import numpy as np import numpy.random as random from numpy.fft import fft from scipy.io import wavfile from scipy import stats 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 but Aneel said to wait until Q4. # 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 = {d:[] for d in digits} # 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 transform_norms = {d:[] for d in digits} x_bar = {d:[] for d in digits} for d in digits: for index in ix_train: transforms[d].append(fft(signals[d][index], n=N)[:ix_cut+1]) transform_norms[d] = np.abs(transforms[d]) for k in range(ix_cut+1): running_sum = 0 for sample in transform_norms[d]: running_sum += sample[k] x_bar[d].append(running_sum/len(ix_train)) for k in range(ix_cut+1): mean_transforms[d].append(x_bar[d][k]/np.linalg.norm(x_bar[d])) assert(len(mean_transforms[d]) == ix_cut+1)

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

# Code Solution to Q2 here xf = np.linspace(0, 1500, ix_cut+1) for d in digits: yf = mean_transforms[d] plt.plot(xf, yf) plt.xlabel("Hz") 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 X = fft(x, n=N)[:ix_cut+1] max_digit = 0 max_sum = 0 for d in digits: running_sum = 0 for k in range(ix_cut+1): running_sum += abs(X[k]) * abs(mean_transforms[d][k]) if(max_sum == 0): max_sum = running_sum max_digit = d elif(running_sum > max_sum): max_sum = running_sum max_digit = d return max_digit

# Write anser for Q3b here # The test did swimmingly. It was about 90% accurate with just the two choices (0 or 1)

# Code 3b Here def test(): correct = 0 total = 0 for d in digits: d_correct = 0 d_total = 0 for index in ix_test: guess = mean_classifier(signals[d][index]) if (guess == d): correct += 1 d_correct += 1 d_total += 1 total += 1 print("Digit " + str(d) + " got " + str(d_correct) + "/" + str(d_total) + " for a score of " + str(np.round(d_correct/d_total * 100)) + "%.") print("Overall: " + str(correct) + "/" + str(total) + " for a score of " + str(np.round(correct/total * 100)) + "%.") return test()

# Write answer for Q4 here # The accuracy here got quite a bit worse (down to about 60 or 70%) but is still pretty good considering guessing we would only expect an average of 10% correct.

# Code Q4 here 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 but Aneel said to wait until Q4. # 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 = {d:[] for d in digits} # 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 transform_norms = {d:[] for d in digits} x_bar = {d:[] for d in digits} for d in digits: for index in ix_train: transforms[d].append(fft(signals[d][index], n=N)[:ix_cut+1]) transform_norms[d] = np.abs(transforms[d]) for k in range(ix_cut+1): running_sum = 0 for sample in transform_norms[d]: running_sum += sample[k] x_bar[d].append(running_sum/80) for k in range(ix_cut+1): mean_transforms[d].append(x_bar[d][k]/np.linalg.norm(x_bar[d])) assert(len(mean_transforms[d]) == ix_cut+1) test()

# Assuming I implemented it correctly (which is admittedly a pretty big if), this nearest neigbor approximation w/ N=5 doesn't seem to do # better than the original classifier, takes considerably longer to run, and is biased heavily towards certain numbers (0,5, and 6) though this could easily # be because I implemented it incorrectly. In theory, one could set up a function to loop over values of N to find the optimal one fairly easily given # how I wrote the function, but seeing as the test for individual values of N is taking upwards of 10 minutes to run, I won't do this. # Code Q5 here def mean_classifier(x, num_neighbors): max_sums = [] max_digits = [] X = fft(x, n=N)[:ix_cut+1] for d in digits: for transform in transforms[d]: running_sum = 0 for k in range(ix_cut+1): running_sum += abs(X[k]) * abs(transform[k]) for i in range(len(max_sums)): if(max_sums[i] > running_sum): max_sums.insert(i, running_sum) max_digits.insert(i, d) break if(i == len(max_sums)-1): max_sums.insert(i+1, running_sum) max_digits.insert(i+1, d) break # need to be sure we can get started if(len(max_sums) == 0): max_sums.insert(0, running_sum) max_digits.insert(0, d) if(len(max_sums) > num_neighbors): max_sums.pop(0) max_digits.pop(0) return stats.mode(max_digits)[0][0] def test(): correct = 0 total = 0 for d in digits: d_correct = 0 d_total = 0 for index in ix_test: guess = mean_classifier(signals[d][index], 5) if (guess == d): correct += 1 d_correct += 1 d_total += 1 total += 1 print("Digit " + str(d) + " got " + str(d_correct) + "/" + str(d_total) + " for a score of " + str(np.round(d_correct/d_total * 100)) + "%.") print("Overall: " + str(correct) + "/" + str(total) + " for a score of " + str(np.round(correct/total * 100)) + "%.") return test()

# Test block for fun test purposes num_neighbors = 3 running_sums = [6,5,4,3,2,1] max_sums = [] max_digits = [] d = 0 for running_sum in running_sums: for i in range(len(max_sums)): if(max_sums[i] > running_sum): max_sums.insert(i, running_sum) max_digits.insert(i, d) break if(i == len(max_sums)-1): max_sums.insert(i+1, running_sum) max_digits.insert(i+1, d) break # need to be sure we can get started if(len(max_sums) == 0): max_sums.insert(0, running_sum) max_digits.insert(0, d) if(len(max_sums) > num_neighbors): max_sums.pop(0) max_digits.pop(0) d += 1 print(max_sums) print(max_digits)