# obspy.signal.invsim.paz_to_freq_resp¶

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.

Parameters: 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 numpy.ndarray complex128 Frequency response of PAZ of length nfft

Note

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)