In [1]:

    

%pylab inline
pylab.rcParams['figure.figsize'] = (18, 6)

import numpy as np


    

    




Populating the interactive namespace from numpy and matplotlib

In [2]:

    

sample_rate = 48000
tau = 2.0 * np.pi


    

In [3]:

    

def exp_ramp(current, target, attack, linearity):
    flip = False
    if current > target:
        flip = True
        current, target = target, current
    out = current
    out_arr = [out]
    sample_count = 0
    for i in range(0, 500):
        out += attack * ((target/linearity) - out)
        if flip:
            out_arr.append(target - out + current)
        else:
            out_arr.append(out)
        if out > target:
            out = target
        else:
            sample_count += 1
    print("reach %s in %s samples" % (target, sample_count))
    return np.array(out_arr)


    

In [4]:

    

plot(exp_ramp(0.0, 1.0, 0.006, 0.63))


    

    




reach 1.0 in 165 samples






    
Out[4]:





[<matplotlib.lines.Line2D at 0x106ef0950>]






    

In [5]:

    

plot(exp_ramp(0.0, 1.0, 0.003, 0.63))


    

    




reach 1.0 in 330 samples






    
Out[5]:





[<matplotlib.lines.Line2D at 0x107372cd0>]






    

In [6]:

    

plot(exp_ramp(0.0, 1.0, 0.003, 0.7))


    

    




reach 1.0 in 400 samples






    
Out[6]:





[<matplotlib.lines.Line2D at 0x1075a8e90>]






    

In [7]:

    

plot(exp_ramp(0.0, 1.0, 0.004, 0.54))


    

    




reach 1.0 in 193 samples






    
Out[7]:





[<matplotlib.lines.Line2D at 0x1077d5510>]






    

In [8]:

    

plot(exp_ramp(0.0, 1.0, 0.008, 0.85))


    

    




reach 1.0 in 236 samples






    
Out[8]:





[<matplotlib.lines.Line2D at 0x1079f7ad0>]






    

In [9]:

    

plot(exp_ramp(0.0, 1.0, 0.008, 0.85))


    

    




reach 1.0 in 236 samples






    
Out[9]:





[<matplotlib.lines.Line2D at 0x107c17d90>]






    

In [10]:

    

plot(exp_ramp(0.5, 1.0, 0.008, 0.85))


    

    




reach 1.0 in 167 samples






    
Out[10]:





[<matplotlib.lines.Line2D at 0x107e48b50>]






    

In [11]:

    

plot(exp_ramp(0.0, 0.5, 0.005, 0.5))


    

    




reach 0.5 in 138 samples






    
Out[11]:





[<matplotlib.lines.Line2D at 0x108079110>]






    

In [12]:

    

plot(exp_ramp(0.0, 1.0, 0.01, 0.875))


    

    




reach 1.0 in 206 samples






    
Out[12]:





[<matplotlib.lines.Line2D at 0x10829a690>]






    

In [ ]:

    




    

In [13]:

    

def exp_ramp2(start, end, attack, linearity):
    # always start at 0, so the curve of the ramp stays consistent
    offset = start
    out_mult = end - start
    
    out = 0.0
    out_arr = [out]
    sample_count = 0
    for i in range(0, 500):
        out += attack * ((1.0/linearity) - out)
        out_arr.append(offset + (out_mult * out))
        if out > 1.0:
            out = 1.0
        else:
            sample_count += 1
    print("reach %s in %s samples" % (1.0, sample_count))
    return np.array(out_arr)


    

In [14]:

    

plot(exp_ramp2(0.0, 1.0, 0.005, 0.5))


    

    




reach 1.0 in 138 samples






    
Out[14]:





[<matplotlib.lines.Line2D at 0x1084bad10>]






    

In [15]:

    

plot(exp_ramp2(0.5, 1.0, 0.005, 0.5))


    

    




reach 1.0 in 138 samples






    
Out[15]:





[<matplotlib.lines.Line2D at 0x1086eb2d0>]






    

In [16]:

    

plot(exp_ramp2(1.0, 0.1, 0.005, 0.5))


    

    




reach 1.0 in 138 samples






    
Out[16]:





[<matplotlib.lines.Line2D at 0x10890d810>]






    

In [17]:

