%pylab inline

f = 10  # Hz
time = 1  #seconds
sr = 44100

phs = linspace(0, 2* pi* f* time, time*sr)
plot(sin(phs))

f2 = 2
phs2 = linspace(0, 2* pi* f2* time, time*sr)
plot(sin(phs2))

out = sin(phs) * sin(phs2) # Ring modulation
plot(out) 

out = sin(phs) * (1 + sin(phs2)) # Amplitude modulation
plot(out) 

phs = linspace(0, 2* pi* 30* time, 300, endpoint=False)
plot(sin(phs))

phs2 = linspace(0, 2* pi* 3* time, 300, endpoint=False)
plot(sin(phs2))

out = sin(phs) * sin(phs2)
plot(out)

plot(abs(fft.rfft(out)))
xlim((0, 40))
grid()

out = sin(phs) * (0.5 + sin(phs2))
plot(out)

plot(abs(fft.rfft(out)))
xlim((0, 40))
grid()

f = 10  # Hz
time = 1  #seconds
sr = 44100

phs = linspace(0, 2* pi* f* time, time*sr)
plot(sin(phs))

fm = 2
mod = sin(linspace(0, 2 * pi * fm * time, time*sr))

mod_phs = phs + mod
plot(mod_phs)


mod_phs = phs + (2*pi*mod)
plot(mod_phs)

plot(sin(mod_phs))

plot(abs(rfft(sin(mod_phs))))

plot(abs(rfft(sin(mod_phs))))
xlim((0, 30))

f = 4410  # Hz
time = 1  #seconds
sr = 44100
phs = linspace(0, 2* pi* f * time, time*sr)

fm = 2205
mod = sin(linspace(0, 2 * pi * fm * time, time*sr))

mod_phs = phs + mod

plot(abs(rfft(sin(mod_phs))))

plot(abs(rfft(sin(mod_phs))))
xlim((2000, 8000))
grid()

from JSAnimation import IPython_display
from matplotlib import animation

fig = plt.figure()
ax = plt.axes(xlim=(0, 22050), ylim=(0,17000))
ax.grid()
line, = ax.plot([], [])
amp_text = ax.text(10000, 15000, "")

x = np.linspace(0, 22050, 22051)

phs = linspace(0, 2* pi* f, time*sr)
mod_amp = linspace(0, 4*pi, 100)

def init():
    line.set_data([], [])
    return line,

def animate(i):
    mod_phs = phs + (mod_amp[i] * mod)
    line.set_data(x, abs(rfft(sin(mod_phs))))
    amp_text.set_text("mod_amp = %f"%mod_amp[i])
    return line,

animation.FuncAnimation(fig, animate, init_func=init,
                        frames=len(mod_amp), interval=300, blit=True)

f = 10
phs_inc = ones((time*sr)) * 2*pi*f/(time*sr)

phs = cumsum(phs_inc)
plot(sin(phs))