# FIR filter delay and window length

How long does it take for FIR filter to produce first output sample for given window / kernel / impulse (not sure what is best name) length?

Does it differ between minimum phase and linear phase variants? Lets say we have two FIR low pass filters,one minimum phase,other linear phase,both have 100 sample long impulse response/window length,how long will it take to obtain first output sample?

My guess is the minimum phase needs 100 sample long delay while the linear phase 50 samples.

For causal FIR linear phase filters the delay you ask for can simply be computed from the group delay and is given by (for an odd length symmetric FIR filter of length $L=2M+1$) $$\tau = - \frac{d\phi(\omega)}{d\omega} = - \frac{d-M\omega}{d\omega} = M$$
So it will shift every input component by $M$ samples at the output.
NOTE: you can always produce your output sample $y[0]$ as soon as the first input sample $x[0]$ arrives. The delay is related with the information processing and not the sample processing;i.e., your initial $M-1$ output samples will be called as the filter transient response, before the steady output is computed.