def desired_highpass():
ripple_low = 0.01
ripple_high = 0.05
# Normalized frequencies vector
F = [0, 0.5, 0.6, 1]
# Desired amplitudes of each point listed in 'F'
Amp = [0, 1]
# Weights vector
W = [1/ripple_low, 1/ripple_high]
M = get_M(ripple_low, ripple_high, 0.5, 0.6)
h = remez(M+1, F, Amp, W, Hz=fs)
A_w = get_amplitude_func(h, 1)
plt.figure()
plt.plot(h)
plt.title("h[n] is GLP filter of type I.")
plt.grid()
plt.legend()
w = np.linspace(-2 * math.pi, 2 * math.pi, 4096)
A = []
for i in w:
A.append(A_w(i))
w /= math.pi
plt.figure()
plt.plot(w, A)
plot_plus("A(w)")
def desired_bandpass():
ripple_low = 0.02
ripple_medium = 0.05
ripple_high = 0.01
# Normalized frequencies vector
F = [0, 0.3, 0.4, 0.7, 0.8, 1]
# Desired amplitudes of each point listed in 'F'
Amp = [0, 0, 1, 1, 0, 0]
# Weights vector
W = [1 / ripple_low, 1 / ripple_medium, 1 / ripple_high]
h = firls(M + 1, F, Amp, W)
A_w = get_amplitude_func(h, 1)
plt.figure()
plt.plot(h)
plt.title("h[n] is GLP filter of type I.")
plt.grid()
plt.legend()
w = np.linspace(-2 * math.pi, 2 * math.pi, 4096)
A = []
for i in w:
A.append(A_w(i))
w /= math.pi
plt.figure()
plt.plot(w, A)
plot_plus("A(w)")
def ex_7():
(M, window) = get_kaiser_window(ripple, delta_w)
# We know that h is simmetric.
# Therefore, it depends on M whether its a type I or II filter.
# k indicates the frequency range to take into account.
if (M % 2 == 0):
filter_type = 1
k = 1
else:
filter_type = 2
k = 2
h_ideal = ideal_lowpass_truncated(w_c, M)
h = np.multiply(h_ideal, window)
A_w = get_amplitude_func(h, filter_type)
plt.figure()
plt.plot(h_ideal)
plt.title("Impulse response corresponds to a type " + str(filter_type) +
" filter.")
plt.grid()
plt.figure()
w = np.linspace(-k * math.pi, k * math.pi, 4096)
A = []
for i in w:
A.append(A_w(i))
w /= math.pi
plt.plot(w, A)
plot_plus(title="Freq. response")
def a():
for beta in np.linspace(0, 10, endpoint=True, num=8):
h = np.kaiser(M + 1, beta)
plt.plot(h, label="Beta = " + str(beta))
plot_plus(title="Kaiser windows comparison with fixed M = " + str(M),
xlabel="n",
ylabel="h[n]")
def b():
w = (np.arange(0, nfft) * 2 * math.pi / nfft) - math.pi
w /= math.pi
for beta in np.linspace(0, 10, endpoint=True, num=8):
h = np.kaiser(M + 1, beta)
plt.plot(w,
fft_and_normalize_and_to_dB(h, nfft),
label="Beta = " + str(beta))
plot_plus(title="FFT Kaiser windows comparison with fixed M = " + str(M),
xlabel="w",
ylabel="H[(e^jw) [dB]")
def ex_4():
M = 80
h = get_impulse_response(M)
A_w = get_amplitude_func(h, 1)
w = np.linspace(-1 * math.pi, math.pi, 4096)
A = []
for i in w:
A.append(A_w(i))
w /= math.pi
plt.figure()
plt.plot(h)
plt.title("Impulse response corresponds to a type I filter")
plt.grid()
plt.legend()
plt.figure()
plt.plot(w, A)
plot_plus(title="Freq. response")
def ex_12():
window = np.hamming(M + 1)
h_ideal = ideal_multiband_truncated(gains, freqs, M)
h = np.multiply(h_ideal, window)
A_w = get_amplitude_func(h, 1)
plt.figure()
plt.plot(h, label="h[n]")
w = np.linspace(-1 * math.pi, math.pi, 4096)
A = []
for i in w:
A.append(A_w(i))
w /= math.pi
plt.figure()
plt.plot(w, A)
plot_plus("Freq. response")
def ex_5():
M = 25
h = get_impulse_response(M)
A_w = get_amplitude_func(h, 2)
plt.figure()
plt.plot(h)
plt.title("Impulse response corresponds to a type II filter")
plt.grid()
plt.legend()
plt.figure()
w = np.linspace(-2 * math.pi, 2*math.pi, 4096)
A = []
for i in w:
A.append(A_w(i))
w/= math.pi
plt.plot(w, A)
plot_plus(title="Freq. response", xlabel="$\omega/\pi$", ylabel="A($\omega$)")
def ex_16():
h_ideal = ideal_hilbert_transformer_truncated(M)
h = np.multiply(h_ideal, window)
A_w = get_amplitude_func(h, 4)
plt.figure()
plt.plot(h)
plt.title("h[n] corresponds to type III filter.")
plt.grid()
plt.legend()
w = np.linspace(-2 * math.pi, 2 * math.pi, 4096)
A = []
for i in w:
A.append(A_w(i))
w /= math.pi
plt.figure()
plt.plot(w, A)
plot_plus("Freq. response")
def ex_3_c():
(bartlett, rectangular, blackman, hamming, hanning) = get_windows()
w = (np.arange(0, nfft) * 2 * math.pi / nfft) - math.pi
w_c = math.pi / 2
h_ideal = ideal_lowpass_truncated(w_c, M - 1)
h_rectangular = fft_and_normalize_and_to_dB(h_ideal, nfft)
h_blackman = fft_and_normalize_and_to_dB(np.multiply(h_ideal, blackman),
nfft)
h_bartlett = fft_and_normalize_and_to_dB(np.multiply(h_ideal, bartlett),
nfft)
h_hamming = fft_and_normalize_and_to_dB(np.multiply(h_ideal, hamming),
nfft)
h_hanning = fft_and_normalize_and_to_dB(np.multiply(h_ideal, hanning),
nfft)
plt.plot(w, h_bartlett, label="Bartlett")
plt.plot(w, h_rectangular, label="Rectangular")
plt.plot(w, h_blackman, label="Blackman")
plt.plot(w, h_hamming, label="Hamming")
plt.plot(w, h_hanning, label="Hann/Hanning")
plot_plus(title="Windows comparison in frequency with M=200")