    

plot(exp_ramp2(1.0, 0.1, 0.0088, 0.88))


    

    




reach 1.0 in 239 samples






    
Out[17]:





[<matplotlib.lines.Line2D at 0x108b30610>]






    

In [18]:

    

sample_rate = 44100
attack_ms = 100
attack_samples = sample_rate / 1000.0 * attack_ms
print("attack samples: %s" % attack_samples)


    

    




attack samples: 4410.0

In [19]:

    

def attack_coef_from_ms(linearity_coef, attack_ms, sample_rate):
    attack_samples = sample_rate / 1000.0 * attack_ms
    coef = np.e * linearity_coef * linearity_coef / attack_samples
    return coef
print(attack_coef_from_ms(0.88, 100, 44100))


    

    




0.000477332754639

In [20]:

    

def exp_ramp_ms(start, end, attack_ms, linearity, sample_rate):
    attack_samples = floor(sample_rate / 1000.0 * attack_ms)
    attack_coef = np.e * linearity * linearity / attack_samples
    print("attack coef: %s" % attack_coef)
    # always start at 0, so the curve of the ramp stays consistent
    offset = start
    out_mult = end - start
    
    out = 0.0
    out_arr = [out]
    sample_count = 0
    while 1:
        out += attack_coef * ((1.0/linearity) - out)
        out_arr.append(offset + (out_mult * out))
        if out > 1.0:
            out = 1.0
            break
        else:
            sample_count += 1
    print("reached target in %s samples" % sample_count)
    return np.array(out_arr)


    

In [21]:

    

plot(exp_ramp_ms(0.0, 1.0, 100, 0.88, 44100))


    

    




attack coef: 0.000477332754639
reached target in 4440 samples






    
Out[21]:





[<matplotlib.lines.Line2D at 0x108d61350>]






    

In [22]:

    

plot(exp_ramp_ms(0.0, 1.0, 30, 0.88, 44100))


    

    




attack coef: 0.00159110918213
reached target in 1331 samples






    
Out[22]:





[<matplotlib.lines.Line2D at 0x108f85390>]






    

In [23]:

    

plot(exp_ramp_ms(0.0, 1.0, 30, 0.8, 44100))


    

    




attack coef: 0.00131496626622
reached target in 1223 samples






    
Out[23]:





[<matplotlib.lines.Line2D at 0x1091a4fd0>]






    

In [24]:

    

plot(exp_ramp_ms(0.0, 1.0, 30, 0.7, 44100))


    

    




attack coef: 0.00100677104758
reached target in 1195 samples






    
Out[24]:





[<matplotlib.lines.Line2D at 0x1093d45d0>]






    

In [25]:

    

def exp_ramp_ms_hard(start, end, attack_ms, linearity, sample_rate):
    attack_samples = int(floor(sample_rate / 1000.0 * attack_ms))
    attack_coef = np.e * linearity * linearity / attack_samples
    print("attack coef: %s" % attack_coef)
    # always start at 0, so the curve of the ramp stays consistent
    offset = start
    out_mult = end - start
    
    out = 0.0
    out_arr = [out]
    sample_count = 0
    for i in range(0, attack_samples):
        out += attack_coef * ((1.0/linearity) - out)
        out_arr.append(offset + (out_mult * out))
        if out > 1.0:
            out = 1.0
            break
        else:
            sample_count += 1
    print("reached %s in %s samples" % (out, sample_count))
    return np.array(out_arr)


    

In [26]:

    

plot(exp_ramp_ms_hard(0.0, 1.0, 30, 0.88, 44100))


    

    




attack coef: 0.00159110918213
reached 0.998139747745 in 1323 samples






    
Out[26]:





[<matplotlib.lines.Line2D at 0x109600910>]






    

In [27]:

    

plot(exp_ramp_ms_hard(0.0, 1.0, 500, 0.44, 44100))


    

    




attack coef: 2.3866637732e-05
reached 0.929983771412 in 22050 samples






    
Out[27]:





[<matplotlib.lines.Line2D at 0x10985f550>]






    

In [28]:

    

plot(exp_ramp_ms_hard(0.0, 1.0, 500, 0.63, 44100))


    

    




attack coef: 4.89290729123e-05
reached 1.0 in 20319 samples






    
Out[28]:





