.  
 


 #4
      ,               .         .    ,          .        ,     ,      . ,           .              .,          .





 

.  



 1:       

1.1.          

  ( )      ,    .         ,   .           :

1.  :  ,    ,     ,      .      ,     ,     ,       .      ,   ,       ,         .                 ,            .

2.   :             ,         .      ,       ,        ,  ,     .           .     ,         ,    ,  ,        .   ,     ,              .

3.   :         ,       .  ,         ,   .  ,     ,         ,         .     ,          .                ,  , ,  ,   .

4.  :         , ,      .       ReLU (Rectified Linear Unit),    .      ,    ,          .            . ,  ReLU       ,           .                   .

5.    (CNN):    (CNN)     ,         .            ,     ,         .           . CNN    ,       ,                  .

6.    (RNN):    (RNN)    ,       .    ,        .       ,       ,         . RNN              ,     ,   ,  ,      .

7.    (LSTM)     (GRU):    (LSTM)     (GRU)       (RNN)        .         ,     ,     . LSTM  GRU    ,         ,    ,      .          ,        .

    :

1.  :       ,  ,    ,   .   :      ,       ,     ,   ,      . ,      :  ,       ,   ,       .        ,      .          .   ,     ,        ,       .

2.  :       ,     .          ,  , ,         .       ,    .  ,    ,     ,       .            ,       .

3.  :         .     ,            .  ,     ,        .          .  ,   GANs   ,    ,           .                .

4.  :           .  ,       ,   ,     ,      .  ,        ,           .   ,       ,       ,       .

 ,           .      ,       ,    ,   ,     ,    ,    .

5.  :        ,    ,     .        ,      ,   , ,   ,        ,         .            ,             .

      ,        ,  ,  ,   .

1.2.        

                 .

     ,          .     (,    )   (,  ).   ,   .  ,           ().         .    .

       .               .       :

1.   (sample rate):  (sample rate)   ,      .    ().         ,           .       ,             .

2.   (bit depth):   (bit depth)      ,       .   ,          .              ,       . , CD-    16 ,          .     ,   24   ,       ,             .

               .         ,     .      ,     .         ,    ,     .       ,   , ,    ,      ,     ,       .                    .

  ,   

      ,    .

  (sample rate)      ,    ().

  (bit depth)   ,       .

          .

         .

    ,     ,     .

   ,    () ,    .

          .

     ,    .

                 .

 2:  

2.1.    ,  , ,   

        ,   ,      .    :

1. :         .         ,   .   ,   , , ,    .    (),     ,        ,  ,    .

        .     ,           ,       .         ,      ,        .  ,       ,       .

2. :       , ,         .      ()  ,           .   ,       .

     .  ,  ,    .            .

            ,     .       .

         .   ,   ,        .

      ,        .        ,       .       ,       .

3. :       ,           .       ,          .    ,           .

         ,      .        ,      ( )    ( ),        .

          .       ,    ,       .     ,    ,           ,     .

4. :          .       ,  ,          ,   .      ,        ,         .

       .    ,    (  ),     ,    .        ,  ,  ,       .       ,     ,           .

       .        ,        ,  , , ,    .

2.2.    ,      -

         ,     -.

 

  ( -)              .         .

  :

          .       .

,    ,      ,    f(t),  t  .             .     :




,   ,    ?    .    ,  ,         .  ,      ,      .

       ,                .



   :

            .   ,           .    ,    ,      .

 :

   ,        .        ,     ,      ,      .      ,      .

 :

        .      ,   ,  ,       .       ,     ,     ,     .

  :

      , ,  (A)  .      ,        .       . ,   ,       ,    .           ,   ,     .

           ,         .

 :

      . ,    :

    ,      .

        .

           .

     .

   ,                 Python.        NumPy     Matplotlib  .

```python

import numpy as np

import matplotlib.pyplot as plt

#    (, )

sample_rate = 1000 #    

duration = 1.0 #    

t = np.linspace(0, duration, int(sample_rate * duration), endpoint=False)

frequency = 5 #    

signal = np.sin(2 * np.pi * frequency * t)

#   

fft_result = np.fft.fft(signal)

freqs = np.fft.fftfreq(len(fft_result), 1 / sample_rate) # 

#   

plt.figure(figsize=(10, 4))

plt.subplot(121)

plt.plot(t, signal)

plt.title('  ')

plt.xlabel(' ()')

plt.ylabel('')

plt.subplot(122)

plt.plot(freqs, np.abs(fft_result))

plt.title('  ')

plt.xlabel(' ()')

plt.ylabel('')

plt.xlim(0, 20) #   

plt.show()

```

      ,        ,   .      ,      ,    .



       ,   ,       


  .

   :

       (FFT),         .       ,   , ,    .

         ,             .

-     ,          . -  ,  -,      .     ,      ,           .

 -     ,          .     :

1.  :      .     ,     .            . ,   (Daubechies)    .






2. :    -,   .         -          .








3.     : -         .        -.       .

4.  :  -     ,        .            .

5.   :  -   , ,    -.      ,        .

