! pip install numpy matplotlib scikit-learn

#PCA

#import libraries
import numpy as np
import matplotlib.pyplot as plt
import sklearn


np.set_printoptions(precision=1)
#
# load MNIST data
#
X = np.load('datasets/MNIST/xtrain.npy')
y = np.load('datasets/MNIST/ytrain.npy')
print(f"MNIST data shape (records,pixels): {X.shape}")
#
# plot vs two pixel values
#
plt.scatter(X[:,200],X[:,400],c=y)
plt.xlabel("pixel 200")
plt.ylabel("pixel 400")
plt.title("MNIST vs pixels 200 and 400")
plt.colorbar(label="digit")
plt.show()
#
# standardize (zero mean, unit variance) to eliminate dependence on data scaling
#
print(f"data mean: {np.mean(X):.2f}, variance: {np.var(X):.2f}")
X = X-np.mean(X,axis=0)
std = np.std(X,axis=0)
Xscale = X/np.where(std > 0,std,1)
print(f"standardized data mean: {np.mean(Xscale):.2f}, variance: {np.var(Xscale):.2f}")
#
# do 50 component PCA
#
pca = sklearn.decomposition.PCA(n_components=50)
pca.fit(Xscale)
Xpca = pca.transform(Xscale)
plt.plot(pca.explained_variance_,'o')
plt.plot()
plt.xlabel('PCA component')
plt.ylabel('explained variance')
plt.title('MNIST PCA')
plt.show()
#
# plot vs first two PCA components
#
plt.scatter(Xpca[:,0],Xpca[:,1],c=y,s=3)
plt.xlabel("principal component 1")
plt.ylabel("principal component 2")
plt.title("MNIST vs two principal components")
plt.colorbar(label="digit")
plt.show()

---------------------------------------------------------------------------
FileNotFoundError                         Traceback (most recent call last)
Cell In[1], line 8
      4 np.set_printoptions(precision=1)
      5 #
      6 # load MNIST data
      7 #
----> 8 X = np.load('datasets/MNIST/xtrain.npy')
      9 y = np.load('datasets/MNIST/ytrain.npy')
     10 print(f"MNIST data shape (records,pixels): {X.shape}")

File c:\Users\senna\AppData\Local\Programs\Python\Python313\Lib\site-packages\numpy\lib\_npyio_impl.py:454, in load(file, mmap_mode, allow_pickle, fix_imports, encoding, max_header_size)
    452     own_fid = False
    453 else:
--> 454     fid = stack.enter_context(open(os.fspath(file), "rb"))
    455     own_fid = True
    457 # Code to distinguish from NumPy binary files and pickles.

FileNotFoundError: [Errno 2] No such file or directory: 'datasets/MNIST/xtrain.npy'

! pip install numpy IPython

# import numpy and IPython libraries
# define variables

import numpy as np
from IPython.display import Audio, display # for creating sliders
digits = "1234567890" 
rate = 44100 # audio frequency rate

#function to assign DTMF (dual-tone multi-frequency) frequencies to digits

def DTMF_tone(digit,duration,rate,amplitude):
    frequencies = {
        '1':(697,1209),'2':(697,1336),'3':(697,1477),
        '4':(770,1209),'5':(770,1336),'6':(770,1477),
        '7':(852,1209),'8':(852,1336),'9':(852,1477),
        '*':(941,1209),'0':(941,1336),'#':(941,1477)} #varible 'frequencies' assigned key-pair tuples of frequency pairs
    low,high = frequencies[digit] #unpacks tuples into 2 variables
    t = np.linspace(0,duration,int(rate*duration),endpoint=False) #create a time-axis from 0 to duration...rate=sample rate, duration=seconds of audio, int(rate*duration)=number of samples
    tone = amplitude*(np.sin(2*np.pi*low*t)+np.sin(2*np.pi*high*t)) #generate a sound wave...assign to tone variable
    return tone

#generate audio tone function 

def generate_DTMF(digits,duration=0.2,silence=0.1,rate=44100,amplitude=0.5):
    data = np.array([]) #create an array called data
    for digit in digits:
        tone = DTMF_tone(digit,duration,rate,amplitude) #call the DTMF_tone function
        silence = np.zeros(int(rate*silence)) #generate silent pauses...ChatGPT suggested replacing Nei's use of 'duration' with 'silence'
        data = np.concatenate((data,tone,silence)) #concaternate tone and silence
    return data

data = generate_DTMF(digits,rate=rate) #call the generate_DTMF function
data = data/np.max(np.abs(data))*(2**15-1) #rescales audio from floating-point waveform to 16-bit integer amplitude range...normalizing with max amp at 1.0. 2**15-1=32767 or max value for 16-bit need by .WAV
data = data.astype(np.int16) #converts floating-point numbers (dtype=float64) into 16-bit signed integers (dtype=int16)
display(Audio(data,rate=rate)) #sends waveform to Jupyter Notebook built-in audio player

#draw 2 plots

import matplotlib.pyplot as plt
plt.plot(data, color='pink') #data plot
plt.title("audio")
plt.show()
plt.plot(data[24000:25000],color='cyan') #waveform plot
plt.title("waveform")
plt.show()

#FFT Plotting

#Import libraries
import matplotlib.pyplot as plt
import numpy as np

#Fast Fourier Transformation calculations
fft = np.fft.fft(data) #computes FFT from audio waveform data
frequencies = np.fft.fftfreq(len(data),d=1/rate) #generates the frequency axis for plotting the FFT

#plot calculated results
plt.plot(frequencies,abs(fft),color='green')
plt.xlim(0,2000)
plt.title('FFT')
plt.xlabel('frequency (Hz)')
plt.ylabel('magnitude')
plt.show()

#plot a spectogram

#import libraries
import matplotlib.pyplot as plt
import numpy as np

#plot the frequencies as a spectogram
plt.specgram(data,Fs=rate,scale='linear',cmap='viridis') #the spectogram command...i changed the color map to 'viridis'
plt.ylim(500,8000)
plt.title("spectrogram")
plt.xlabel('time (s)')
plt.ylabel('frequency (Hz)')
plt.ylim(0,2000)
plt.show()

Research > Transforms¶

Transforms > Key Topics¶

Principal Components Analysis (PCA)¶

Independent Component Analysis (ICA)¶

Time Series¶

Sonification¶

Fourier Fast Transform¶

Spectogram¶

Wavelets¶

Filters¶

Compressed Sensing¶

References¶