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#       Lowpass FIR filter design.

#

# Authors:

#    Daniel C.K. Kho 

#    Tan Hooi Jing 

#

# Copyright(c) 2012 Daniel C.K. Kho and Tan Hooi Jing. All rights reserved.

#

# This library is free software; you can redistribute it and/or

# modify it under the terms of the GNU Library General Public

# License as published by the Free Software Foundation; either

# version 2 of the License, or (at your option) any later version.

#

# This library is distributed in the hope that it will be useful,

# but WITHOUT ANY WARRANTY; without even the implied warranty of

# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

# Library General Public License for more details.

#

# You should have received a copy of the GNU Library General Public

# License along with this library; if not, write to the

# Free Software Foundation, Inc., 59 Temple Place - Suite 330,

# Boston, MA 02111-1307, USA.

#

#       @dependencies:

#       @revision history: See Mercurial log.

#       @info:

#

# This notice and disclaimer must be retained as part of this text at all times.

#

# Note:

#    For an equivalent Matlab model, contact Tan Hooi Jing (hooijingtan@gmail.com).

#reset();

from scipy import *;

from scipy.signal import freqz;

from scipy.fftpack import fftshift, fftfreq;

from scipy import signal;

# Filter specifications

# Here, we specify the ideal filter response

# Window method: Hamming

# N = filter order = number of unit delays

# M = filter length = number of taps = number of coefficients

# wp = passband frequency

# ws = sampling frequency

# wm = mainlobe width, transition edge

# wc = cutoff frequency

N=30; M=N+1;

ws=10;

wm=3.3/N;    #ws-wp;

wp=0.5;    #in kHz

wc=2*pi*(wp+wm/2)/ws;    #    (wp+ws)/2;

# Specify the ideal impulse response (filter coefficients) for cutoff frequency at w_c = 20kHz:

j=complex(0,1);

n01=r_[0:M-1:j*M];

print(n01);

# Infinite-duration impulse response. This impulse response will later be truncated using

# a discrete-time window function (here we use the Hamming window).

h_n=sin(n01*wc)/(n01*pi);

print(h_n);

# Hamming window

w_n=0.54-0.46*cos(2*pi*n01/N);

# Hann window

#w_n=0.5*(1+cos(2*pi*n/(M)));

print(w_n);

# Impulse response of ideal filter in time domain:

## FIR filter design using the window method.

#    Usage:

#    scipy.signal.firwin(numtaps,cutoff,width=None,window='hamming',pass_zero=True,scale=True,nyq=1.0)

b_n01=signal.firwin(M,wc,width=None,window='hamming',pass_zero=True,scale=True,nyq=10*wc);

# Impulse response data in time domain.

#

# Time-domain impulse response data, simulated with ModelSim and measured with Altera's on-chip

# SignalTap II embedded logic analyser.

# The DSP computations operate on up-scaled values, which is then down-scaled with the same scaling factor

# to produce the results below. This is for fixed-point conversion.

#

# Digital simulation and hardware measurements yield exactly the same results (in Volts):

b_n02=[-0.0017,

    -0.0019,

    -0.0024,

    -0.0026,

    -0.0021,

    0,

    0.0044,

    0.0117,

    0.022,

    0.0351,

    0.05,

    0.0654,

    0.0799,

    0.0916,

    0.0993,

    0.102,

    0.0993,

    0.0916,

    0.0799,

    0.0654,

    0.05,

    0.0351,

    0.022,

    0.0117,

    0.0044,

    0,

    -0.0021,

    -0.0026,

    -0.0024,

    -0.0019,

    -0.0017];

n=r_[0:len(b_n02)-1:j*len(b_n02)];

# Calculate the z-domain frequency responses:

w_n01,h_n01 = signal.freqz(b_n01,1);

w_n02,h_n02 = signal.freqz(b_n02,1);

print("Theoretical computation of the time-domain impulse response,\nb_n01: "); print(b_n01);

print("Digital simulation and hardware measurements of the time-domain impulse response,\nb_n02: "); print(b_n02);

## Graphing methods. ##

import pylab as plt0;

graph0=plt0.figure();

#html("Theoretical response curves to a unit impulse excitation:");

plt0.title("Theoretical response curves to a unit impulse excitation:");

#

# Filter response curves simulated from impulse response equation (Sage's firwin() method).

# The time-domain impulse response is used to specify the FIR filter coefficients.

#

graph0.add_subplot(2,1,1);    # #rows, #columns, plot#

plt0.plot(n01,b_n01);

#

# Frequency response of the impulse excitation, or I'd just say,

# frequency-domain (z-domain) impulse response.

#

graph0.add_subplot(2,1,2);

plt0.plot(w_n01,20*log10(abs(h_n01)));

# TODO: Frequency response plot based on wc calculation:

plt0.show();

import pylab as plt1;

graph1=plt1.figure();

plt1.title("Measured vs. theoretical response curves");

#

# Filter response curves digitally simulated using ModelSim, and measured using Altera's

# SignalTap II embedded logic analyser. Digital simulation and hardware measurements yield

# exactly the same data, i.e. they have exactly the same curves, hence we only plot them once.

#

# Impulse response in time domain.

graph1.add_subplot(2,1,1);

simulated_t=plt1.plot(n01,b_n01,'r');

measured_t=plt1.plot(n,b_n02,'b');

# Impulse response in frequency domain (z domain).

graph1.add_subplot(2,1,2);

simulated_w=plt1.plot(w_n01,20*log10(abs(h_n01)),'r');

measured_w=plt1.plot(w_n02,20*log10(abs(h_n02)),'b');

plt1.savefig('plt1.png');

plt1.show();