# Generate FIR filter coefficients from Mag and Phase response

I have the target filter response in the form of (bin #, value) for every fft bin, for Magnitude and Phase. As an example, (bin 100, +12dB) for Magnitude and (bin 100, -90 degrees) for Phase.

How do I generate the corresponding FIR filter coefficients?

• Reconstruct the complex frequency response for each FFT bin, do an IFFT and you get an impulse response which is the FIR coefficients. May 25 at 7:04

Define your frequency response with $$N$$ complex-valued samples (real parts and imaginary parts). The first sample, $$F(0)$$, is associated with zero Hz. The last sample, $$F(N-1)$$, is associated with $$(N-1)F_s/N$$ Hz. Make sure the $$F(m)$$ frequency samples are conjugate symmetrical. Then perform the inverse DFT (IDFT) of the complex-valued $$F(m)$$ sequence.
If your $$F(m)$$ sequence is truly conjugate symmetrical then the imaginary parts of your IDFT results will be VERY small in value. (In theory the imaginary parts of your IDFT results should be zero-valued.) After performing your IDFT, ignore the imaginary parts of your IDFT results.