ax21 = fig2.add_subplot(211)
W, H = sig.freqz(h)
F = W /(2 * pi)
plot(F, abs(H))
ax21.set_ylabel(r'$|H(\mathrm{e}^{\mathrm{j} 2 \pi F})| \rightarrow$')
#ax2.xaxis.set_label_coords(2, 0.5, transform=ax1.transData)
#ax2.yaxis.set_label_coords(-0.3, 2.3, transform=ax1.transData)
#ax2.set_ylim([-2,3])
ax22 = fig2.add_subplot(212)
plot(F, angle(H) /pi *180)
ax22.set_ylabel(r'$\angle H(\mathrm{e}^{\mathrm{j} 2 \pi F})\; \mathrm {in} \; \deg \rightarrow$')
ax22.set_xlabel(r'$F \rightarrow$')
if EXPORT:
fig2.savefig(BASE_DIR + FILENAME +"_Hf" + FMT)
fig3 = figure(num=3)
ax3 = fig3.add_subplot(111)
dsp.zplane(h, zpk=False, plt_ax = ax3)
ax3.set_xlabel(r'reell $\rightarrow$')
ax3.set_ylabel(r'imaginÀr $ \rightarrow$')
if EXPORT:
fig3.savefig(BASE_DIR + FILENAME +"_PN" + FMT)
ax3.set_ylim([-1.1,1.1])
ax3.set_xlim([-2.5,1])
plt.show()
#################################################################
# #
# Plot the Results #
# #
#################################################################
plt.close('all') # close all "old" figures
#mlab.close(all=True) # alle Mayavi (3D) Fenster schließen
#=========================================
## Pol/Nullstellenplan
#=========================================
if SHOW_POLE_ZERO == True:
plt.figure(1)
[z, p, k] = dsp.zplane(bb, aa)
plt.title('Pol/Nullstellenplan')
plt.grid('on')
# plt.text(-0.95,0.0 ,'(2)')
plt.axis([-1.1, 1.1, -1.1, 1.1])
plt.tight_layout()
if DEF_PRINT == True:
plt.savefig((PRINT_PATH +'PZ' + PRINT_TYPE))
#=========================================
## Impulsantwort
#=========================================
if SHOW_IMPZ == True:
plt.figure(2)
[h, td]=dsp.impz(bb, aa, f_S) #Impulsantwort / Koeffizienten
#################################################################
# #
# Plot the Results #
# #
#################################################################
plt.close('all') # close all "old" figures
#mlab.close(all=True) # alle Mayavi (3D) Fenster schließen
#=========================================
## Pol/Nullstellenplan
#=========================================
if SHOW_POLE_ZERO == True:
plt.figure(1)
[z, p, k] = dsp.zplane(bb, aa)
plt.title('Pol/Nullstellenplan')
plt.grid('on')
# plt.text(-0.95,0.0 ,'(2)')
plt.axis([-1.1, 1.1, -1.1, 1.1])
plt.tight_layout()
if DEF_PRINT == True:
plt.savefig((PRINT_PATH + 'PZ' + PRINT_TYPE))
#=========================================
## Impulsantwort
#=========================================
if SHOW_IMPZ == True:
plt.figure(2)
[h, td] = dsp.impz(bb, aa, f_S) #Impulsantwort / Koeffizienten
Hmax = max(H_abs); Hmax_dB = 20*log10(Hmax)
Wmax = W[np.argmax(H_abs)] # frequency where |H(Omega)| is max.
