%pylab inline

from scipy.special import eval_chebyt

res = 1024
x_space = linspace(-1,1,res)
plot(x_space, eval_chebyt(2, x_space))

t2 = eval_chebyt(2, x_space)

source = cos(2* pi * ((x_space + 1)/2))
plot(source)

index = floor((res - 1) * (source + 1)/ 2).astype(int)
index.dtype

plot(index)

waveshaped = t2[index]
plot(waveshaped)

stem(abs(rfft(waveshaped)))
xlim(0, 10)

depth = 0.5
index = floor(depth * (res - 1) * (source + 1)/ 2).astype(int)
waveshaped = t2[index]
plot(waveshaped)

stem(abs(rfft(waveshaped)))
xlim(0, 10)

t5 = eval_chebyt(5, x_space)
waveshaped = t5[index]
plot(waveshaped)

stem(abs(rfft(waveshaped)))
xlim(0, 10)

t15 = eval_chebyt(15, x_space)
waveshaped = t15[index]
subplot(121)
plot(waveshaped)
subplot(122)
stem(abs(rfft(waveshaped)))
xlim(0, 50)

res = 102400
x_space = linspace(-1,1,res)
source = cos(2* pi * 1000 * ((x_space + 1)/2))
depth = linspace(0, 1, res)
index = floor(depth * (res - 1) * (source + 1)/ 2).astype(int)

t15 = eval_chebyt(15, x_space)
waveshaped = t15[index]
specgram(waveshaped, NFFT=1024);
ylim(0, 0.5)

t50 = eval_chebyt(50, x_space)
waveshaped = t50[index]
specgram(waveshaped, NFFT=1024);
ylim(0, 1)

plot(t50)

t49 = eval_chebyt(49, x_space)
waveshaped = t49[index]
specgram(waveshaped, NFFT=1024);
ylim(0, 1)

plot(t49)

shaper1 = eval_chebyt(10, x_space)
shaper2 = tanh(x_space * 6)
plot(shaper1)
plot(shaper2)

waveshaped1 = shaper1[index]
waveshaped2 = shaper2[index]

plot((waveshaped1 + waveshaped2)/2)

specgram((waveshaped1 + waveshaped2)/2, NFFT=2048);

newshaper = (shaper1 + shaper2)/2

waveshaped = newshaper[index]

plot(waveshaped)

specgram((waveshaped1 + waveshaped2)/2, NFFT=2048);

waveshaped1 = shaper1[index /2]
waveshaped2 = shaper2[index /2]

Pxx, freqs, bins, im = specgram((waveshaped1 + waveshaped2)/2, NFFT=2048);

plot(Pxx[:,50])