Signal processing
FIR coefficient symmetry
Check real FIR coefficients for symmetric or antisymmetric linear-phase structure.
Your inputs
Start with an exampleYour result
Example resultAa — A small example of your colors.
How it works
Compare each coefficient with its reflected partner and its negative. Combine exact/tolerance matches with odd/even length to identify candidate types I–IV.
The five coefficients 1,2,3,2,1 are exactly symmetric, giving type I and a nominal delay of 2 samples.
Limits
Up to 4096 finite real coefficients. Tolerance matches are labeled approximate; forced zeros and delay applicability require exact symmetry. The zero filter is degenerate. This does not design a filter or measure stopband attenuation, quantization error or phase at response zeros.