H_angle = np.unwrap(angle(H))
H_abs = abs(H)/Hmax
print('--------------------------------')
print('zeta[i] = ',zeta[i])
print('W_3dB[i] = ', W_3dB[i])
print('W_max, H_max (calc.) = ',W_max[i], H_max[i])
print('Wmax, Hmax (sim.) = ',Wmax, Hmax)
print('H_max_rel = ', H_max_rel)
#===============================================================
## Poles and zeros
#===============================================================
figure(1)
dsp.zplane(bb, aa, analog=True, style = 'square', anaCircleRad=W_c,
mpc = (1-i/len(zeta),i/len(zeta),i/len(zeta)), plabel = zeta_label, lw = 3)
axzp = plt.gca()
axzp.set_xlabel(r'$\sigma \; \rightarrow$',fontsize=18)
# axzp.set_xlabel(r'$\sigma \,/ \omega_{3dB}\; \rightarrow$',fontsize=18)
axzp.set_ylabel(r'$j \omega \; \rightarrow$',fontsize=18)
# axzp.set_ylabel(r'$j \omega \,/ \omega_{3dB}\; \rightarrow$',fontsize=18)
axzp.legend(loc = 'best')
plt.tight_layout()
#===============================================================
## Magnitude Response
#===============================================================
fig2 = figure(2)
ax21 = fig2.add_subplot(111)
l1, = ax21.plot(W,H_abs, label = zeta_label)
from matplotlib.pyplot import (figure, plot, stem, grid, xlabel, ylabel,
subplot, title, clf, xlim, ylim)
import sys
sys.path.append('..')
import dsp_fpga_lib as dsp
# Definiere Nullstellen auf EK:
N = np.asarray([np.exp(1j * 0.3 * 2 * pi), np.exp(-1j * 0.3 * 2 * pi)])
# Pole: gleicher Winkel, kleinerer Radius:
P = 0.95 * N
# "Ausmultiplizieren" von P/N ergibt Koeff.
b = np.poly(N)
a = np.poly(P)
figure(1)
dsp.zplane(N, P, zpk=True)
figure(2)
subplot(211)
# Frequenzgang an 2048 Punkten:
[W, H] = sig.freqz(b, a, 2048)
F = W / (2 * pi)
plot(F, 20 * log10(abs(H)))
grid(True)
subplot(212)
plot(F, angle(H))
xlabel('F ->')
grid(True)
plt.tight_layout()
# Testfreq. (normierte Kreisfreq.):
W_test = array([0, 0.29, 0.3, 0.31, 0.5]) * 2 * pi
# Frequenzgang bei Testfrequenzen:
ax21 = fig2.add_subplot(211)
W, H = sig.freqz(h)
F = W /(2 * pi)
plot(F, abs(H))
ax21.set_ylabel(r'$|H(\mathrm{e}^{\mathrm{j} 2 \pi F})| \rightarrow$')
#ax2.xaxis.set_label_coords(2, 0.5, transform=ax1.transData)
#ax2.yaxis.set_label_coords(-0.3, 2.3, transform=ax1.transData)
#ax2.set_ylim([-2,3])
ax22 = fig2.add_subplot(212)
plot(F, angle(H) /pi *180)
ax22.set_ylabel(r'$\angle H(\mathrm{e}^{\mathrm{j} 2 \pi F})\; \mathrm {in} \; \deg \rightarrow$')
ax22.set_xlabel(r'$F \rightarrow$')
if EXPORT:
fig2.savefig(BASE_DIR + FILENAME +"_Hf" + FMT)
fig3 = figure(num=3)
ax3 = fig3.add_subplot(111)
dsp.zplane(h, zpk=False, plt_ax = ax3)
ax3.set_xlabel(r'reell $\rightarrow$')
ax3.set_ylabel(r'imaginÀr $ \rightarrow$')
if EXPORT:
fig3.savefig(BASE_DIR + FILENAME +"_PN" + FMT)
ax3.set_ylim([-1.1,1.1])
ax3.set_xlim([-2.5,1])
plt.show()
[Lb,F_b] = sig.buttord(F_DB,F_SB,A_DB,A_SB)
#[b, a] = sig.butter(Lb, F_b)
#=== IIR-Wrapper (nur Python) =====
#[b, a] = sig.iirdesign(F_DB, F_SB,
# A_DB, A_SB, ftype='ellip')
############################################
print('Filterkoeffizienten:')
print('a = ', a); print('b = ', b)
