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Week 7 - Wednesday
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What did we talk about last time? Introduction to arrays Lab 6
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When you declare an array, you are only creating a variable that can hold an array At first, it holds nothing, also know as null To use it, you have to create an array, supplying a specific size: This code creates an array of 100 int s int[] list; list = new int[100]; int[] list; list = new int[100];
![ When you declare an array, you are only creating a variable that can hold an array At first, it holds nothing, also know as null To use it, you have to create an array, supplying a specific size: This code creates an array of 100 int s int[] list; list = new int[100]; int[] list; list = new int[100];](http://images.slideplayer.com./22/6415316/slides/slide_7.jpg " When you declare an array, you are only creating a variable that can hold an array At first, it holds nothing, also know as null To use it, you have to create an array, supplying a specific size: This code creates an array of 100 int s int[] list; list = new int[100]; int[] list; list = new int[100];")
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You can access an element of an array by indexing into it, using square brackets and a number Once you have indexed into an array, that variable behaves exactly like any other variable of that type You can read values from it and store values into it Indexing starts at 0 and stops at 1 less than the length list[9] = 142; System.out.println(list[9]); list[9] = 142; System.out.println(list[9]);
![ You can access an element of an array by indexing into it, using square brackets and a number Once you have indexed into an array, that variable behaves exactly like any other variable of that type You can read values from it and store values into it Indexing starts at 0 and stops at 1 less than the length list[9] = 142; System.out.println(list[9]); list[9] = 142; System.out.println(list[9]);](http://images.slideplayer.com./22/6415316/slides/slide_8.jpg " You can access an element of an array by indexing into it, using square brackets and a number Once you have indexed into an array, that variable behaves exactly like any other variable of that type You can read values from it and store values into it Indexing starts at 0 and stops at 1 less than the length list[9] = 142; System.out.println(list[9]); list[9] = 142; System.out.println(list[9]);")
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When you instantiate an array, you specify the length Sometimes (like in the case of args ) you are given an array of unknown length You can use its length member to find out int[] list = new int[42]; int size = list.length; System.out.println("List has " + size + " elements"); //prints 42 int[] list = new int[42]; int size = list.length; System.out.println("List has " + size + " elements"); //prints 42
![ When you instantiate an array, you specify the length Sometimes (like in the case of args ) you are given an array of unknown length You can use its length member to find out int[] list = new int[42]; int size = list.length; System.out.println( List has + size + elements ); //prints 42 int[] list = new int[42]; int size = list.length; System.out.println( List has + size + elements ); //prints 42](http://images.slideplayer.com./22/6415316/slides/slide_9.jpg " When you instantiate an array, you specify the length Sometimes (like in the case of args ) you are given an array of unknown length You can use its length member to find out int[] list = new int[42]; int size = list.length; System.out.println( List has + size + elements ); //prints 42 int[] list = new int[42]; int size = list.length; System.out.println( List has + size + elements ); //prints 42")
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Recently, we showed you how to add a set of numbers together as they were input by a user Although this is a useful technique, not every operation is possible We can find the sum or the average of the numbers because we only need to see the numbers once What operation needs to see the numbers more than once?
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Variance is a measurement of how spread out numbers are from their mean To calculate it, you have to calculate the mean first The formula is: Where N is the number of elements, x i is the i th element, and is the mean
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Given an array of doubles called numbers, here’s the code for finding their variance double average = 0; double variance = 0; double temp; for( int i = 0; i < numbers.length; i++ ) average += numbers[i]; average /= numbers.length; for( int i = 0; i < numbers.length; i++ ) { temp = numbers[i] – average; variance += temp*temp; } variance /= numbers.length; double average = 0; double variance = 0; double temp; for( int i = 0; i < numbers.length; i++ ) average += numbers[i]; average /= numbers.length; for( int i = 0; i < numbers.length; i++ ) { temp = numbers[i] – average; variance += temp*temp; } variance /= numbers.length;
![ Given an array of doubles called numbers, here’s the code for finding their variance double average = 0; double variance = 0; double temp; for( int i = 0; i < numbers.length; i++ ) average += numbers[i]; average /= numbers.length; for( int i = 0; i < numbers.length; i++ ) { temp = numbers[i] – average; variance += temp*temp; } variance /= numbers.length; double average = 0; double variance = 0; double temp; for( int i = 0; i < numbers.length; i++ ) average += numbers[i]; average /= numbers.length; for( int i = 0; i < numbers.length; i++ ) { temp = numbers[i] – average; variance += temp*temp; } variance /= numbers.length;](http://images.slideplayer.com./22/6415316/slides/slide_13.jpg " Given an array of doubles called numbers, here’s the code for finding their variance double average = 0; double variance = 0; double temp; for( int i = 0; i < numbers.length; i++ ) average += numbers[i]; average /= numbers.length; for( int i = 0; i < numbers.length; i++ ) { temp = numbers[i] – average; variance += temp*temp; } variance /= numbers.length; double average = 0; double variance = 0; double temp; for( int i = 0; i < numbers.length; i++ ) average += numbers[i]; average /= numbers.length; for( int i = 0; i < numbers.length; i++ ) { temp = numbers[i] – average; variance += temp*temp; } variance /= numbers.length;")
