Use FFmpeg fftfilt for 2D Frequency Domain Filtering

This article explains how to use the FFmpeg fftfilt filter to apply 2D frequency-domain filtering to video streams. You will learn the core concepts behind the filter, the mathematical variables used to target specific frequencies, and practical command-line examples for implementing low-pass, high-pass, and custom band-pass filters to modify your video’s spatial frequencies.

Understanding the fftfilt Filter

The fftfilt filter in FFmpeg performs a 2D Fast Fourier Transform (FFT) on each video frame to transition it from the spatial domain to the frequency domain. In this domain, you can manipulate specific frequency coefficients using custom mathematical expressions. After applying your filter, FFmpeg performs an Inverse Fast Fourier Transform (IFFT) to convert the frame back into the viewable spatial domain.

This process is highly effective for tasks like noise reduction, image sharpening, edge detection, and removing repetitive pattern noise (like moiré patterns).

Basic Syntax and Variables

The basic syntax for the fftfilt filter is:

ffmpeg -i input.mp4 -vf "fftfilt=weight_Y='expression':weight_U='expression':weight_V='expression'" output.mp4

You can target the Luma (Y) and Chroma (U, V) channels independently.

To define your filter expressions, FFmpeg provides several built-in variables representing the frequency coordinates:

• X and Y: The horizontal and vertical coordinate of the current frequency coefficient.
• W and H: The width and height of the channel matrix.
• hypot(X,Y): The distance from the top-left corner (0,0), which represents the lowest frequency (DC component). As hypot(X,Y) increases, you target higher spatial frequencies.

The output of your expression acts as a multiplier (weight) for each frequency coefficient. A weight of 1 keeps the frequency intact, while 0 completely removes it.

Practical Examples

1. Low-Pass Filter (Blurring / Noise Reduction)

A low-pass filter allows low frequencies to pass through while blocking high frequencies. This results in a blurred or smoothed image, which is useful for removing high-frequency grain and noise.

To keep only the frequencies within a radius of 30 pixels from the origin:

ffmpeg -i input.mp4 -vf "fftfilt=weight_Y='lte(hypot(X,Y),30)'" output.mp4

• lte(hypot(X,Y),30) evaluates to 1 if the frequency coordinate is within 30 pixels of the origin, and 0 otherwise.

2. High-Pass Filter (Edge Detection / Sharpening)

A high-pass filter blocks low frequencies (smooth gradients) and passes high frequencies (sharp details and edges).

To eliminate all frequencies within a radius of 15 pixels of the origin:

ffmpeg -i input.mp4 -vf "fftfilt=weight_Y='gt(hypot(X,Y),15)'" output.mp4

• gt(hypot(X,Y),15) evaluates to 1 for all high frequencies beyond a radius of 15, removing the overall illumination and leaving only sharp transitions and edges.

3. Band-Pass Filter

A band-pass filter isolates a specific range of frequencies. This is highly useful if you want to target and eliminate a specific repetitive pattern or frequency band of noise.

To pass only frequencies between a radius of 10 and 50:

ffmpeg -i input.mp4 -vf "fftfilt=weight_Y='between(hypot(X,Y),10,50)'" output.mp4

4. Custom Frequency Modification (Sharpening Effect)

Instead of completely cutting off frequencies with 1 and 0, you can amplify certain frequencies to sharpen the video. For example, to boost mid-to-high frequencies while leaving low frequencies untouched:

ffmpeg -i input.mp4 -vf "fftfilt=weight_Y='1+gt(hypot(X,Y),20)*0.5'" output.mp4

• This expression keeps the base weight at 1 for low frequencies, but multiplies frequencies beyond a radius of 20 by 1.5, boosting fine image details.