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 = [1,2] # 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 = {} # 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 transforms = {d:[] for d in digits} mean_transforms = {d:[] for d in digits} for d in digits: for ind in ix_train: transforms[d].append(np.fft.fft(signals[d][ind], n = N)) for d in digits: for i in range(80): transforms[d][i] = transforms[d][i][:ix_cut] for d in digits: mean_transforms[d] = np.sum(np.abs(transforms[d]), axis = 0)/80 mean_transforms[d] /= np.linalg.norm(mean_transforms[d])

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

# Code Solution to Q2 here avg_spec_mag = {d:[] for d in digits} for d in digits: avg_spec_mag[d] = np.sum(np.abs(transforms[d]), axis = 0)/80 plt.title("Avg. Spectral Magnitude d="+ str(d)) plt.xlabel("Frequency (Hz)") plt.ylabel("Magnitude") plt.plot(np.fft.fftfreq(N, Ts)[:ix_cut],avg_spec_mag[d]) plt.show()

# classifier function # receives a vector, computes the product with average digits, and returns the max inner product # Input: sample x (vector) def mean_classifier(x): # Code Q3a Here xft = np.fft.fft(x)[:ix_cut] max_similarity = 0 highest = 0 for d in digits: similarity = np.inner(np.abs(xft), np.abs(mean_transforms[d])) if similarity > max_similarity: max_similarity = similarity highest = d return highest

# Write anser for Q3b here #The classifier performs pretty poorly, categorizing only about 1/4 of samples correctly, a lower accuracy than guessing at random.

# Code 3b Here tests = 0 correct = 0 for d in digits: for ind in ix_test: if mean_classifier(signals[d][ind]) == d: correct += 1 tests += 1 print(correct/tests)

# Write answer for Q4 here #The accuracy is now very close to the accuracy I would predict had classifications been given at random.

# Code Q4 here # 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]]) transforms = {d:[] for d in digits} mean_transforms = {d:[] for d in digits} for d in digits: for ind in ix_train: transforms[d].append(np.fft.fft(signals[d][ind], n = N)) for d in digits: for i in range(80): transforms[d][i] = transforms[d][i][:ix_cut] for d in digits: mean_transforms[d] = np.sum(np.abs(transforms[d]), axis = 0)/80 mean_transforms[d] /= np.linalg.norm(mean_transforms[d]) tests = 0 correct = 0 for d in digits: for ind in ix_test: if mean_classifier(signals[d][ind]) == d: correct += 1 tests += 1 print(correct/tests)