import numpy
import scipy.signal
from matplotlib.pyplot import *
b=[1,1]
a=[1,-1]
w,h=scipy.signal.freqz(b,a)

figure()
subplot(211)
plot(w/(2*numpy.pi),20*numpy.log10(numpy.absolute(h)))
xlabel("f/fe")
ylabel("GdB")
grid()
subplot(212)      
plot(w/(2*numpy.pi),numpy.angle(h)/numpy.pi)
xlabel("f/fe")
ylabel("phase/pi")
axis([0,0.5,-1,1])
grid()
                   

r=0.8
G=1
b0 = (1-r)*G/2
b=[b0,b0]
a=[1,-r]
w,h=scipy.signal.freqz(b,a)

figure()
subplot(211)
plot(w/(2*numpy.pi),20*numpy.log10(numpy.absolute(h)))
xlabel("f/fe")
ylabel("GdB")
grid()
subplot(212)      
plot(w/(2*numpy.pi),numpy.angle(h)/numpy.pi)
xlabel("f/fe")
ylabel("phase/pi")
axis([0,0.5,-1,1])
grid()
                 

r=0.99
G=1
b0 = (1-r)*G/2
b=[b0,b0]
a=[1,-r]
w,h=scipy.signal.freqz(b,a)

figure()
subplot(211)
plot(w/(2*numpy.pi),20*numpy.log10(numpy.absolute(h)))
xlabel("f/fe")
ylabel("GdB")
grid()
subplot(212)      
plot(w/(2*numpy.pi),numpy.angle(h)/numpy.pi)
xlabel("f/fe")
ylabel("phase/pi")
axis([0,0.5,-1,1])
grid()
                 

b=[0,1-r]
a=[1,-r]
w,h=scipy.signal.freqz(b,a)

figure()
subplot(211)
plot(w/(2*numpy.pi),20*numpy.log10(numpy.absolute(h)))
xlabel("f/fe")
ylabel("GdB")
grid()
subplot(212)      
plot(w/(2*numpy.pi),numpy.angle(h)/numpy.pi)
xlabel("f/fe")
ylabel("phase/pi")
axis([0,0.5,-1,1])
grid()
                 

r=0.2
G=1
b0 = (1-r)*G/2
b=[b0,-b0]
a=[1,r]
w,h=scipy.signal.freqz(b,a)

figure()
subplot(211)
plot(w/(2*numpy.pi),20*numpy.log10(numpy.absolute(h)))
xlabel("f/fe")
ylabel("GdB")
grid()
subplot(212)      
plot(w/(2*numpy.pi),numpy.angle(h)/numpy.pi)
xlabel("f/fe")
ylabel("phase/pi")
axis([0,0.5,-1,1])
grid()
                 

r=0.999
G=1
b0 = (1+r)*G/2
b=[b0,-b0]
a=[1,-r]
w,h=scipy.signal.freqz(b,a)

figure()
subplot(211)
plot(w/(2*numpy.pi),20*numpy.log10(numpy.absolute(h)))
xlabel("f/fe")
ylabel("GdB")
grid()
subplot(212)      
plot(w/(2*numpy.pi),numpy.angle(h)/numpy.pi)
xlabel("f/fe")
ylabel("phase/pi")
axis([0,0.5,-1,1])
grid()
                 

r1=0.9
r2=0.95

b=[1,0,-1]
a=[1,-(r1+r2),r1*r2]
w,h=scipy.signal.freqz(b,a)

figure()
subplot(211)
plot(w/(2*numpy.pi),20*numpy.log10(numpy.absolute(h)))
xlabel("f/fe")
ylabel("GdB")
grid()
subplot(212)      
plot(w/(2*numpy.pi),numpy.angle(h)/numpy.pi)
xlabel("f/fe")
ylabel("phase/pi")
axis([0,0.5,-1,1])
grid()
                 

r1=0.98
r2=0.99

b=[1,0,-1]
a=[1,-(r1+r2),r1*r2]
w,h=scipy.signal.freqz(b,a)

figure()
subplot(211)
plot(w/(2*numpy.pi),20*numpy.log10(numpy.absolute(h)))
xlabel("f/fe")
ylabel("GdB")
grid()
subplot(212)      
plot(w/(2*numpy.pi),numpy.angle(h)/numpy.pi)
xlabel("f/fe")
ylabel("phase/pi")
axis([0,0.5,-1,1])
grid()
                 

x = numpy.zeros(1000)
x[0] = 1.0
zi = scipy.signal.lfiltic(b,a,y=[0,0],x=[0,0])
[y,zf] = scipy.signal.lfilter(b,a,x,zi=zi)

figure()
plot(y)
xlabel("n")
ylabel("y")
grid()
                   

omega_a=numpy.pi/5
r=0.95
b=[1,0,-1]
a=[1,-2*r*numpy.cos(omega_a),r*r]
w,h=scipy.signal.freqz(b,a)

figure()
subplot(211)
plot(w/(2*numpy.pi),20*numpy.log10(numpy.absolute(h)))
xlabel("f/fe")
ylabel("GdB")
grid()
subplot(212)      
plot(w/(2*numpy.pi),numpy.angle(h)/numpy.pi)
xlabel("f/fe")
ylabel("phase/pi")
axis([0,0.5,-1,1])
grid()

                  

x = numpy.zeros(100)
x[0] = 1.0
zi = scipy.signal.lfiltic(b,a,y=[0,0],x=[0,0])
[y,zf] = scipy.signal.lfilter(b,a,x,zi=zi)

figure()
stem(y)
xlabel("n")
ylabel("y")
grid()