import numpy
import matplotlib.pyplot as p
import lab6
from lab2_3 import unit_sample_response
from lab6_1 import freq_res_usr

# compute coefficients for a difference equation with
# a pair of complex conjugate poles at the specified
# frequency and with a scale factor of r.
def pole_to_coeffs(pole_freq,r):
    pass  # your code here

# use the differential equation solver to convert
# diffeq coefficients into a unit-sample response
def pole_to_usr(pole_freq,r):
    ycoeffs = pole_to_coeffs(pole_freq,r)
    xcoeffs = [1.0] + [0.0]*(len(ycoeffs) - 1)
    channel = lab6.de_solver(ycoeffs,xcoeffs)
    return unit_sample_response(channel)

if __name__ == '__main__':
    # get unit-sample response for filter with a pole at pi/2
    pole_freq = numpy.pi/2
    r = 0.98
    usr_pole = pole_to_usr(pole_freq,r)

    # plot the frequency response
    omega_pole, mag_hejw_pole = freq_res_usr(usr_pole)
    lab6.plot_freq_response(omega_pole,mag_hejw_pole,
      'pole filter @ $\Omega=%3.2g$, r=%3.2g' % (pole_freq,r))

    p.show()