FIR Filter Coefficient Designer (Hamming Window)
Enter sampling frequency, cutoff frequency, and filter order to generate Hamming-windowed FIR lowpass coefficients — outputs a C array ready to paste into firmware.
Filter Specifications
- Nyquist theorem: Fc must be less than Fs / 2.
- Higher order M → steeper stopband roll-off, but increases computation delay and complexity proportionally.
Filter Frequency Response (Magnitude)
Generated C Array
// Hamming Window FIR Lowpass Filter Coefficients
// Fs = 8000 Hz, Fc = 1000 Hz, Taps = 31
#define FIR_LPF_COEFFS_30_TAPS 31
const double FIR_LPF_COEFFS_30[FIR_LPF_COEFFS_30_TAPS] = {
-0.0012039,
-0.0020534,
-0.0020796,
0.0000000,
0.0047649,
0.0098960,
0.0099785,
0.0000000,
-0.0189638,
-0.0362933,
-0.0347620,
0.0000000,
0.0686323,
0.1532658,
0.2234585,
0.2507202,
0.2234585,
0.1532658,
0.0686323,
0.0000000,
-0.0347620,
-0.0362933,
-0.0189638,
0.0000000,
0.0099785,
0.0098960,
0.0047649,
0.0000000,
-0.0020796,
-0.0020534,
-0.0012039
};FIR Digital Filter Fundamentals
An FIR (Finite Impulse Response) filter is the most fundamental digital filter in DSP. It multiplies incoming digital samples by a weighted coefficient array and sums the products — a convolution operation — to attenuate high-frequency noise components.
Why a Hamming Window?
The ideal mathematical sinc lowpass filter has infinite duration in time. Real microcontrollers and DSPs must truncate it to a finite number of taps, which causes severe ringing at the cutoff edge (Gibbs phenomenon). Applying a Hamming window function smoothly tapers the coefficient ends, trading a small amount of transition sharpness for a flat, well-behaved stopband attenuation.