#!/usr/bin/env python
# coding: utf-8

# In[1]:


get_ipython().run_line_magic('pylab', 'inline')


# In[2]:


from __future__ import print_function
from deltasigma import *
from IPython.core.display import Image


# In[3]:


# skip this, this is just to display nice tables.
from itertools import izip_longest
class Table(list):
    def _repr_html_(self):
        html = ["<table>"]
        for row in self:
            html.append("<tr>")
            for col in row:
                try:
                    float(col)
                    html.append("<td>%.6f</td>" % col)
                except(ValueError):
                    html.append("<td><b>%s</b></td>" % col)
            html.append("</tr>")
        html.append("</table>")
        return ''.join(html)


# # Modulator realization and dynamic range scaling - # demo3

# In this ipython notebook, the following is demonstrated:
# 
#  * A 5th order delta sigma modulator is synthesized, with optimized zeros and an OSR equal to 42.
# 
#  * We then convert the synthesized NTF into `a`, `g`, `b`, `c` coefficients for the `CRFB` modulator structure.
#  
#  * The maxima for each state are evaluated.
#  
#  * The `ABCD` matrix is scaled so that the state maxima are less than the specified limit.
# 
#  * The state maxima are re-evaluated and limit compliance is checked.
# 
# **NOTE:** This is an ipython port of `dsdemo3.m`, from the **[MATLAB Delta Sigma Toolbox](http://www.mathworks.com/matlabcentral/fileexchange/19-delta-sigma-toolbox)**, written by Richard Schreier.

# ## Delta sigma modulator synthesis

# In[4]:


order = 5
R = 42
opt = 1
H = synthesizeNTF(order, R, opt)


# Let's inspect the NTF, printing out the transfer function and plotting poles and zeros with respect to the unit circle.

# In[5]:


print(pretty_lti(H))


# In[6]:


figure(figsize=(10, 5))
plotPZ(H, showlist=True)
title('NTF');


# ## Evaluation of the coefficients for a CRFB topology
# The CRFB topology is depicted in the following diagram.

# In[7]:


Image(url='http://python-deltasigma.readthedocs.org/en/latest/_images/CRFB.png', retina=True)


# Since the modulator order is 5, we're interested in the topology for odd order modulators.

# ## Unscaled modulator

# ### Calculate the coefficients

# In[8]:


a, g, b, c = realizeNTF(H)


# ### Feed-in selection
# We'll use a single feed-in for the input, to have a maximally flat STF.
# 
# This means setting $\ b_n = 0, \ \forall n > 1$.

# In[9]:


b = np.concatenate((b[0].reshape((1, )), np.zeros((b.shape[0] - 1, ))), axis=0)


# In[10]:


t = Table()
ilabels = ['#1', '#2', '#3', '#4', '#5', '#6']
t.append(['Coefficients', 'DAC feedback', 'Resonator feedback', 
          'Feed-in', 'Interstage'])
t.append(['', 'a(n)', 'g(n)', ' b(n)', ' c(n)'])
[t.append(x) for x in izip_longest(ilabels, a.tolist(), g.tolist(), b.tolist(), c.tolist(), fillvalue="")]
t


# ### Calculate the state maxima

# In[11]:


ABCD = stuffABCD(a, g, b, c);
u = np.linspace(0, 0.6, 30);
N = 1e4; 
T = np.ones((1, N))
maxima = np.zeros((order, len(u)))
for i in range(len(u)):
    ui = u[i]
    v, xn, xmax, _ = simulateDSM(ui*T, ABCD);
    maxima[:, i] = np.squeeze(xmax)
    if any(xmax > 1e2):
        umax = ui;
        u = u[:i];
        maxima = maxima[:, :i]
        break;
# save the maxima
prescale_maxima = np.copy(maxima)
print('The state maxima have been evaluated through simulation.')


# ### Plot of the state maxima

# In[12]:


for i in range(order):
    semilogy(u, maxima[i, :], 'o-', label=('State %d' % (i+1)))
    if not i:
        hold(True)
grid(True)
title('State Maxima'); ylabel('Peak value'); xlabel('DC input')
xlim([0, 0.6]); ylim([1e-6, 10]);
legend(loc=4);


# ## Scaled modulator
# ### Calculate the scaled coefficients

# In[13]:


ABCDs, umax, _ = scaleABCD(ABCD, N_sim=1e5)
as_, gs, bs, cs = mapABCD(ABCDs)
print('\nScaled modulator, umax = %.2f\n' % umax)


# In[14]:


t = Table()
ilabels = ['#1', '#2', '#3', '#4', '#5', '#6']
t.append(['Coefficients', 'DAC feedback', 'Resonator feedback', 
          'Feed-in', 'Interstage'])
t.append(['', 'a(n)', 'g(n)', ' b(n)', ' c(n)'])
[t.append(x) for x in izip_longest(ilabels, as_.tolist(), gs.tolist(), bs.tolist(), cs.tolist(), fillvalue="")]
t


# ### Calculate the state maxima

# In[15]:


u = np.linspace(0, umax, 30)
N = 1e4
T = np.ones((N,))
maxima = np.zeros((order, len(u)))
for i in range(len(u)):
    ui = u[i]
    v, xn, xmax, _ = simulateDSM(ui*T, ABCDs)
    maxima[:, i] = xmax.squeeze()
    if any(xmax > 1e2):
        umax = ui;
        u = u[:i]
        maxima = maxima[:, :i]
        break
print('The state maxima have been re-evaluated through simulation.')
print("The maximum input was found to be %.6f" % umax)


# ### Plot of the state maxima after scaling

# In[16]:


for i in range(order):
    semilogy(u, maxima[i, :], 'o-', label=('State %d' % (i+1)))
    if not i:
        hold(True)
grid(True)
title('State Maxima'); ylabel('Peak value'); xlabel('DC input')
xlim([0, 0.6]); ylim([6e-2, 1.2]);
legend(loc=4);


# ### System version information

# In[17]:


#%install_ext http://raw.github.com/jrjohansson/version_information/master/version_information.py
get_ipython().run_line_magic('load_ext', 'version_information')
get_ipython().run_line_magic('reload_ext', 'version_information')

get_ipython().run_line_magic('version_information', 'numpy, scipy, matplotlib, deltasigma')