CS 121Week 7 - Wednesday

Last time

What did we talk about last time? Introduction to arrays Lab 6

Questions?

Project 3

Mid-Semester Evaluations

Arrays

Instantiation of an array

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 ints

int[] list;list = new int[100];

Accessing elements of an array 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]);

Length of an array

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

Array Examples

Statistics

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?

Variance

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, xi is the ith element, and is the mean

N

ii xx

N 1

22 )(1

x

Code for variance

Given an array of doubles called numbers, here’s the code for finding their variancedouble 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;

Cards

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

Array swap

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

Swap code

Here is an example of swapping two Strings indexed i and j in an array of Strings called array

int i = in.nextInt();int j = in.nextInt();

int temp;temp = array[i];array[i] = array[j];array[j] = temp;

Shuffling Cards

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 elementsfor( int i = 0; i < n; i++ )

{exchange = i + (int)(Math.random() * (n - i));temp = deck[i];deck[i] = deck[exchange];deck[exchange] = temp;

}

Searching

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

Sound

Sound

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

Frequency

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 octaveabove A440 has twice the frequency

Each half-step is an increase in the frequency by a factor of about 1.06

Note Frequency

A 440

B 493.88

C 523.25

D 587.33

E 659.26

F 698.46

G 783.99

A 880

Example of frequency change 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

Amplitude

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

Example of amplitude change

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

Real sounds

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:

Digital Sampling

Sampling

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

Sample rate

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

Sample values

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

Sample format

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

StdAudio Class

Purpose of the StdAudio class 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

StdAudio methods

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

Method Use

double[] read(String file) Read a WAV file into an array of doubles

void save(String file, double[] input)

Save an array of doubles (samples) into a WAV file

void play(String file) Play a WAV file

void play(double[] input) Play an array of doubles (samples)

StdAudio example

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);

-.9 -.7 -.6 -.4 -.2 -.1 .1 .2 .3 .4 .5 .6 .6 .5 .4 .3 .2 0 -.2 -.4

StdAudio example

With the audio samples loaded into the array named samples, we can play them as follows:

StdAudio.play(samples);

Generating sound with StdAudio

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);

Breaking a sound into parts

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);

Quiz

Upcoming

Next time…

Finish StdAudio Lab 7

Reminders

Keep reading Chapter 6 of the textbook

Start working on Project 3