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COS 126 Digital Signal Processing

Programming Assignment Due: Monday

Write a program to generate sound waves, apply an echo filter to an MP3 file,and plot the waves.

A crash course in sound.A music note can be characterized by its frequency of oscillation.For example, the music note concert Ais a sine wave repeated 440 times per second (440 Hz);the note C is a sine wave repeated approximately523.25 times per second. We amplify the signal to an audible level by multiplying it by a constant, say 0.8.Below are pictures of an A and a C with duration 15 milliseconds and amplitude 0.8.The picture for A consists of 0.015 × 440 = 6.6 sine waves.

Below is a table containing the frequencies in Hertz of all twelvemusical notes in the fifth octave. The ratio between the frequency ofsuccessive notes is the 12th root of two (1.05946).An octave is a doubling or halving of the frequency.For reference, the normal range of human hearing is between20 and 20,000 Hz.

A	A#	B	C	C#	D	D#	E	F	F#	G	G#	A
440.00	466.16	493.88	523.25	554.37	587.33	622.25	659.26	698.46	739.99	783.99	830.61	880.00

Digital audio.Digital audio is produced by sampling theinstantaneous amplitude of the continuous sound wave many times a second. Eachsample is a real number between -1 and +1 that represents theamplitude of the sound wave at a particular instant in time. The sampling rateis the number of samples taken per second. Audio from CDs typically uses a samplingrate of 44,100 and two channels (left and right). Below is a picture of an A usinga sampling rate of 44,100 and a duration of approximately 1/440th of a second.The figure below displays every 10th sample.

The following arrays contain the values representing the height of the waveabove, at a sampling rate of 44,100:

Sample i is given by .8 sin(2 π * 440 * i / 44,100), and we've roundedthe numbers towards zero.

Sound synthesis. Your first task is to create a data type Wave to store and manipulate sound wave samples so that the programA.javabelow plays concert A for 2 seconds with maximum amplitude 0.8.Similarly, FurElise.javaplays the first nine notes of Fur Elise.

For this part of the assignment, you need to write a data type Wave to initialize and access the data.Implement the samples for the left and right channels using two arrays of typedouble[].First, implement the constructor

It should create a new Wave object that represents a sine wave of the specified number of Hz thatis sampled 44,100 times per second over the specified number of seconds. UseMath.sin() and Math.PI to initialize the left and right channels.Initialize both arrays with the same values so that the note will play in both speakers.Next, implement a methodthat sends the Wave data to the sound card. Use thestatic library method StdPlayer.playWave(left, right),which takes as input two double arrays representingthe left and the right channel.

Compilation and execution.In order to play music on your computer, you will need to use a specialized library.Download the filestdplayer.jar andput in your working directory. A .jar file is an archive like a .zip file, butthere is no need to unzip it or peek inside this one unless youare extremely curious.This library is a modified version of theJavaLayer 1.0 MP3 Player.(As per the GPL license, the jar file contains the original JavaLayerlibrary and our modified source code.)To test the library on your system, use theJavaLayer Player that comes with stdplayer.jar by typing the following command:

You can replacefelten.mp3with the name of another MP3 file in the working directory.In order to use the library in your Java program, you must putthe following import statement at the beginning:You also need to tell Java where to find the libraryby compiling and executing with the following commands:

Compile	Execute
OS X / Linux	javac -cp .:stdplayer.jar A.java	java -cp .:stdplayer.jar A
Windows	javac -cp .;stdplayer.jar A.java	java -cp .;stdplayer.jar A

Creating a tune.Now that you can play single notes, your next challenge is to play several notes at once, for example, to play a chord.To accomplish this, first add a new constructor

to Wave.java that takes two double arrays as arguments andinitializes a new Wave object with the given data.Now, to create a chord, you can create individual notes and combine themtogether by writing a method:so that a.plus(b) returns the sum of a and

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b.To add two Waves, add the corresponding array entries for the left and right channels, element-by-element.Test your data type by using the programStairwayToHeaven.java,which is the beginning of the famous Led Zeppelin tune.Note the fifth wave played is created by the following sequence of statements:

Playing an MP3 file.The programMP3Player.javadecodes the MP3 file specified by the command line input and plays it.Assuming that you implemented the Wave API above,there is no need to write any code for this part(but you should test it and enjoy).Compile and execute the program with the following commands.

The key part of the code is the following loop. It will be useful forthe remaining parts of the assignment.This program uses three new methods from the StdPlayer libraryto decode data from an MP3 file.The

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String argument to the function StdPlayer.open() specifies which MP3file to use.The function StdPlayer.getLeftChannel() returns an array of 1,152 real numbers between -1 and +1 that are the samples of the music intendedfor the left speaker.The function StdPlayer.getRightChannel() is analogous.

Echo filter. Now that you can decode and play MP3 files, you're ready to modify the data andchange the characteristics of the sound waves.An analog filter accomplishes this by manipulating the electrical signals thatrepresent the sound wave;a digital filter does this by manipulating the digital data thatrepresents that Wave. Your task is to write a programEchoFilter.java that implements a digital echo filter.An echo filter of delay 10 is a filter that adds an echo to the soundby adding the sound wave at time t - 10 to the one at time t.To create this effect, maintain an array of the past 10 Wave objectsand add the Wave that was originally read10 waves ago to the current Wave.The echo filter is a client program and should be written entirely in EchoFilter.java.To test the filter, you can usepearlharbor.mp3which contains the speech President Roosevelt delivered after the attack on Pearl Harbor.

Plotting the waves.The final part of the assignmentis to write a program MP3Viewer.java that takes the name of an MP3 fileas a command line argument and animates both stereo channels.This program is not supposed to play the MP3 file,only to animate the sound waves. Add the following method to Wave.javato plot the left channel on the top half of the screen, and the rightchannel on the bottom half:

Deliverables.Submit Wave.java, EchoFilter.java, and MP3Viewer.javaalong with a readme.txt file.

Challenge for the bored.Write a program MP3Visualizer.java that plays the MP3 file and simultaneously displays a cool effect based on the raw data. To keep the music and animation smooth,you may need to tweak a few parameters. For example, adjust the delay in themethod StdDraw.show() to keep the wave from scrolling by too fast. Also,try plotting every other wave if your computer is too slow.

This assignment was created by Bradley Zankel and Kevin Wayne.