from __future__ import division
from deltasigma import *

order = 5
OSR = 32

# Synthesize!
H0 = synthesizeNTF(order, OSR, opt=0)
# 1. Plot the singularities.
subplot(121)
plotPZ(H0, markersize=5)
title('NTF Poles and Zeros')
f = np.concatenate((np.linspace(0, 0.75/OSR, 100), np.linspace(0.75/OSR, 0.5, 100)))
z = np.exp(2j*np.pi*f)
magH0 = dbv(evalTF(H0, z))
# 2. Plot the magnitude responses.
subplot(222)
plot(f, magH0)
figureMagic([0, 0.5], 0.05, None, [-100, 10], 10, None, (16, 8))
xlabel('Normalized frequency ($1\\rightarrow f_s)$')
ylabel('dB')
title('NTF Magnitude Response')
# 3. Plot the magnitude responses in the signal band.
subplot(224)
fstart = 0.01
f = np.linspace(fstart, 1.2, 200)/(2*OSR)
z = np.exp(2j*np.pi*f)
magH0 = dbv(evalTF(H0, z))
semilogx(f*2*OSR, magH0)
axis([fstart, 1.2, -100,- 30])
grid(True)
sigma_H0 = dbv(rmsGain(H0, 0, 0.5/OSR))
semilogx([fstart, 1], sigma_H0*np.array([1, 1]))
plot([fstart, 1], sigma_H0*np.array([1, 1]),'o')
text(0.15, sigma_H0 + 5, 'rms gain = %5.0fdB' % sigma_H0)
xlabel('Normalized frequency ($1\\rightarrow f_B$)')
ylabel('dB')
tight_layout()

# Synthesize again!
H0 = None
H1 = synthesizeNTF(order, OSR, opt=1)
# 1. Plot the singularities.
subplot(121)
plotPZ(H1, markersize=5)
title('NTF Poles and Zeros')
f = np.concatenate((np.linspace(0, 0.75/OSR, 100), np.linspace(0.75/OSR, 0.5, 100)))
z = np.exp(2j*np.pi*f)
magH1 = dbv(evalTF(H1, z))
# 2. Plot the magnitude responses.
subplot(222)
plot(f, magH1)
figureMagic([0, 0.5], 0.05, None, [-100, 10], 10, None, (16, 8))
xlabel('Normalized frequency ($1\\rightarrow f_s)$')
ylabel('dB')
title('NTF Magnitude Response')
# 3. Plot the magnitude responses in the signal band.
subplot(224)
fstart = 0.01
f = np.linspace(fstart, 1.2, 200)/(2*OSR)
z = np.exp(2j*np.pi*f)
magH1 = dbv(evalTF(H1, z))
semilogx(f*2*OSR, magH1)
axis([fstart, 1.2, -100,- 30])
grid(True)
sigma_H1 = dbv(rmsGain(H1, 0, 0.5/OSR))
semilogx([fstart, 1], sigma_H1*np.array([1, 1]))
plot([fstart, 1], sigma_H1*np.array([1, 1]),'o')
text(0.15, sigma_H1 + 5, 'RMS gain = %5.0fdB' % sigma_H1)
xlabel('Normalized frequency ($1\\rightarrow f_B$)')
ylabel('dB')
tight_layout()

