deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 2e2099f..b050e2b 100644  --- a/untitled.tex  +++ b/untitled.tex 
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\textit{Oh, an empty article!}   You can get started by \textbf{double clicking} this text block and begin editing. You can also click the \textbf{Insert} button below to add new block elements. Or you can \textbf{drag and drop an image} right onto this text. Happy writing!  \begin{lstlisting}[language=MATLAB]  Wc = 0.2 * pi; % passing frequency  L = 51; % length of filter (inversely correlated with bandwidth)  n = 0:L-1;  ww = 0:pi/1000:pi;  bb = cos(Wc * n); % coefficients (extracted from given h[n])  HH = freqz(bb, 1 ,ww); % frequency response  subplot(211)  plot(ww, abs(HH))  title('Frequency Response')  xlabel('Frequency')  ylabel('Amplitude')  max_value = max(abs(HH)); % get the highest peak value of the frequency response  bb2 = 1 / max_value * bb; % normalize the coefficients  HH2 = freqz(bb2,1,ww);  subplot(212)  plot(ww, abs(HH2))  title('Normalized Frequency Response')  xlabel('Frequency')  ylabel('Amplitude')  passband = find(abs(HH2) >= 0.707); % fetches the passing frequencies  lower_freq = ww(passband(1)); % gets the lower 3dB freq value  upper_freq = ww(passband(length(passband))); % upper 3dB freq value  BW = abs(ww(passband(1)) - ww(passband(length(passband)))); % bandwidth  samp_rate = 8000; % 8000Hz  lower_analog = lower_freq * 8000 / (2 * pi); % 736 Hz  upper_analog = upper_freq * 8000 / (2 * pi); % 868 Hz  \end{lstlisting}.