## Calculate H(w), w = 0 ... pi, 1024 Pts.
[w, H] = sig.freqz(b, a, 1024)
# Translate w to physical frequencies:
f = w / (2 * pi) * f_S
############## Plot the Results #########
## Pol/Nullstellenplan
fig1 = figure(1); ax1 = fig1.add_subplot(111)
[z, p, k] = dsp.zplane(b, a, plt_ax = ax1)
## ----- Impulsantwort -----
figure(2); grid('on')
[h, td] = dsp.impz(b, a, f_S) #Impulsantwort / Koeffizienten
[ml, sl, bl] = stem(td, h)
plt.setp(ml, 'markerfacecolor', 'r', 'markersize', 8)
title(r'Impulsantwort h[n]')
## ----- Linear frequency plot -----
figure(3); grid('on')
plot(f, abs(H))
title(r'Betragsfrequenzgang')
## Log. Frequenzgang mit Spezifikationen
figure(5)
subplot (211)
plot(f,20 * log10(abs(H)), 'r'); plt.grid('on')
plot([0, f_DB],[-A_DB, -A_DB],'b--') # untere Spec-Grenze
#=== IIR-Wrapper (nur Python) =====
#[b, a] = sig.iirdesign(F_DB, F_SB,
# A_DB, A_SB, ftype='ellip')
############################################
print('Filterkoeffizienten:')
print('a = ', a)
print('b = ', b)
## Calculate H(w), w = 0 ... pi, 1024 Pts.
[w, H] = sig.freqz(b, a, 1024)
# Translate w to physical frequencies:
f = w / (2 * pi) * f_S
############## Plot the Results #########
## Pol/Nullstellenplan
fig1 = figure(1)
ax1 = fig1.add_subplot(111)
[z, p, k] = dsp.zplane(b, a, plt_ax=ax1)
## ----- Impulsantwort -----
figure(2)
grid('on')
[h, td] = dsp.impz(b, a, f_S) #Impulsantwort / Koeffizienten
[ml, sl, bl] = stem(td, h)
plt.setp(ml, 'markerfacecolor', 'r', 'markersize', 8)
title(r'Impulsantwort h[n]')
## ----- Linear frequency plot -----
figure(3)
grid('on')
plot(f, abs(H))
title(r'Betragsfrequenzgang')
## Log. Frequenzgang mit Spezifikationen
figure(5)
subplot(211)
W_max = 2 # normalized circular frequency; W = 2 pi f tau
W = np.linspace(0, W_max, 201) # start, stop, step. endpoint is included
[W,H] = sig.freqs(bb, aa, W) # Calculate H(w) at the frequency points w1
#[w,H]=sig.freqs(bb,aa) # calculate H(w) at 200 frequencies "around the
# interesting parts of the response curve"
f = W
H_abs = abs(H)
H_max = max(H_abs); H_max_dB = 20*log10(H_max)
W_max = W[np.argmax(H_abs)] # frequency where |H(Omega)| is max.
H_angle = np.unwrap(angle(H))
#====================================================
figure(1)
dsp.zplane(bb, aa, analog=True, style = 'square', anaCircleRad=W_c,
mzc = (0,0.5,0) )
axzp = plt.gca()
axzp.set_xlabel(r'$\sigma \, / \,\omega_n \; \rightarrow$',fontsize=18)
axzp.set_ylabel(r'$j \omega \, / \,\omega_n \; \rightarrow$',fontsize=18)
plt.tight_layout()
#====================================================
fig2 = figure(2)
ax21 = fig2.add_subplot(111)
ax22 = ax21.twinx()
l1, = ax21.plot(W,abs(H))
l2, = ax22.plot(W,H_angle/pi,'g')
ax21.set_xlabel(r'$\omega\, / \,\omega_n \; \rightarrow$')
ax21.set_ylabel(r'$|H(j \omega)| \; \rightarrow$')
ax22.set_ylabel(r'$\angle H(j \omega)/\pi \; \rightarrow$')
from matplotlib.pyplot import (figure, plot, stem, grid, xlabel, ylabel,
subplot, title, clf, xlim, ylim)
import sys
sys.path.append('..')
import dsp_fpga_lib as dsp
alpha = 0.9; f_S = 1
b = [1, 0] # z + 0
# b = [1 0 0] # z^2 + 0
a = [1, -alpha] # z - 0.9; Add., 1 Verzögerung
#a = [1 +alpha] # z + 0.9; Subtr., 1 Verz.