  Python       PyWavelets:

```python

import pywt

import pywt.data

import numpy as np

import matplotlib.pyplot as plt

#   

signal = np.sin(2 * np.pi * np.linspace(0, 1, 1000))

#  -

coeffs = pywt.wavedec(signal, 'db1', level=5)

#  

plt.figure(figsize=(12, 4))

plt.subplot(121)

plt.plot(signal)

plt.title(' ')

plt.subplot(122)

plt.plot(coeffs[0]) #  

plt.title('-')

plt.show()

```






          -,     .           .



 -,          ,          .

 ,    -,      .          ,      . -            ,       .

        ,        .

 3:     

3.1.   ,      

        ,       .         .

   (Convolutional Neural Networks, CNN)

 :    ,  ,    .

 :  ,     .

 :    (CNN)      ,          ,     .    CNN               .

      ,             .         ,   .     ,  ReLU,     .

            .         .      (Max Pooling)   (Average Pooling),           .        CNN        ,            .

2.    (Recurrent Neural Networks, RNN)

 :   ,   , ,  .

 :  ,  LSTM (Long Short-Term Memory)  GRU (Gated Recurrent Unit).

 :    (RNN)     ,       ,   , ,    .      RNN   ,             ,            .

     ,    (,       )     .              .

        RNN, LSTM (Long Short-Term Memory)  GRU (Gated Recurrent Unit). LSTM  GRU             ,       RNN.

 RNN            .      ,  ,  ,     ,     .      ,      ,       ,      (CRNN)  ,              .

3.      (LSTM)

:     ,   ,       ,      .    (RNN)      ,   RNN          -   .

           (LSTM). LSTM       ,                 .

  LSTM   :

 : LSTM   ,         .       ,            .

  : LSTM      ,      ,    ,         .

: LSTM     ,    ,  ,  ,      .               .

   LSTM,           ,              .

4.     (Memory Networks)

:        (LSTM  External Memory)        (LSTM),          .      ,       -.

     :

 : LSTM  External Memory   ,      .       ,     ,           .

   -:      , LSTM  External Memory     -,           ,    .

  :           ,      ,    ,     ,      .

 LSTM  External Memory          ,       ,  -,  ,      ,        .           ,         .

5.    (Deep Learning)

:    (Deep Neural Networks, DNNs)     ,    ,            .    ,            .

    :

 : DNNs   ,   .    ,         .    ,         .

  :               . ,       , ,     ,     .

   :          ,   , ,  ,     .        ,  ,   ,         .

  ,        (CNNs)     (RNNs),        .                   ,      .

6.   (Autoencoders)

:   (Autoencoders)     ,        .          ,         .       :   .

 (Encoder):            ,     .          .      ,     .

 (Decoder):    .            .       ,          .

            .     ,         .  ,       ,       ,     ,  ,      .

           ,   ,     .                   .

7.     (GANs)

 :    ,  , ,    -.

: GANs    ,    .     ,   .

    (GANs)        ,     .     GANs   ,     :   .         ,     ,       .

 (Generator):     GANs    ,     .             ,   .        ,         .

 (Discriminator):      GANs.         .         ,    ,     .            .

    :   GANs     .       :    ,   ,         .       ,              ,   .

GANs     ,   , , ,      .                 .           ,         .

8.      (LSTM  Attention)

:        (LSTM  Attention)       (LSTM),    .    ,        ,     .

   LSTM     LSTM,                 . ,           .

  ? ? LSTM     .     ,         ,     .  ,        ,        .    LSTM          ,     ,      .

       .                 .

3.2.       

     ,              .           (loss function),         .          ,        .            .

   :

1.  :         .      ,   ,     .     ,    .

2.   :       ,   ,         (, ,   ).

3.   :      .         .       :        (MSE),      -.

4. :       .      ,      (SGD)   ,  Adam  RMSprop.

5.   :       ,        .        .

6. :           ,      .

   

        .    :



  

(MSE

):

             

.

  (Mean Squared Error, MSE)                 .                 . MSE  ,   ,     ,        .

  MSE   :

1.          .      ,      ,          .

2.        ( )    .    ""  ""     .

3.     ,         ,    .    ,      .

4.       .      MSE.

 MSE    (i)   :

MSE(i) = ( (i)   (i))^2

     N   MSE  :

MSE = (1/N) * ? ( (i)   (i))^2  i=1  N

   MSE,       , , ,    .   ,  MSE         ,        .





-



:

          

,

 

,

   

.

- (Cross-Entropy)     ,     ,       .      ,  ,      . -   ,         .

  -     :          . Ÿ    :

1.               .         ,           .

2.           ,      1 (,    ),     0.

3.  ,  ,    ,  -   .    -    i  :

Cross-Entropy(i) = -? ( (i) * log( (i)))

 ?     .

4.  -         -   .   ,      .

-    :

        .

       ,        .

          ,      .

 -        ,       ,       .



 

-



:

    

,

   

.

 - (Categorical Cross-Entropy)    ,       ,                   .        ,  ,    .

  -       :

1.               .     ,          .

