft.R
filter_highpass_fft.Rd

This function implements a highpass filter using the Fast Fourier Transform (FFT). It provides a sharp frequency cutoff but may introduce ringing artifacts (Gibbs phenomenon).

Usage

filter_highpass_fft(
  x,
  cutoff_freq,
  sampling_rate,
  na_action = c("linear", "spline", "stine", "locf", "value", "error"),
  keep_na = FALSE,
  ...
)

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).

na_action

Method to handle NA values before filtering. One of: - "linear": Linear interpolation (default) - "spline": Spline interpolation for smoother curves - "stine": Stineman interpolation preserving data shape - "locf": Last observation carried forward - "value": Replace with a constant value - "error": Raise an error if NAs are present

keep_na

Logical indicating whether to restore NAs to their original positions after filtering (default = FALSE)

...

Additional arguments passed to replace_na(). 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

FFT-based filtering applies a hard cutoff in the frequency domain. This can be advantageous for:

  • Precise frequency selection

  • Batch processing of long signals

  • Cases where sharp frequency cutoffs are desired

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

Limitations:

  • May introduce ringing artifacts

  • Assumes periodic signal (can cause edge effects)

  • Less suitable for real-time processing

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

See also

replace_na for details on NA handling methods filter_lowpass_fft for FFT-based low-pass filtering filter_highpass for Butterworth-based 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_fft(x, cutoff_freq = 2, sampling_rate = 1000)

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

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

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

# Compare with Butterworth filter
butter_filtered <- filter_highpass(x, 2, 1000)