[<matplotlib.lines.Line2D at 0x109b79d50>]






    

In [31]:

    

def plot_lin(start, end, time_ms, sample_rate):
    samples = sample_rate / 1000 * time_ms
    increment = float(end - start) / samples
    out = start
    out_arr = [out]
    for i in range(0, samples):
        out += increment
        out_arr.append(out)
    return np.array(out_arr)


    

In [32]:

    

plot(exp_ramp_ms_hard(0.0, 1.0, 30, 0.88, 44100))
plot(plot_lin(0.0, 1.0, 30, 44100))


    

    




attack coef: 0.00159110918213
reached 0.998139747745 in 1323 samples






    
Out[32]:





[<matplotlib.lines.Line2D at 0x10960dad0>]






    

In [33]:

    

plot(exp_ramp_ms(0.0, 1.0, 30, 0.8, 44100))
plot(plot_lin(0.0, 1.0, 30, 44100))


    

    




attack coef: 0.00131496626622
reached target in 1223 samples






    
Out[33]:





[<matplotlib.lines.Line2D at 0x10a0f7350>]






    

In [34]:

    

plot(exp_ramp_ms(0.0, 1.0, 30, 0.63, 44100))
plot(plot_lin(0.0, 1.0, 30, 44100))


    

    




attack coef: 0.000815484548538
reached target in 1218 samples






    
Out[34]:





[<matplotlib.lines.Line2D at 0x10a326710>]






    

In [35]:

    

plot(exp_ramp_ms(0.0, 1.0, 100, 0.63, 44100))
plot(plot_lin(0.0, 1.0, 100, 44100))


    

    




attack coef: 0.000244645364561
reached target in 4063 samples






    
Out[35]:





[<matplotlib.lines.Line2D at 0x10a552bd0>]






    

In [36]:

    

plot(exp_ramp_ms(0.0, 1.0, 500, 0.63, 44100))
plot(plot_lin(0.0, 1.0, 500, 44100))


    

    




attack coef: 4.89290729123e-05
reached target in 20319 samples






    
Out[36]:





[<matplotlib.lines.Line2D at 0x10a780a90>]






    

In [37]:

    

plot(exp_ramp_ms(0.0, 1.0, 500, 0.75, 44100))
plot(plot_lin(0.0, 1.0, 500, 44100))


    

    




attack coef: 6.93439241954e-05
reached target in 19990 samples






    
Out[37]:





[<matplotlib.lines.Line2D at 0x10aad3f10>]






    

In [38]:

    

plot(exp_ramp_ms(0.0, 1.0, 500, 0.44, 44100))
plot(plot_lin(0.0, 1.0, 500, 44100))


    

    




attack coef: 2.3866637732e-05
reached target in 24293 samples






    
Out[38]:





[<matplotlib.lines.Line2D at 0x10a5b6ed0>]






    

In [41]:

    

plot(exp_ramp_ms(0.0, 1.0, 500, 0.525, 44100))
plot(plot_lin(0.0, 1.0, 500, 44100))


    

    




attack coef: 3.39785228557e-05
reached target in 21908 samples






    
Out[41]:





[<matplotlib.lines.Line2D at 0x10b6fa610>]






    

In [61]:

    

plot(exp_ramp_ms(0.0, 1.0, 500, 0.7, 48000))
plot(plot_lin(0.0, 1.0, 500, 48000))


    

    




attack coef: 5.54982539977e-05
reached target in 21693 samples






    
Out[61]:





[<matplotlib.lines.Line2D at 0x10fe8ccd0>]






    

In [65]:

    

plot(exp_ramp_ms(0.0, 1.0, 10, 0.55, 48000))
plot(plot_lin(0.0, 1.0, 10, 48000))


    

    




attack coef: 0.00171308386064
reached target in 465 samples






    
Out[65]:





[<matplotlib.lines.Line2D at 0x110cc2cd0>]






    

In [66]:

    

plot(exp_ramp_ms(67, 73, 10, 0.55, 48000))
plot(plot_lin(67, 73, 10, 48000))


    

    




attack coef: 0.00171308386064
reached target in 465 samples






    
Out[66]:





[<matplotlib.lines.Line2D at 0x110f09450>]






    

In [ ]: