import numpy as np import numpy.random as random from numpy.fft import fft from scipy.io import wavfile import matplotlib.pyplot as plt import seaborn as sns import os %matplotlib inline sns.set() sns.set(font_scale=1.5)

data_dir = './recordings/' # determine digits of interest (0 to 9) digits = [0,1,2,3,4,5,6,7,8,9] # change here to load more digits # dictionary that will store our values signals = {d:[] for d in digits} file_names = {d:[] for d in digits} # import files for filename in os.listdir(data_dir): # iterate over digits for d in digits: if filename.startswith(str(d)+'_'): wav = wavfile.read(data_dir+filename)[1] if len(wav.shape)<2: signals[d].append(wav) file_names[d].append(filename) # find maximum of vector length N = max([len(v) for d in digits for v in signals[d]])

# next we split our dataset in train and test # we will use a 80/20 random split. # create train/test split ix = np.arange(100) random.shuffle(ix) # select train entries ix_train = ix[:80] #select test entries ix_test = ix[80:]

# next we compute the average spectrum of each spoken digit in the training set. # we will consider a window up to 1.5 KHz # sampling rate is 8kHz Ts = 1.0/8000 ix_cut = int(np.ceil(1500*Ts*N)) # initialize dictionary for storing transforms transforms = {d:[] for d in digits} # initialize dictionary for storing mean transforms mean_transforms = {} # compute mean transform of each digit and in the training set. # Make sure to only keep the spectrum up to 1.5kHz

# Code Solution to Q1 Here for d in digits: for i in ix_train: yt = signals[d][i] yf = fft(yt) if len(yf) < ix_cut: yf = np.append(yf,np.zeros(ix_cut-len(yf))) transforms[d].append(yf[:ix_cut]) Xd = (1/len(ix_train)) * np.sum(np.abs(transforms[d]),axis=0) norm = np.sqrt(np.sum(np.abs(Xd**2),axis=0)) mean_transforms[d] = Xd/norm

# In this next part, plot the average spectral magnitude of each digit.

# Code Solution to Q2 here plt.figure(figsize=(15,5)) for d in digits: xf = np.linspace(0.0,1500, int(ix_cut)) plt.plot(xf, 2.0/ix_cut * np.abs(mean_transforms[d][0:int(ix_cut)]),label='%s' % d) plt.xlabel("Hz") plt.ylabel("Average spectral magnitude") plt.legend() plt.show()

# classifier function # receives a vector, computes the product with average digits, and returns the max inner product # Input: sample x (vector)

# Code Q3a Here def mean_classifier(x): p_max = 0 d_max = 1 for d in digits: # Calculate p(X,Xd) p = np.sum(np.abs(x) * np.abs(mean_transforms[d])) if p > p_max: d_max = d p_max = p return d_max

# Write answer for Q3b here # Step 1: compute mean transforms of test set signals # Step 2: use mean classifier to compare training mean transform with test mean transform

# Code 3b Here test_transforms = {d:[] for d in digits} test_mean_transforms = {} for d in [1,2]: correct = 0 for i in ix_test: yt = signals[d][i] yf = fft(yt)[:ix_cut] if len(yf) < ix_cut: yf = np.append(yf,np.zeros(ix_cut-len(yf))) class_d = mean_classifier(yf) if class_d == d: correct += 1 a = correct/len(ix_test) print(f'Accuracy for {d:d}: {a:.2f}') # Use mean_classifier to determine digit with highest similiarity

# Write answer for Q4 here # The accuracy would decrease because it has more spectral magnitude signals of each of the digits to compare with.

# Code Q4 here correct = 0 for d in digits: correct = 0 for i in ix_test: yt = signals[d][i] yf = fft(yt)[:ix_cut] if len(yf) < ix_cut: yf = np.append(yf,np.zeros(ix_cut-len(yf))) class_d = mean_classifier(yf) if class_d == d: correct += 1 a = correct/len(ix_test) print(f'Accuracy for {d:d}: {a:.2f}')