Filter Designer Online — Design & Visualize Digital Filters
Design lowpass, highpass, bandpass, and notch FIR filters using the windowed-sinc method. Visualize frequency response, phase response, impulse response, and apply your filter to test signals — entirely in your browser.
Frequency Response (Magnitude)
Phase Response
Impulse Response h[n]
Filtered Signal
How FIR Filter Design Works
A Finite Impulse Response (FIR) filter produces output samples as a weighted sum of input samples. The weights are the filter coefficients h[n], and the process of computing the output is convolution. The windowed-sinc method is a classic technique for designing FIR filters with a desired frequency response.
Step 1: Ideal Filter
An ideal lowpass filter passes all frequencies below a cutoff and completely blocks everything above it. Its impulse response is a sinc function that extends infinitely in both directions — which is impossible to implement directly.
Step 2: Truncate to Finite Length
We truncate the ideal sinc to a finite number of samples (the filter order). This truncation introduces ripple and spectral leakage due to the abrupt cutoff in the time domain, known as the Gibbs phenomenon.
Step 3: Apply a Window Function
To reduce the Gibbs effect, we multiply the truncated sinc by a smooth window function that tapers to zero at the edges. Popular choices are the Hann, Hamming, and Blackman windows. Each offers a different trade-off between transition bandwidth (how sharp the cutoff is) and stopband attenuation (how well unwanted frequencies are suppressed).
Highpass, Bandpass, and Notch Filters
These are derived from the lowpass design using spectral inversion (highpass), bandpass subtraction (bandpass = highpass − lowpass), or complement (notch = 1 − bandpass). The windowed-sinc coefficients are adjusted at the center tap accordingly.
Filter Design FAQ
What is a digital FIR filter?
A Finite Impulse Response (FIR) filter computes each output sample as a weighted sum of a finite number of past and present input samples. The weights are the filter coefficients (also called taps). FIR filters are inherently stable, can have exactly linear phase (symmetric coefficients), and are easy to design. The trade-off is that they typically require more coefficients (higher order) than IIR filters to achieve sharp frequency cutoffs.
How does the windowed-sinc filter design method work?
The ideal lowpass filter has a sinc-shaped impulse response that extends infinitely in both directions. The windowed-sinc method truncates this ideal response to a finite number of taps and multiplies it by a smooth window function (Hann, Hamming, Blackman, etc.) to reduce spectral leakage and ripple. The cutoff frequency determines the sinc period, the filter order determines the number of taps, and the window type controls the trade-off between mainlobe width and sidelobe suppression.
What is the difference between lowpass, highpass, bandpass, and notch filters?
A lowpass filter passes frequencies below its cutoff and attenuates higher frequencies — useful for anti-aliasing and noise removal. A highpass filter does the opposite, passing high frequencies and removing low ones — used for DC removal and edge detection. A bandpass filter passes a range of frequencies between two cutoffs. A notch (band-stop) filter rejects a range of frequencies and passes everything else — commonly used to remove powerline interference (50/60 Hz).
What does filter order mean and how does it affect performance?
The filter order (number of taps minus one) determines the length of the impulse response. Higher-order filters have sharper transitions between passband and stopband (steeper roll-off) and better stopband attenuation, but they require more computation per sample and introduce more delay (latency). For a linear-phase FIR filter, the group delay equals (N−1)/2 samples, where N is the number of taps.
How do I choose between Hann, Hamming, and Blackman windows?
The Hann window offers a good balance between mainlobe width and sidelobe level (about −31 dB first sidelobe). The Hamming window has a slightly wider mainlobe but better sidelobe suppression (−43 dB). The Blackman window has the widest mainlobe but excellent sidelobe suppression (−58 dB), making it ideal when stopband attenuation is critical. For most general-purpose filter designs, Hamming or Blackman are recommended.
Cite This Tool
APA
Fourier Tools. (2026). Filter Designer Online — Design & Visualize Digital Filters. Retrieved February 17, 2026, from https://fourier.tools/tools/filter-designer
BibTeX
@misc{fouriertools2026filter,
title = {Filter Designer Online — Design & Visualize Digital Filters},
author = {Fourier Tools},
year = {2026},
url = {https://fourier.tools/tools/filter-designer},
note = {Accessed: 2026-02-17}
}