%pylab inline
rcParams['figure.figsize'] = (10, 4) #wide graphs by default
from __future__ import print_function
from __future__ import division

impulse = r_[1,zeros(15)]
stem(arange(16),impulse)
xlim((-0.5, 16))
ylim((-1.1, 1.1))

ir = 2*(random.random(3) -0.5)

stem(arange(3),ir)

xlim((-0.5, 2.5))
ylim((-1.1, 1.1))

stem(arange(18),convolve(impulse, ir))
xlim(-1,18)

impulse2 = r_[zeros(5), -1, zeros(10)]
stem(arange(16),impulse2)
xlim((-0.5, 16))
ylim((-1.1, 1.1))

stem(arange(18),convolve(impulse2, ir));

subplot(121)
added_after = convolve(impulse, ir) + convolve(impulse2, ir)
stem(arange(18),added_after)

added_before = convolve(impulse + impulse2, ir)
subplot(122)
stem(arange(18),added_before);

f = [1,2,3,0,0,0]
g = [-0.5, 0.5, 0.1]

subplot(121)
stem(arange(6),f)
xlim((-0.5, 4.5))
subplot(122)
stem(arange(3),g)
xlim((-0.5, 4.5))

markerline, stemlines, baseline  = stem(arange(5),convolve(array([1,0,0]),g))

markerline, stemlines, baseline  = stem(arange(5),convolve(array([0,2,0]),g), 'g', 'og')

markerline, stemlines, baseline  = stem(arange(5),convolve(array([0,0 ,3]),g), 'r', 'or')
markerline.set_color('r')
grid()

xlim((-0.5, 4.5))
ylim((-2, 2))

f = array([0.3, 0.2, -0.5, 0, -0.1, 0.1, 0.25 ])
stem(f)

g = array([0.1, 0.2, -0.1])
stem(g)

fg0 = f[0] * g
subplot(211)
stem(fg0)
subplot(212)
stem(g)

fg1 = f[1] * g
stem(fg1)

fg1 = r_[0, fg1]
stem(fg1)

fg2 = f[2] * g
fg2 = r_[0, 0, fg2]
stem(fg2)

def hide_axes(ax):
    ax.spines["top"].set_visible(False)  
    ax.spines["right"].set_visible(False) 
    ax.spines["bottom"].set_visible(False) 
    ax.spines["left"].set_visible(False)
    tick_params(axis="both", which="both", bottom="off", top="off",  
                labelbottom="off", left="off", right="off", labelleft="on")
    


subplot(511)
stem(fg0)
xlim(0,6)
ylim(-0.1, 0.1)
hide_axes(gca())

subplot(512)
stem(fg1)
xlim(0,6)
ylim(-0.1, 0.1)
hide_axes(gca())


subplot(513)
stem(fg2)
xlim(0,6)
ylim(-0.1, 0.1)
hide_axes(gca())


subplot(514)
stem(f)

xlim(0,6)


subplot(515)
stem(g[::-1])

xlim(0,6)


gcf().set_figheight(8)

def apply_ir(f , n, g):
    fg = f[n] * g
    fg = r_[zeros(n), fg, zeros(len(g) + len(f) - len(fg) - n - 1 )]
    return fg

fg = apply_ir(f, 6, g)
stem(fg)

convolved = zeros(9)
for i in range(len(f)):
    convolved += apply_ir(f, i, g)

stem(convolved)

stem(convolve(f,g))

f = random.random(4096) - 0.5
specgram(f);

g = ones(30)/30.0

plot(f)
figure()
stem(g)

fg = convolve(f, g)

Pxx, freqs, bins, im = specgram(fg);

plot(Pxx[:, 10])

from scipy.signal import freqz
w, h = freqz(g)
plot(w, abs(h))
twinx()
plot(w, angle(h), 'r')

plot(abs(fft.rfft(g)), 'o-')

plot(abs(fft.rfft(g, n=512)))
twinx()
plot(angle(fft.rfft(g, n=512)), 'r')

window = f[:256]
plot(abs(rfft(window)))

plot(abs(rfft(window)*rfft(g, n=256)))