# This file is part of librefdatool. librefdatool is free software: you can # redistribute it and/or modify it under the terms of the GNU General Public # License as published by the Free Software Foundation, version 2. # # This program 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 General Public License for more # details. # # You should have received a copy of the GNU General Public License along with # this program; if not, write to the Free Software Foundation, Inc., 51 # Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. # # Copyright (C) 2013 Javier D. Garcia-Lasheras # import warnings import numpy as np from numpy import pi, log10 from scipy import signal from matplotlib import pyplot as plt from matplotlib import patches, mlab import sys, os, random '''This module include the figure plotters used in Libre-FDATool. ''' class Waveform: def __init__(self, value=[0], label='waveform', color='#000000', linestyle='-', marker='o', markersize=8): self.value = value self.label = label self.color = color self.linestyle = linestyle self.marker = marker self.markersize = markersize def analyze_pole_zero(figure, b, a, p, q, grid): '''Plot graphical zero/pole analysis in Z-plane: * b: LTI transfer function Numerator. * a: LTI transfer function Denominator. * filename: optional file for storing plot and not showing it. ''' print('Plotting Z Analysis...') #TODO: use DAC / ADC like function, this is bad!!! # Quantize coefficients b2 = np.zeros(len(b)) for ii in range(len(b)): b2[ii] = int(b[ii]*(2**(p+q-1))) b2 = b2/(2**(p+q-1)) a2 = np.zeros(len(a)) for ii in range(len(a)): a2[ii] = int(a[ii]*(2**(p+q-1))) a2 = a2/(2**(p+q-1)) # Temporal assignation: only valid for FIR print('Coefficients') b1 = b a1 = a # 1 - The coefficients must be less than 1, normalize the coefficients if np.max(b1) > 1: kn1 = np.max(b1) b1 = b1/float(kn1) else: kn1 = 1 if np.max(a1) > 1: kd1 = np.max(a1) a1 = a1/float(kd1) else: kd1 = 1 # 2 - The coefficients must be than 1, normalize the coefficients if np.max(b2) > 1: kn2 = np.max(b2) b2 = b2/float(kn2) else: kn2 = 1 if np.max(a2) > 1: kd2 = np.max(a2) a2 = a2/float(kd2) else: kd2 = 1 warningMessage = '' warnings.simplefilter('error') try: # Get the poles and zeros p1 = np.roots(a1) z1 = np.roots(b1) p2 = np.roots(a2) z2 = np.roots(b2) except ValueError as exVE: warningMessage = '%s' % exVE except ZeroDivisionError as exZDE: warningMessage = '%s' % exZDE except RuntimeWarning as exRW: warningMessage = '%s' % exRW if warningMessage != '': return False, warningMessage else: # Clear the figure figure.clear() # get a figure/plot poleZeroSubplot = figure.add_subplot(111) # create the unit circle uc = patches.Circle((0,0), radius=1, fill=False, color='black', ls='dashed') #ax.add_patch(uc) poleZeroSubplot.add_patch(uc) # 1 - Plot the zeros and set marker properties poleZeroSubplot.plot(z1.real, z1.imag, 'bo', ms=10) # 1 - Plot the poles and set marker properties poleZeroSubplot.plot(p1.real, p1.imag, 'bx', ms=10) # 2 - Plot the zeros and set marker properties poleZeroSubplot.plot(z2.real, z2.imag, 'ro', ms=10) # 2 - Plot the poles and set marker properties poleZeroSubplot.plot(p2.real, p2.imag, 'rx', ms=10) # set axis poleZeroSubplot.axis('scaled') poleZeroSubplot.set_ylabel('Imaginary Component') poleZeroSubplot.set_xlabel('Real Component') poleZeroSubplot.set_title(r'Zero-Pole Diagram (Blue=Float; Red=Int)') poleZeroSubplot.grid(grid) return True, 'OK' def analyze_frequency_response(figure, b, a, p, q, grid): '''Plot graphical Magnitude/Phase analysis in frequency domain: * c: FIR filter coefficients array. * filename: optional file for storing plot and not showing it. ''' # Quantize coefficients b2 = np.zeros(len(b)) for ii in range(len(b)): b2[ii] = int(b[ii]*(2**(p+q-1))) b2 = b2/(2**(p+q-1)) a2 = np.zeros(len(a)) for ii in range(len(a)): a2[ii] = int(a[ii]*(2**(p+q-1))) a2 = a2/(2**(p+q-1)) # TODO: If