2.           ,     1 (,    ),     0.

3.  ,  ,    ,   -   .     -    i   :

Categorical Cross-Entropy(i) = -? ( (i) * log( (i)))

 ?     .

4.   -          -   .

 ,       - ,        .       ,    -    ,      .

    -     "Softmax"    ,       .  -     ,        .



 

-



:

    

,

   

.

 - (Binary Cross-Entropy),      (Logistic Loss),   ,     ,    :  ""  "".            .

  -       :

1.      "" (    1)     "" (    0)   .        "Sigmoid",       ,     0  1.

2.            ,      1 ( 1  ""),     0 ( 0  "").

3.        ,   -   .     -    i   :

Binary Cross-Entropy(i) = -[ (i) * log( (i)) + (1   (i)) * log(1   (i))]

4.   -          -   .

 -    :

        ,        .

       ,      .

           .

 -               ,      ,        ,     .

    (MAE):    (Mean Absolute Error, MAE)    ,    .              . MAE          ,     .

  MAE   :

1.         .      ,      ,          .

2.        ( )    .    ""  ""     .

3.       ,       .

4.          .

 MAE    i   :

MAE(i) = | (i)   (i)|

     N   MAE  :

MAE = (1/N) * ? | (i)   (i)|  i=1  N

  MAE   ,         ,         .  MAE ,    ,           . MAE     ,    (MSE),      ,       .

          ,    .    ,                .

3.3.     

           ,            ,    .          ,   ,    ,  ,  ,  ,     .

          :

1.   (ASR  Automatic Speech Recognition):          .  ,    ,   ,      .   ,    ,              .        ,   Siri, Google Assistant  Amazon Alexa,          .

2.  :         .         , ,   , ,      .       ,   .

3.  :  ,         ,          .         ,         .

4.   (TTS  Text-to-Speech):  ,    Text-to-Speech (TTS),         .   ,      ,      ,        .      ,    ,    .

 ,   Siri, Google Assistant  Cortana,  TTS       .            .  , TTS    ,     ,            .

   ,  TTS     ,          .   TTS        ,         ,       ,          .

5.    :           .      ,     .    ,      :

  :                .              .

  :     ,  ,      .          ,       .

  :         ,        ,   "".            .

 :         .    ,      (GAN),    ,     .         .

                 ,     .              .

6.  :          ,       ,    .            .   ,     :

    :              ,    ,         .            .

    :                .    ,      ,          .

 :        ,    . ,          ,    .      ,      .

    :           ,    .     ,   ,         .

                ,         .       ,     ,       .

7.    :  ,          ,            .         .        :

 :       ,    ,    .    ,         ,     .

 :            ,   , ,   .        ,       .

 :          .        ,  ,       .       ,    .

 :         ,   ,     .            .

   ,   ,   ,       .           ,        .

8.    :           ,            .        ,  , ,    .   ,        :

  :     ,    ,     ,     .               .

  :                 .   ,         ,     .

  :             . ,       ,     ,          .

:                  .         ,             .

             .     ,   ,           .

9.     :        ,          .       ,   ,         .   :

   :         ,        .     ,  ,    ,        .

  :         ,   , ,   ..         ,      .

    :             . ,               ,    ,    .

  :       ,             ,      .

    ,   ,             .        ,           .

        ,      (CNN),    (RNN),     (CRNN),      .  ,          .

      ,             .

 4:  

4.1.     

           .        ,          .          :

1. Hidden Markov Models (HMM)

   ,     ,       .          ,     .

  HMM   :

:          .

:

1)   HMM:   HMM      ,      .            .

2)  :         ,  ,       .

3)  :   ,  ,        ,       .

4)  :     HMM   ,         .

5)   :            .          ,      .

  HMM          ,    .      DNN      , HMM -      ,     ,   .

 Hidden Markov Models (HMM)          ,      .        Python,  ,     `hmmlearn`   HMM     . ,              .

       `hmmlearn`.

      pip:

```bash

pip install hmmlearn

```

  :

```python

import numpy as np

from hmmlearn import hmm

#      "yes"  "no"

X = [

np.array([[1.1], [2.0], [3.3]]),

np.array([[0.9], [2.2], [3.1], [4.0]]),

]

#    HMM

model = hmm.GaussianHMM(n_components=2, covariance_type="full")

model.fit(X)

#  HMM   

test_data = np.array([[0.8], [2.1], [3.0], [4.2]])

log_likelihood = model.score(test_data)

if log_likelihood > -10:

print(" 'yes' .")

else:

print(" 'no' .")

```

      HMM-   ,    "yes"  "no".         ,       .

,                      HMM.





`pip`          Python.  "pip"     "pip" (  "Pip Installs Packages"),      ,        Python.

  `pip`     ,    ,      .        ,       .

    `pip`:

`pip install package_name`:  .

`pip install -r requirements.txt`:     `requirements.txt`,          .

`pip uninstall package_name`:   .

`pip freeze > requirements.txt`:          `requirements.txt`,      .

`pip list`:    .

`pip`       Python          .




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