Elec 484. Assignment 4

Transcription

1 Elec 484 Assignment 4 Matthew Pierce V

2 Part 1 Implement a limiter using the ideas in the text Figures 5.3 and 5.8 and test it on two carefully chosen sound files (e.g. voice, drums). Adjust the parameters so that the limiting effect can be clearly heard. Clearly document the algorithm and your code, and comment on when and how the limiter is working. Plot the static gain f(n) and dynamic gain g(n), along with the input waveform, level measurement and output waveform. Post the input and output sound files, software and text file on your website. The following Matlab function takes an audio file and runs it through a limiter with various function parameters (this program can also be found on the website): % A limiter function which takes in an audio file and limiting parameters % and ouputs the limited audio signal function y = limiter(in_file, out_file, LT, AT, RT) % Read in the audio file [x, f_s, bps] = wavread(in_file); % Set delay value and the limiter slope D = 1; LS = 1; % Initialize the envelope, static gain, dynamic gain, and output signals x_peak = zeros(1, length(x)); x_peak(1) = AT*abs(x(1)); f = zeros(1, length(x)); g = zeros(1, length(x)); y = zeros(1, length(x)); for n=2:1:length(x) % Get the peak values (signal envelope) x_peak(n) = (1 - AT - RT)*x_peak(n-1) + AT*abs(x(n)); % Do linear/log conversion X = 20*log10(x_peak(n)); % Check the value against the threshold if X > LT % Obtain the static gain value F = -LS*(X - LT); % Do log/linear conversion f(n) = 10^(F/20); else % If it's less than the threshold, take the input signal f(n) = x(n);

3 end end end % Obtain the dynamic gain value g(n) = (1-AT)*g(n-1) + AT*f(n); % Get the output samples y(n) = x(n-d)*g(n); % Plot each of the vectors found above n = 1:length(x); subplot(3, 2, 1); plot(n, x(n)); title('input signal'); xlabel('time'), ylabel('amplitude'); subplot(3, 2, 2); plot(n, x_peak(n)); title('envelope detector'); xlabel('time'), ylabel('peak'); subplot(3, 2, 3); plot(n, f(n)); title('static gain f(n)'); xlabel('time'), ylabel('gain'); subplot(3, 2, 4); plot(n, g(n)); title('dynamic gain g(n)'); xlabel('time'), ylabel('gain'); subplot(3, 2, 5); plot(n, y(n)); title('output signal'); xlabel('time'), ylabel('amplitude'); % Write the limited output file to a new wav wavwrite(y, f_s, bps, out_file); Process:

4 I ran the limiter function with two specifically chosen audio files. The first, claire_oubli_voix.wav, was chosen because it contains vocals and some ambience. The second, beat.wav is a percussive track. The settings for each track were as follows; Input Track Limiter Attack Release Output Track Threshold Time Time claire_oubli_voix.wav limit_claire.wav beat.wav limit_beat.wav All tracks can be found on the website and listened to for comparison. The output plots for each track s input, peak values, static gain, dynamic gain, and output, are as follows: limit_claire.wav Matlab plots

5 limit_beat.wav Matlab plots Discussion: The limiter filters out all gain values above the threshold value, which has been normalized between 0 and 1 (it is not a hard limiter, however, and uses a linear slope while leveling). The output plot (plot 5) shows the limited audio, and a we can see that a lower threshold value allows more output through, which is evident when comparing limit_claire.wav (threshold = 0.9) to limit_beat.wav (threshold = 0.5). Part 2 Repeat Part 1 for a compressor/expander using the ideas in the text. The following Matlab function takes an audio file and runs it through the compressor/expander with various function parameters (this program can also be found on the website): % A compressor/expander function which takes in an audio file and required % parameters and ouputs the compressed/expanded audio signal function y = compressor(in_file, out_file, thresh, TAV, R) % Read in the audio file [x, f_s, bps] = wavread(in_file);