# Synthesize!
H0 = synthesizeNTF(order, OSR, opt=0)
H1 = synthesizeNTF(order, OSR, opt=1)
# 1. Plot the singularities.
subplot(121)
# we plot the singularities of the optimized NTF in light 
# green with slightly bigger markers so that we can better
# distinguish the two NTF's when overlayed.
plotPZ(H1, markersize=7, color='#90EE90')
hold(True)
plotPZ(H0, markersize=5)
title('NTF Poles and Zeros')
f = np.concatenate((np.linspace(0, 0.75/OSR, 100), np.linspace(0.75/OSR, 0.5, 100)))
z = np.exp(2j*np.pi*f)
magH0 = dbv(evalTF(H0, z))
magH1 = dbv(evalTF(H1, z))
# 2. Plot the magnitude responses.
subplot(222)
plot(f, magH0, label='All zeros in z=1')
hold(True)
plot(f, magH1, label='Optimized zeros')
figureMagic([0, 0.5], 0.05, None, [-100, 10], 10, None, (16, 8))
xlabel('Normalized frequency ($1\\rightarrow f_s)$')
ylabel('dB')
legend(loc=4)
title('NTF Magnitude Response')
# 3. Plot the magnitude responses in the signal band.
subplot(224)
fstart = 0.01
f = np.linspace(fstart, 1.2, 200)/(2*OSR)
z = np.exp(2j*np.pi*f)
magH0 = dbv(evalTF(H0, z))
magH1 = dbv(evalTF(H1, z))
semilogx(f*2*OSR, magH0, label='All zeros in z=1')
hold(True)
semilogx(f*2*OSR, magH1, label='Optimized zeros')
axis([fstart, 1.2, -100,- 30])
grid(True)
sigma_H0 = dbv(rmsGain(H0, 0, 0.5/OSR))
sigma_H1 = dbv(rmsGain(H1, 0, 0.5/OSR))
semilogx([fstart, 1], sigma_H0*np.array([1, 1]))
plot([fstart, 1], sigma_H0*np.array([1, 1]),'o')
text(0.15, sigma_H0 + 5, 'RMS gain = %5.0fdB' % sigma_H0)
semilogx([fstart, 1], sigma_H1*np.array([1, 1]))
plot([fstart, 1], sigma_H1*np.array([1, 1]),'o')
text(0.15, sigma_H1 + 5, 'RMS gain = %5.0fdB' % sigma_H1)
xlabel('Normalized frequency ($1\\rightarrow f_B$)')
ylabel('dB')
legend(loc=4)
tight_layout()

order = 8
OSR = 64
opt = 2
f0 = 0.125
H = synthesizeNTF(order, OSR, opt, 1.5, f0)
subplot(121)
plotPZ(H)
title('Bandpass NTF Poles and Zeros')
f = np.concatenate((np.linspace(0, f0 - 1./(2.*OSR), 50), 
                    np.linspace(f0 - 1./ (2 * OSR), f0 + 1./(2.*OSR), 100), 
                    np.linspace(f0 + 1./(2.*OSR), 0.5, 50)))
z = np.exp(2j * pi * f)
magH = dbv(evalTF(H, z))
subplot(222)
plot(f, magH)
hold(True)
G = (np.zeros((order/2,)), H[1], 1)
k = 1./np.abs(evalTF(G, exp(2j*np.pi*f0)))
G = (G[0], G[1], k)
magG = dbv(evalTF(G, z))
plot(f, magG, 'r')
figureMagic([0, 0.5], 0.05, None, [-100, 10], 10, None, (16, 8))
#axis([0, 0.5, -100, 10])
grid(True)
xlabel('Normalized frequency ($1 \\rightarrow fs$)')
ylabel('dB')
title('Bandpass NTF/STF Magnitude Response')
f = np.linspace(f0 - 0.3/OSR, f0 + 0.3/OSR)
z = np.exp(2j*np.pi*f)
magH = dbv(evalTF(H, z))
subplot(224)
fstart = -.5
plot(2*OSR*(f - f0), magH)
axis([- 0.6, 0.6, -100, -60])
grid(True)
sigma_H = dbv(rmsGain(H, f0 - 0.25/OSR, f0 + 0.25/OSR))
hold(True)
plot([-0.5, 0.5], sigma_H*np.array([1, 1]))
plot([-0.5, 0.5], sigma_H*np.array([1, 1]), 'o')
text(-.2, sigma_H + 5, 'rms gain = %5.0fdB' % sigma_H)
xlabel('Normalized frequency offset')
ylabel('dB')
tight_layout()