wmin, wmax, num_w = 2**-9.5, 2**4.5, 1000
w = np.logspace(np.log10(wmin), np.log10(wmax), num=num_w)
# Filter design
shelving_filters = []
H = np.zeros((len(Biquad_per_octave), num_w), dtype='complex')
Gain = np.zeros(len(Biquad_per_octave))
Gain_biquad = np.zeros(len(Biquad_per_octave))
for n, biquad_per_octave in enumerate(Biquad_per_octave):
num_biquad, Gb, G = \
shelving_filter_parameters(biquad_per_octave=biquad_per_octave,
Gd=Gd, BWd=BWd)
Gain[n] = G
Gain_biquad[n] = Gb
sos = low_shelving_2nd_cascade(w0, Gb, num_biquad, biquad_per_octave)
H[n] = sosfreqs(sos, worN=w)[1]
shelving_filters.append(sos)
# Plots
wlim = wmin, wmax
wticks = 2**(np.arange(np.ceil(np.log2(w)[0]/2)*2,
np.floor(np.log2(w[-1])/2)*2 + 2, 2))
kw = {'lw': 2, 'alpha': 1, 'basex': 2}
colors = cm.get_cmap('Blues')
fig, ax = plt.subplots(figsize=(10, 4), ncols=2, gridspec_kw={'wspace': 0.25})
# frequency response
for n, H_n in enumerate(H):
col = colors((n + 3) / (len(H) + 3))
ax[0].semilogx(w, db(H_n), c=col, **kw)
Gd = 10 * np.log10(0.5) * BWd
biquad_per_octave = 1
slope = shelving_slope_parameters(BWd=BWd, Gd=Gd)[0]
wl, wh = w0 * 2**(-BWd), w0
# Frequency-domain evaluation
wmin, wmax, num_w = 2**-9.5, 2**4.5, 1000
w = np.logspace(np.log10(wmin), np.log10(wmax), num=num_w)
# Filter design
num_biquad, Gb, G = shelving_filter_parameters(
biquad_per_octave=biquad_per_octave, Gd=Gd, BWd=BWd)
Hmag = np.clip(np.log2(w / w0) * slope, G, 0) # desired response
sos = low_shelving_2nd_cascade(w0, Gb, num_biquad, biquad_per_octave)
H_biquads = np.stack(
[sosfreqs(sosi[np.newaxis, :], worN=w)[1] for sosi in sos])
H = sosfreqs(sos, worN=w)[1]
# Plots
Glim = -9.5, 1
wlim = wmin, wmax
wticks = 2**(np.arange(
np.ceil(np.log2(w)[0] / 2) * 2,
np.floor(np.log2(w[-1]) / 2) * 2 + 2, 2))
kw = dict(lw=2, alpha=1, basex=2)
kw_dotted = dict(color='gray', linestyle=':', linewidth=1)
kw_artist = dict(edgecolor='gray', linestyle=':', linewidth=1)
colors = cm.get_cmap('Blues')
# frequency response
fig, ax = plt.subplots(figsize=(10, 4), ncols=2, gridspec_kw={'wspace': 0.1})