paz_to_freq_resp(poles, zeros, scale_fac, t_samp, nfft, freq=False)[source]

Convert Poles and Zeros (PAZ) to frequency response. The output contains the frequency zero which is the offset of the trace.

  • poles (list of complex) The poles of the transfer function
  • zeros (list of complex) The zeros of the transfer function
  • scale_fac (float) Gain factor
  • t_samp (float) Sampling interval in seconds
  • nfft (int) Number of FFT points of signal which needs correction
Return type:

numpy.ndarray complex128


Frequency response of PAZ of length nfft


In order to plot/calculate the phase you need to multiply the complex part by -1. This results from the different definition of the Fourier transform and the phase. The numpy.fft is defined as A(jw) = int_{-inf}^{+inf} a(t) e^{-jwt}; where as the analytic signal is defined A(jw) = | A(jw) | e^{jphi}. That is in order to calculate the phase the complex conjugate of the signal needs to be taken. E.g. phi = angle(f,conj(h),deg=True) As the range of phi is from -pi to pi you could add 2*pi to the negative values in order to get a plot from [0, 2pi]: where(phi<0,phi+2*pi,phi); plot(f,phi)