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

# In[1]:


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


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from __future__ import division
from deltasigma import *


# NTF synthesis - demo #1
# =======================
# 
# Demonstration of the **`synthesizeNTF`** function, as done in the **MATLAB Delta Sigma Toolbox**, employing its Python port **`deltasigma`**.
# 
# 
# 
#  * The **Noise Transfer Function** (NTF) is synthesized for a **5th-order**, **low-pass** modulator.
# 
#      * The first section deals with an **NTF without optimized zeros** (`opt=0`), 
#      * while the second section with an **NTF *with optimized* zeros** (`opt=1`). 
#      * Finally the two transfer functions are compared.
# 
#  * Then we move on to the synthesis of an **8th-order band-pass modulator** with optimized zeros.

# 5th-order modulator
# -------------------
# 
# General parameters:

# In[3]:


order = 5
OSR = 32


# ### 5th-order modulator: NTF without zeros optimization
# 
# The synthesis of an NTF can be performed with the `synthesizeNTF(order, OSR, opt)`.
# 
# We intentionally disable the zeros optimization, setting `opt=0`.

# In[4]:


# 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]))
semilogx([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()


# ### 5th-order modulator: NTF *with* zeros optimization
# 
# This time we enable the zeros optimization, setting `opt=1` when calling synthesizeNTF(), then replot the NTF as above.

# In[5]:


# 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]))
semilogx([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()


# 5th-order modulator: comparison
# -------------------------------
# 
# Overlayed plots follow to ease comparison of the two synthetization approaches.

# In[6]:


# 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()


# 8th-order bandpass Modulator
# ----------------------------
# In the following, we synthesize an 8th-order modulator with optimized zeros.

# In[7]:


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, np.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()


# Further information about NTF synthesis
# ---------------------------------------
# 
# Please refer to `help(synthesizeNTF)` for detailed - and possibly more updated - documentation!
# 
# ###`help(synthesizeNTF)` as of writing:

# 
# Help on function synthesizeNTF in module deltasigma._synthesizeNTF:
# 
# **synthesizeNTF(order=3, osr=64, opt=0, H_inf=1.5, f0=0.0)**
# 
# Synthesize a noise transfer function for a delta-sigma modulator.
# 
# **Parameters:**
# 
# order : *int, optional*
#     the order of the modulator, defaults to 3
# 
# osr : *float, optional*
#     the oversamping ratio, defaults to 64
# 
# opt : *int or list of floats, optional*
#     flag for optimized zeros, defaults to 0
# 
# * 0 -> not optimized,
# * 1 -> optimized,
# * 2 -> optimized with at least one zero at band-center,
# * 3 -> optimized zeros (with optimizer)
# * 4 -> same as 3, but with at least one zero at band-center
# * [z] -> zero locations in complex form
# 
# H_inf : *real, optional*
#     max allowed peak value of the NTF. Defaults to 1.5
# 
# f0 : *real, optional*
#     center frequency for BP modulators, or 0 for LP modulators.
#     Defaults to 0.
# 
#     1 corresponds to the sampling frequency, so that 0.5 is the
#     maximum value. A value of 0 specifies an LP modulator.
# 
# **Returns:**
# 
# ntf : *tuple*
#     noise transfer function in zpk form.
# 
# **Raises:**
# 
# ValueError
# 
# * 'Error. f0 must be less than 0.5' if f0 is out of range
# 
# * 'Order must be even for a bandpass modulator.' if the order is
#   incompatible with the modulator type.
# 
# * 'The opt vector must be of length xxx' if opt is used to explicitly
#   pass the NTF zeros and these are in the wrong number.
# 
# **Warns:**
# 
# * 'Creating a lowpass ntf.' if the center frequency is different
#   from zero, but so low that a low pass modulator must be designed.
# 
# * 'Unable to achieve specified H_inf ...' if the desired H_inf
#   cannot be achieved.
# 
# * 'Iteration limit exceeded' if the routine converges too slowly.
# 
# **Notes:**
# 
# This is actually a wrapper function which calls the appropriate version
# of synthesizeNTF, based on the module control flag `optimize_NTF` which
# determines whether to use optimization tools.
# 
# Parameter ``H_inf`` is used to enforce the Lee stability criterion.
# 
# **See also:**
# 
# * `clans()` : Closed-Loop Analysis of Noise-Shaper. 
# 
# An alternative method for selecting NTFs based on the 1-norm of the 
#       impulse response of the NTF
#     
# * `synthesizeChebyshevNTF()` : Select a type-2 highpass Chebyshev NTF.
# 
# This function does a better job than synthesizeNTF if osr
#    or H_inf is low.

# ### System version information

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#%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')


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