#a = [1 0 -alpha] # z^2 - 0.9; Add., 2 Verz.
#a = [1 0 +alpha] # z^2 - 0.9; Subtr., 2 Verz.
dsp.zplane(b,a)#, plt_ax = ax) # Plotte P/N Diagramm
# H(f) entlang der oberen Hälfte des EK:
[W,H] = sig.freqz(b,a,1024, f_S)
fig2 = figure(2)
plot(W/(2*pi),abs(H),linewidth = 2) # H(F)
xlabel(r'$F$ bzw. $\Omega / 2 \pi$')
ylabel(r'$|H(F)| \; \rightarrow$')
# Berechne 20 Werte der Impulsantwort:
[himp,t] = dsp.impz(b,a,20,f_S)
figure(3)
(ml, sl, bl) = stem(t,himp) # Impulsantwort
plt.setp(ml,'markerfacecolor','r',
'markersize',8)
plt.setp(sl,'linewidth',2)
xlabel('$n$'); ylabel(r'$h[n]$')
plt.show()
TC = np.empty(max) # time constants
# go through all the powers of two
for l in range(max):
# H(z)=B/A=2**-l/(z-(1-2**l)) # first order
b = [2**-l, 0] # first order
a = [1, -(1 - (2**-l))] # first order
# b=[2**-(2*l),0,0] # second order
# a=[1,-2*(1-2**-l),(1-2**-l)**2] # second order
plt.figure(0)
flog = np.logspace(-8, 1, 1000)
[f, Hf] = signal.freqz(b, a, flog)
Hf = 20 * np.log10(abs(Hf))
fHz = (f / (2 * np.pi)) * f_s
plt.plot(fHz, Hf)
plt.figure(1)
zplane(b, a)
fc[l] = fHz[np.argmin(abs(Hf + 3))]
TC[l] = 1 / (2 * np.pi * fc[l])
print(f"2^{l}: fc= {fc[l]}Hz TC={TC[l]} sec ")
plt.figure(0)
plt.minorticks_on()
plt.grid(b=True, which='both', axis='both')
plt.xscale('log')
plt.xlim(10E-4, 450E3)
plt.show()
from matplotlib.pyplot import (figure, plot, stem, grid, xlabel, ylabel,
subplot, title, clf, xlim, ylim)
import sys
sys.path.append('..')
import dsp_fpga_lib as dsp
alpha = 0.9; f_S = 1
b = [1, 0] # z + 0
# b = [1 0 0] # z^2 + 0
a = [1, -alpha] # z - 0.9; Add., 1 Verzögerung
#a = [1 +alpha] # z + 0.9; Subtr., 1 Verz.
#a = [1 0 -alpha] # z^2 - 0.9; Add., 2 Verz.
#a = [1 0 +alpha] # z^2 - 0.9; Subtr., 2 Verz.
dsp.zplane(b,a)#, plt_ax = ax) # Plotte P/N Diagramm
# H(f) entlang der oberen Hälfte des EK:
[W,H] = sig.freqz(b,a,1024, f_S)
fig2 = figure(2)
plot(W/(2*pi),abs(H),linewidth = 2) # H(F)
xlabel(r'$F$ bzw. $\Omega / 2 \pi$')
ylabel(r'$|H(F)| \; \rightarrow$')
# Berechne 20 Werte der Impulsantwort:
[himp,t] = dsp.impz(b,a,20,f_S)
figure(3)
(ml, sl, bl) = stem(t,himp) # Impulsantwort
plt.setp(ml,'markerfacecolor','r',
'markersize',8)
plt.setp(sl,'linewidth',2)
xlabel('$n$'); ylabel(r'$h[n]$')
plt.show()
Ts = 1/200.0 # sampling period
f1 = 50.0 # signal frequency
phi0 = 0 # signal initial phase
Tmax = 6.0/f1 # time for 6 signal periods
N_Ts = Tmax / Ts # No. of samples in Tmax
# -- Sampled input signal and filter coeffs.
n = arange(0,round(N_Ts)) # sample n
xn = 1.5 + 0.5*cos(2.0*pi*f1*n*Ts + phi0)
b = np.ones(4)/4; a = 1 # MA-filter, N = 5
#b = np.convolve([1,1,1],[1,1,1]); a = 1
#b = [1, 0]; a = [1, -0.9] # lossy integr.