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We can represent a deck of cards as an array of 52 items One easy way is to make each item a String giving the name of the card We can extend last time's lab and store each of these names in an array
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Swapping the values of two variables is a fundamental operation in programming It is going to become more important in arrays because now the order of variables has become important The simplest way to swap two variables involves using a third variable as a temporary location
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Here is an example of swapping two String s indexed i and j in an array of String s called array int i = in.nextInt(); int j = in.nextInt(); int temp; temp = array[i]; array[i] = array[j]; array[j] = temp; int i = in.nextInt(); int j = in.nextInt(); int temp; temp = array[i]; array[i] = array[j]; array[j] = temp;
![ Here is an example of swapping two String s indexed i and j in an array of String s called array int i = in.nextInt(); int j = in.nextInt(); int temp; temp = array[i]; array[i] = array[j]; array[j] = temp; int i = in.nextInt(); int j = in.nextInt(); int temp; temp = array[i]; array[i] = array[j]; array[j] = temp;](http://images.slideplayer.com./22/6415316/slides/slide_16.jpg " Here is an example of swapping two String s indexed i and j in an array of String s called array int i = in.nextInt(); int j = in.nextInt(); int temp; temp = array[i]; array[i] = array[j]; array[j] = temp; int i = in.nextInt(); int j = in.nextInt(); int temp; temp = array[i]; array[i] = array[j]; array[j] = temp;")
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Using the swap code, we can do a random shuffling of a deck To do so, we go through each element of the array, and randomly swap it with any of the later elements for( int i = 0; i < n; i++ ) { exchange = i + (int)(Math.random() * (n - i)); temp = deck[i]; deck[i] = deck[exchange]; deck[exchange] = temp; } for( int i = 0; i < n; i++ ) { exchange = i + (int)(Math.random() * (n - i)); temp = deck[i]; deck[i] = deck[exchange]; deck[exchange] = temp; }
![ Using the swap code, we can do a random shuffling of a deck To do so, we go through each element of the array, and randomly swap it with any of the later elements for( int i = 0; i < n; i++ ) { exchange = i + (int)(Math.random() * (n - i)); temp = deck[i]; deck[i] = deck[exchange]; deck[exchange] = temp; } for( int i = 0; i < n; i++ ) { exchange = i + (int)(Math.random() * (n - i)); temp = deck[i]; deck[i] = deck[exchange]; deck[exchange] = temp; }](http://images.slideplayer.com./22/6415316/slides/slide_17.jpg " Using the swap code, we can do a random shuffling of a deck To do so, we go through each element of the array, and randomly swap it with any of the later elements for( int i = 0; i < n; i++ ) { exchange = i + (int)(Math.random() * (n - i)); temp = deck[i]; deck[i] = deck[exchange]; deck[exchange] = temp; } for( int i = 0; i < n; i++ ) { exchange = i + (int)(Math.random() * (n - i)); temp = deck[i]; deck[i] = deck[exchange]; deck[exchange] = temp; }")
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Searching through an array is an important operation The simplest way to do so is just linear search: check every element in the array Searching and sorting are really key to all kinds of problems We’ll cover both topics in depth in a few weeks
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Like light, sound is a wave For those physics buffs here, sound is usually transmitted as a compression wave In contrast, light is a transverse wave It doesn’t really matter, we can pretend that sound is a transverse wave
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The human ear can hear between about 12 Hz and 20,000 Hz The higher the frequency of the wave, the higher the frequency of the note Note (ha, ha) that the A an octave above A440 has twice the frequency Each half-step is an increase in the frequency by a factor of about 1.06 NoteFrequency A440 B493.88 C523.25 D587.33 E659.26 F698.46 G783.99 A880
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We can take a sound: And reproduce that sound at double the frequency: Notice that we have to add twice as much information to have the sound fill the same amount of time
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The amplitude of a wave is the distance from the trough of a wave to its peak In sound, amplitude is a measure of volume The larger the amplitude, the louder the sound Amplitude
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We can take a sound: And make the sound with half the amplitude: The frequency is exactly the same, but the sound is half is loud
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Something that looks like a sine wave is called a pure tone No real instruments play anything like that Even the purest real sound has overtones and harmonics Real sound is the result of many messy waves added together:
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On a computer, we cannot record a wave form directly As usual, we have to figure out a way to store a wave as a series of numbers We are going to use these numbers to approximate the heights of the wave at various points
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As we all know by now, Hertz (Hz) is a unit that means a number of times per second Equivalent to Hz is s -1 We are going to break down the wave into lots of slices We are going to have 44,100 slices in a second Thus, we are slicing at 44,100 Hz