the coefficients are extremely low, the discretized version # may be equal to zero, which suppose a log10 crash - divide by zero! # We need to rise an advice about rising the coefficient bits!! warningMessage = '' warnings.simplefilter('error') try: wc,hc = signal.freqz(b,a) hc_dB = 20 * log10 (abs(hc)) wd,hd = signal.freqz(b2,a2) hd_dB = 20 * log10 (abs(hd)) except ValueError as exVE: warningMessage = '%s' % exVE except ZeroDivisionError as exZDE: warningMessage = '%s' % exZDE except RuntimeWarning as exRW: warningMessage = '%s' % exRW figure.clear() magnitudeSubplot = figure.add_subplot(211) magnitudeSubplot.set_ylim(-150, 5) magnitudeSubplot.set_ylabel('Magnitude (dB)') magnitudeSubplot.set_xlabel(r'Normalized Frequency (x$\pi$rad/sample)') magnitudeSubplot.grid(grid) phaseSubplot = figure.add_subplot(212) phaseSubplot.set_ylabel('Phase (radians)') phaseSubplot.set_xlabel(r'Normalized Frequency (x$\pi$rad/sample)') phaseSubplot.grid(grid) figure.subplots_adjust(hspace=0.5) if warningMessage != '': magnitudeSubplot.plot(wc/max(wc),hc_dB,'b') hc_Phase = np.unwrap(np.arctan2(np.imag(hc),np.real(hc))) magnitudeSubplot.set_title(r'Magnitude response (Float=Blue; Int=Error)') phaseSubplot.plot(wc/max(wc),hc_Phase,'b') phaseSubplot.set_title(r'Phase response (Float=Blue; Int=Error)') return False, warningMessage else: magnitudeSubplot.plot(wc/max(wc),hc_dB,'b') magnitudeSubplot.plot(wd/max(wd),hd_dB,'r') magnitudeSubplot.set_title(r'Magnitude response (Float=Blue; Int=Red)') hc_Phase = np.unwrap(np.arctan2(np.imag(hc),np.real(hc))) hd_Phase = np.unwrap(np.arctan2(np.imag(hd),np.real(hd))) phaseSubplot.plot(wc/max(wc),hc_Phase,'b') phaseSubplot.plot(wd/max(wd),hd_Phase,'r') phaseSubplot.set_title(r'Phase response (Float=Blue; Int=Error)') return True, 'OK' def scopeTime(figure, waveform, grid): '''this method shows a dual time domain scope: * s1: channel-1 input signal (blue, float) * s2: channel-2 input signal (red, int) ''' # Simulate float system response: print('Run Scope Time') figure.clear() scopeTimeSubplot = figure.add_subplot(111) scopeTimeSubplot.set_ylabel('Value') scopeTimeSubplot.set_xlabel('Sample') scopeTimeSubplot.set_title(r'Time Scope') scopeTimeSubplot.grid(grid) for ii in range(len(waveform)): scopeTimeSubplot.plot(waveform[ii].value, color = waveform[ii].color, label = waveform[ii].label, linestyle = waveform[ii].linestyle, marker = waveform[ii].marker, markersize = waveform[ii].markersize) scopeTimeSubplot.legend().draggable(state=True, use_blit=True) def scopePower(figure, waveform, grid): '''this method shows the estimated power spectrum for a signal: * s: channel-1 assigned signal (blue) ''' print('Plotting Power Spectrum...') figure.clear() scopePowerSubplot = figure.add_subplot(111) scopePowerSubplot.set_ylabel('Power (dB)') scopePowerSubplot.set_xlabel('Normalized Frequency') scopePowerSubplot.set_title(r'Signal Power') scopePowerSubplot.grid(grid) for ii in range(len(waveform)): Ps,fs = mlab.psd(waveform[ii].value) scopePowerSubplot.plot(fs, 10*log10(abs(Ps)), color = waveform[ii].color, label = waveform[ii].label, linestyle = waveform[ii].linestyle) scopePowerSubplot.legend().draggable(state=True, use_blit=True) def scopeError(figure, s1, s2, grid): '''this method shows an error analysis between input signals: * s1: channel-1 input signal * s1: channel-2 input signal ''' # *** Error Analisys *** sdiff = np.abs(s1 - s2) print('- Maximum error = ', np.max(sdiff)) print('- Mean error = ', np.mean(sdiff**2)) # Check for error tolerance # assert np.max(sdiff) < 1e-3, "check if error is too large" # Plot Error report figure.clear() scopeErrorSublot = figure.add_subplot(111) scopeErrorSublot.plot(sdiff, 'go-') title = 'Error Max=', np.max(sdiff), ' Mean=', np.mean(sdiff**2) scopeErrorSublot.set_title(title) scopeErrorSublot.set_ylabel('abs(error)') scopeErrorSublot.set_xlabel('sample') scopeErrorSublot.grid(grid)