#
# ----- P/Z-Plot -----
figure(1)
title('Pole/Zero-Plan')
dsp.zplane(b,a)
# ----- frequency response -----
figure(2)
[W, H] = sig.freqz(b, a, whole=0);
f = W / (Ts * 2 * pi)
(w,Asig) = sig.freqz(b,a, f1*Ts*2*pi)
H_mx = np.max(abs(H))
H = H / H_mx; Asig = abs(Asig)/H_mx
#
subplot(311)
plot(f,abs(H))
ylabel(r'$|H(e^{j \Omega})| \rightarrow$')
title('Frequency Response')
plt.annotate('Attenuation @ %.1f Hz \n \
= %1.3f (%3.1f dB)'%(f1,Asig,20*log10(Asig)),\
(f1, Asig),(0.5,0.5),textcoords='axes fraction',\
H_abs = abs(H) / Hmax
print('--------------------------------')
print('zeta[i] = ', zeta[i])
print('W_3dB[i] = ', W_3dB[i])
print('W_max, H_max (calc.) = ', W_max[i], H_max[i])
print('Wmax, Hmax (sim.) = ', Wmax, Hmax)
print('H_max_rel = ', H_max_rel)
#===============================================================
## Poles and zeros
#===============================================================
figure(1)
dsp.zplane(bb,
aa,
analog=True,
style='square',
anaCircleRad=W_c,
mpc=(1 - i / len(zeta), i / len(zeta), i / len(zeta)),
plabel=zeta_label,
lw=3)
axzp = plt.gca()
axzp.set_xlabel(r'$\sigma \; \rightarrow$', fontsize=18)
# axzp.set_xlabel(r'$\sigma \,/ \omega_{3dB}\; \rightarrow$',fontsize=18)
axzp.set_ylabel(r'$j \omega \; \rightarrow$', fontsize=18)
# axzp.set_ylabel(r'$j \omega \,/ \omega_{3dB}\; \rightarrow$',fontsize=18)
axzp.legend(loc='best')
plt.tight_layout()
#===============================================================
## Magnitude Response
#===============================================================
from matplotlib.pyplot import (figure, plot, stem, grid, xlabel, ylabel,
subplot, title, clf, xlim, ylim)
import sys
sys.path.append('..')
import dsp_fpga_lib as dsp
# Definiere Nullstellen auf EK:
N = np.asarray([np.exp(1j*0.3*2*pi),
np.exp(-1j*0.3*2*pi)])