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We slice up a wave and record the height of the wave Each height value is called a sample By getting 44,100 samples per second, we get a pretty accurate picture of the wave
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There are many different formats for sampling audio In our system, each sample will be recorded as a double The minimum value of a sample will be -1.0 and the maximum value of a sample is 1.0 A series of samples with value 0.0 represents silence Our samples will be stored in an array
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Audio data on Windows machines is sometimes stored in a WAV file A WAV file is much simpler than an MP3 because it has no compression Even so, it contains two channels (for stereo) and can have many different sample rates and formats for recording sound The StdAudio class lets you read and write a WAV file easily and always deal with a single array of sound, sampled at 44,100 Hz
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Everything you’d want to do with sound: To do interesting things, you have to manipulate the array of samples Make sure you added StdAudio.java to your project before trying to use it MethodUse double[] read(String file) Read a WAV file into an array of double s void save(String file, double[] input) Save an array of double s (samples) into a WAV file void play(String file) Play a WAV file void play(double[] input) Play an array of double s (samples)
![ Everything you’d want to do with sound: To do interesting things, you have to manipulate the array of samples Make sure you added StdAudio.java to your project before trying to use it MethodUse double[] read(String file) Read a WAV file into an array of double s void save(String file, double[] input) Save an array of double s (samples) into a WAV file void play(String file) Play a WAV file void play(double[] input) Play an array of double s (samples)](http://images.slideplayer.com./22/6415316/slides/slide_33.jpg " Everything you’d want to do with sound: To do interesting things, you have to manipulate the array of samples Make sure you added StdAudio.java to your project before trying to use it MethodUse double[] read(String file) Read a WAV file into an array of double s void save(String file, double[] input) Save an array of double s (samples) into a WAV file void play(String file) Play a WAV file void play(double[] input) Play an array of double s (samples)")
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Let’s load a file into an array: If the song has these samples: Perhaps samples will contain: String file = "song.wav"; double[] samples = StdAudio.read(file); String file = "song.wav"; double[] samples = StdAudio.read(file); -.9-.7-.6-.4-.2-.1.1.2.3.4.5.6.5.4.3.20-.2-.4
![ Let’s load a file into an array: If the song has these samples: Perhaps samples will contain: String file = song.wav ; double[] samples = StdAudio.read(file); String file = song.wav ; double[] samples = StdAudio.read(file);](http://images.slideplayer.com./22/6415316/slides/slide_34.jpg " Let’s load a file into an array: If the song has these samples: Perhaps samples will contain: String file = song.wav ; double[] samples = StdAudio.read(file); String file = song.wav ; double[] samples = StdAudio.read(file);")
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With the audio samples loaded into the array named samples, we can play them as follows: StdAudio.play(samples);
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Or, we could generate sound from scratch with StdAudio This example from the book creates 1 second of the pitch A440: double[] sound = new double[StdAudio.SAMPLE_RATE + 1]; for( int i = 0; i < sound.length; i++ ) sound[i] = Math.sin(2 * Math.PI * i * 440 / StdAudio.SAMPLE_RATE); StdAudio.play(sound); double[] sound = new double[StdAudio.SAMPLE_RATE + 1]; for( int i = 0; i < sound.length; i++ ) sound[i] = Math.sin(2 * Math.PI * i * 440 / StdAudio.SAMPLE_RATE); StdAudio.play(sound);
![ Or, we could generate sound from scratch with StdAudio This example from the book creates 1 second of the pitch A440: double[] sound = new double[StdAudio.SAMPLE_RATE + 1]; for( int i = 0; i < sound.length; i++ ) sound[i] = Math.sin(2 * Math.PI * i * 440 / StdAudio.SAMPLE_RATE); StdAudio.play(sound); double[] sound = new double[StdAudio.SAMPLE_RATE + 1]; for( int i = 0; i < sound.length; i++ ) sound[i] = Math.sin(2 * Math.PI * i * 440 / StdAudio.SAMPLE_RATE); StdAudio.play(sound);](http://images.slideplayer.com./22/6415316/slides/slide_36.jpg " Or, we could generate sound from scratch with StdAudio This example from the book creates 1 second of the pitch A440: double[] sound = new double[StdAudio.SAMPLE_RATE + 1]; for( int i = 0; i < sound.length; i++ ) sound[i] = Math.sin(2 * Math.PI * i * 440 / StdAudio.SAMPLE_RATE); StdAudio.play(sound); double[] sound = new double[StdAudio.SAMPLE_RATE + 1]; for( int i = 0; i < sound.length; i++ ) sound[i] = Math.sin(2 * Math.PI * i * 440 / StdAudio.SAMPLE_RATE); StdAudio.play(sound);")
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What if we wanted to play the second half of a sound followed by the first half? I know, why would we want to do that? double[] samples = StdAudio.read(file); double[] switched = new double[samples.length]; for(int i = 0; i < samples.length/2; i++ ) switched[i + samples.length/2] = samples[i]; for(int i = samples.length/2; i < samples.length; i++ ) switched[i - samples.length/2] = samples[i]; StdAudio.play(switched); double[] samples = StdAudio.read(file); double[] switched = new double[samples.length]; for(int i = 0; i < samples.length/2; i++ ) switched[i + samples.length/2] = samples[i]; for(int i = samples.length/2; i < samples.length; i++ ) switched[i - samples.length/2] = samples[i]; StdAudio.play(switched);
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Finish StdAudio Lab 7
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Keep reading Chapter 6 of the textbook Start working on Project 3
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