diff --git a/FT_times.m b/FT_times.m
index d18fccf..46402f4 100644
--- a/FT_times.m
+++ b/FT_times.m
@@ -16,4 +16,6 @@ for j = 1:item_num
 endfor
 
 printf('Average DFT time: %d \n', mean(times(1:item_num, 1)))
-printf('Average FFT time: %d \n', mean(times(1:item_num, 2)))
\ No newline at end of file
+printf('Standard deviation of DFT time: %d \n', std(times(1:item_num, 1)))
+printf('Average FFT time: %d \n', mean(times(1:item_num, 2)))
+printf('Standard deviation of FFT time: %d \n', std(times(1:item_num, 2)))
\ No newline at end of file
diff --git a/one.png b/one.png
new file mode 100644
index 0000000..1cbb2e5
Binary files /dev/null and b/one.png differ
diff --git a/sound/output.wav b/sound/output.wav
index b00d743..ce603f2 100644
Binary files a/sound/output.wav and b/sound/output.wav differ
diff --git a/spectral_analysis.m b/spectral_analysis.m
index c79bb80..8963dd3 100644
--- a/spectral_analysis.m
+++ b/spectral_analysis.m
@@ -3,7 +3,44 @@ close all
 clc
 
 [y, fs] = audioread("sound/modulator22.wav");
-%frequencySpectrum(y, fs, 0); %true does FFT, false DFT
-step_size = 5; %ms
-window_size = 30;%ms
-spectrogram(y, fs, step_size, window_size)
\ No newline at end of file
+ranges = [17000, 20000; 29000, 37000; 41000, 46000];
+one = y(ranges(1,1):ranges(1,2));
+two = y(ranges(2,1):ranges(2,2));
+three = y(ranges(3,1):ranges(3,2));
+
+word = one;
+
+n = length(word);   
+f = (0:n-1)*(fs/n);
+f1 = 0;%Hz
+f2 = 4000;%Hz
+idx = find(f >= f1 & f <= f2); %define the index of the freq range
+f = f(idx);
+y = fft(word, n);% compute DFT of input signal
+power = abs(y).^2/n;
+power = power(idx);
+[val, ind] = max(power);
+
+%lowpass for the formant
+
+Fc = 2000; % define the cutoff frequency of the low-pass filter
+[b, a] = butter(6, Fc/(fs/2), 'low'); % design a 4th-order Butterworth low-pass filter
+Pxx_filt = filter(b, a, power); % apply the filter to the power spectrum
+length(Pxx_filt)
+length(f)
+
+
+figure;
+
+subplot(1,2,1) % time plot 
+plot(0:1/fs:(length(word)-1)/fs,word);
+xlabel('Time (s)');
+ylabel('Amplitude (a.u.)');
+
+subplot(1,2,2) % freq range plot 
+plot(f,10*log10(power/power(ind))); hold on;
+plot(f, 10*log10(Pxx_filt), 'r');
+xlabel('Frequency (Hz)')
+ylabel('Power (dB)')
+
+
diff --git a/spectrogram_analysis.m b/spectrogram_analysis.m
new file mode 100644
index 0000000..8d0ba45
--- /dev/null
+++ b/spectrogram_analysis.m
@@ -0,0 +1,8 @@
+clear all
+close all
+clc
+
+[y, fs] = audioread("sound/modulator22.wav");
+step_size = 5; %ms
+window_size = 30;%ms, ideal value 25
+spectrogram(y, fs, step_size, window_size)
\ No newline at end of file
diff --git a/three.png b/three.png
new file mode 100644
index 0000000..e43cf70
Binary files /dev/null and b/three.png differ
diff --git a/two.png b/two.png
new file mode 100644
index 0000000..acd8f7b
Binary files /dev/null and b/two.png differ