# Pole: gleicher Winkel, kleinerer Radius:
P = 0.95 * N
# "Ausmultiplizieren" von P/N ergibt Koeff.
b = np.poly(N); a = np.poly(P)
figure(1)
dsp.zplane(N,P,zpk = True)
figure(2)
subplot(211)
# Frequenzgang an 2048 Punkten:
[W,H] = sig.freqz(b,a,2048)
F = W / (2* pi)
plot(F, 20*log10(abs(H))); grid(True)
subplot(212)
plot(F,angle(H))
xlabel('F ->'); grid(True)
plt.tight_layout()
# Testfreq. (normierte Kreisfreq.):
W_test = array([0, 0.29, 0.3, 0.31, 0.5])*2*pi
# Frequenzgang bei Testfrequenzen:
[H_test, W_test]=sig.freqz(b,a,W_test)
print('H_test =', H_test)
#=======================================================1
# Hilbert-Transformer: zero at f = 0 and f = fS/2
# -> antisymmetric, odd numtaps
b = sig.firwin2(L, [0, 0.01, 0.5, 0.99, 1], [0, 1, 1, 1, 0],
antisymmetric=True)
#b = sig.remez(L, [0, 0.1, 0.11, 0.4, 0.41, 0.5], [0,1,0], [0.1,10,0.1],type = 'hilbert')
b = b / sum(abs(b))
print(b)
[w, H] = sig.freqz(b, a, 1024)
# Translate w to physical frequencies:
f = w / (2 * pi) * f_S
############## Plot the Results #########
## Pol/Nullstellenplan
figure(1)
[z, p, k] = dsp.zplane(b, a)
## ----- Impulsantwort -----
figure(2)
[h, td] = dsp.impz(b, a, f_S) #Impulsantwort / Koeffizienten
[ml, sl, bl] = stem(td, h)
plt.setp(ml, 'markerfacecolor', 'r', 'markersize', 8)
title(r'Impulsantwort h[n]')
## ----- Linear frequency plot -----
figure(3)
plot(f, abs(H))
title(r'Betragsfrequenzgang')
## Log. Frequenzgang mit Spezifikationen
figure(4)
subplot(211)
plot(f, 20 * log10(abs(H)), 'r')
plt.grid('on')
Ts = 1/200.0 # sampling period
f1 = 50.0 # signal frequency
phi0 = 0 # signal initial phase
Tmax = 6.0/f1 # time for 6 signal periods
N_Ts = Tmax / Ts # No. of samples in Tmax
# -- Sampled input signal and filter coeffs.
n = arange(0,round(N_Ts)) # sample n
xn = 1.5 + 0.5*cos(2.0*pi*f1*n*Ts + phi0)
b = np.ones(4)/4; a = 1 # MA-filter, N = 5
#b = np.convolve([1,1,1],[1,1,1]); a = 1
#b = [1, 0]; a = [1, -0.9] # lossy integr.
#
# ----- P/Z-Plot -----
figure(1)
title('Pole/Zero-Plan')
dsp.zplane(b,a)
# ----- frequency response -----
figure(2)
[W, H] = sig.freqz(b, a, whole=0);
f = W / (Ts * 2 * pi)
(w,Asig) = sig.freqz(b,a, f1*Ts*2*pi)
H_mx = np.max(abs(H))
H = H / H_mx; Asig = abs(Asig)/H_mx
#
subplot(311)
plot(f,abs(H))
ylabel(r'$|H(e^{j \Omega})| \rightarrow$')
title('Frequency Response')
plt.annotate('Attenuation @ %.1f Hz \n \
= %1.3f (%3.1f dB)'%(f1,Asig,20*log10(Asig)),\
(f1, Asig),(0.5,0.5),textcoords='axes fraction',\
#=======================================================1
# Hilbert-Transformer: zero at f = 0 and f = fS/2
# -> antisymmetric, odd numtaps
b = sig.firwin2(L, [0,0.01, 0.5, 0.99, 1], [0,1, 1, 1,0], antisymmetric = True)
#b = sig.remez(L, [0, 0.1, 0.11, 0.4, 0.41, 0.5], [0,1,0], [0.1,10,0.1],type = 'hilbert')
b = b / sum(abs(b))
print (b)
[w, H] = sig.freqz(b, a, 1024)
# Translate w to physical frequencies:
f = w / (2 * pi) * f_S
############## Plot the Results #########
## Pol/Nullstellenplan
figure(1)
[z, p, k] = dsp.zplane(b, a)
## ----- Impulsantwort -----
figure(2)
[h, td] = dsp.impz(b, a, f_S) #Impulsantwort / Koeffizienten
[ml, sl, bl] = stem(td, h)
plt.setp(ml, 'markerfacecolor', 'r', 'markersize', 8)
title(r'Impulsantwort h[n]')
## ----- Linear frequency plot -----
figure(3)
plot(f, abs(H))
title(r'Betragsfrequenzgang')
## Log. Frequenzgang mit Spezifikationen
figure(4)
subplot (211)
plot(f,20 * log10(abs(H)), 'r'); plt.grid('on')
plot([0, f_DB],[-A_DB, -A_DB],'b--') # untere Spec-Grenze