6 % Set the slope based on the R value and set delay slope = 1-1/R; D = 1; % Initialize the envelope, static gain, dynamic gain, and output signals x_rms = zeros(1, length(x)); x_rms(1) = TAV*(x(1)^2); f = zeros(1, length(x)); g = zeros(1, length(x)); y = zeros(1, length(x)); for n=2:1:length(x) end % Get the rms values (signal envelope) x_rms(n) = (1 - TAV)*x_rms(n-1) + TAV*(x(n)^2); % Do linear/log conversion X = 20*log10(x_rms(n)); % Obtain the static gain value F = -slope*abs((x - thresh)); % Do log/linear conversion f(n) = 10^(F/20); % Obtain the dynamic gain value g(n) = (1-0.5)*g(n-1) + 0.5*f(n); % Get the output samples y(n) = x(n-d)*g(n); % Plot each of the vectors found above n = 1:length(x); subplot(3, 2, 1); plot(n, x(n)); title('input signal'); xlabel('time'), ylabel('amplitude'); subplot(3, 2, 2); plot(n, x_rms(n)); title('envelope detector'); xlabel('time'), ylabel('average');

7 end subplot(3, 2, 3); plot(n, f(n)); title('static gain f(n)'); xlabel('time'), ylabel('gain'); subplot(3, 2, 4); plot(n, g(n)); title('dynamic gain g(n)'); xlabel('time'), ylabel('gain'); subplot(3, 2, 5); plot(n, y(n)); title('output signal'); xlabel('time'), ylabel('amplitude'); % Write the compressed output file to a new wav wavwrite(y, f_s, bps, out_file); Process: I ran the compressor/expander function with the two audio files from part 1. I created a compressed and expanded audio file for each of the two files for a total of four. The parameters of the four files are as follows: Input Track Threshold TAV Ratio (R) Output Track claire_oubli_voix.wav compress_claire.wav beat.wav compress_beat.wav claire_oubli_voix.wav expand_claire.wav beat.wav expand_beat.wav All tracks can be found on the website and listened to for comparison. The output plots for compress_claire.wav are as follows:

8 compress_claire.wav Matlab plots Discussion: The filter acts as a compressor when the static curve ratio R is a value greater than 1 (an acute angle compared with the input gain level). When the value is between 0 and 1 the filter acts as an expander (an obtuse angle compared with the input gain level). The compressed audio gives a smaller dynamic range from the input audio, while retaining the basic shape. The expanded audio makes everything over the threshold volume more exaggerated; for instance, the peak drum hits in beat.wav become much bigger and sound much longer (also creating a smearing effect). Part 3 Repeat Part 1 for a noise gate, using the ideas in the text. The following Matlab function takes an audio file and runs it through the noise gate with various function parameters (this program can also be found on the website): % A noise gate function which takes in an audio file and required % parameters and ouputs the gated audio signal function y = noise_gate(in_file, out_file, NT, TAV) % Read in the audio file [x, f_s, bps] = wavread(in_file);

9 % Set the Ratio (R), Delay (D) and k (gain smooting) values R = 0; D = 1; k = 0.5; % Initialize the envelope, static gain, dynamic gain, and output signals x_rms = zeros(1, length(x)); x_rms(1) = TAV*(x(1)^2); f = zeros(1, length(x)); g = zeros(1, length(x)); y = zeros(1, length(x)); for n=2:1:length(x) end % Get the rms values (signal envelope) x_rms(n) = (1 - TAV)*x_rms(n-1) + TAV*(x(n)^2); % Get the threshold value x_d = -(1-1/R)*(x_rms(n) - NT); % Check the value against 0 if x_d > 0 % If the input is above the threshold let it through f(n) = 1; else % If not remove the signal f(n) = 0; end % Obtain the dynamic gain value g(n) = (1-k)*g(n-1) + k*f(n); % Get the output samples y(n) = x(n-d)*g(n); % Plot each of the vectors found above n = 1:length(x); subplot(3, 2, 1); plot(n, x(n)); title('input signal'); xlabel('time'), ylabel('amplitude'); subplot(3, 2, 2);

10 end plot(n, x_rms(n)); title('envelope detector'); xlabel('time'), ylabel('average'); subplot(3, 2, 3); plot(n, f(n)); title('static gain f(n)'); xlabel('time'), ylabel('gain'); subplot(3, 2, 4); plot(n, g(n)); title('dynamic gain g(n)'); xlabel('time'), ylabel('gain'); subplot(3, 2, 5); plot(n, y(n)); title('output signal'); xlabel('time'), ylabel('amplitude'); % Write the gated output file to a new wav wavwrite(y, f_s, bps, out_file); Process: I ran the noise gate function with the two audio files from part 1. I created a gated output file for each input file. The settings for each track were as follows; Input Track Threshold (NT) TAV Output Track claire_oubli_voix.wav gate_claire.wav beat.wav gate_beat.wav All tracks can be found on the website and listened to for comparison. The output plots for each track s input, peak values, static gain, dynamic gain, and output, are as follows:

11 gate_claire.wav Matlab plots gate_beat.wav Matlab plots

12 Discussion: From the output plots for both input files we can see that the noise gate acts as expected, in that it maintains the same shape of the input at points where the gain is above the threshold and is zero otherwise. Using a much smaller NT value for the vocal audio, one can hear how it acts more as a low-level noise removal system (like its name suggests) while keeping most of the vocal line intact. Using a higher NT value, as I did on the drum track, the result is much more dramatic, as only the very high values get through and everything else is silent. Some noise is present due to the rapid transition between silences and high-gain output. A more robust system would work better in practice. Part 4 Repeat the vibrato exercise (Assignment 3 part 4) using a real instrument such as a trumpet or flute. Post both the original sound file (with no vibrato) and the processed file. Choose the vibrato parameters (depth, rate) to yield a pleasing sound. The Matlab program below was used to create the vibrato. It is a modified version of the vibrato program from assignment 3. The only change is that it implements allpass interpolation rather than linear interpolation for a more robust filter (this software is also available from the website): % Add a vibrato effect to an audio vector and write to a new wav file function y = vibrato(wav_src, wav_out, mod, width) % Read in the audio vector and get sampling rate and bps [x, f_s, bps] = wavread(wav_src); % Set the "basic" delay and find all variables in samples as well delay = width; sample_delay = round(delay*f_s); sample_width = round(width*f_s); sample_mod = mod/f_s; ya_alt = 0; % Get the entire length of the delay src_length = length(x); total_delay = 2 + sample_delay + sample_width*2; % Allocate memory for the delay line and output vector delay_line = zeros(total_delay, 1); y = zeros(size(x)); for n=1:src_length-1 % Create the delay line oscillator osc = sin(sample_mod*2*pi*n);

13 end end % Set the z value using the oscillator and subtract from its floor z = 1 + sample_delay + sample_width*osc; i = floor(z); frac = z - i; % New fractional delay % Set the delay line delay_line = [x(n);delay_line(1:total_delay-1)]; % Do Allpass interpolation y(n,1) = (delay_line(i+1)+(1-frac)*delay_line(i)-(1-frac)*ya_alt); ya_alt = y(n,1); % Write the output vector to file wavwrite(y, f_s, bps, wav_out); Process: I found a single, unwavering trumpet tone from ( C_trumpet_E4.wav ). I filtered this file with the vibrato program a number of times, testing various mod and width values to listen to their output. I compared these output to various other vibrato sounds that I downloaded. The settings I finally chose, which are present in the output file vib_trumpet.wav are as follows: Mod = 2.4Hz Width = 0.001s Discussion: Both the original trumpet sound and vib_trumpet.wav are available on the website for comparison. I found that with a relatively fast oscillation, but a small width, I was able to achieve the most realistic sounding vibrato (based on my other listenings).