// Fourier.java (C) 2001 by Paul Falstad, www.falstad.com
import java.io.InputStream;
import java.awt.*;
import java.awt.image.ImageProducer;
import java.applet.Applet;
import java.applet.AudioClip;
import java.util.Vector;
import java.util.Hashtable;
import java.util.Enumeration;
import java.util.StringTokenizer;
import java.io.File;
import java.net.URL;
import java.util.Random;
import java.awt.image.MemoryImageSource;
import java.lang.Math;
import java.awt.event.*;
import java.text.DecimalFormat;
import java.text.NumberFormat;
import java.lang.reflect.Constructor;
import java.lang.reflect.Method;
class FourierCanvas extends Canvas {
FourierFrame pg;
FourierCanvas(FourierFrame p) {
pg = p;
}
public Dimension getPreferredSize() {
return new Dimension(300,400);
}
public void update(Graphics g) {
pg.updateFourier(g);
}
public void paint(Graphics g) {
pg.updateFourier(g);
}
};
class FourierLayout implements LayoutManager {
public FourierLayout() {}
public void addLayoutComponent(String name, Component c) {}
public void removeLayoutComponent(Component c) {}
public Dimension preferredLayoutSize(Container target) {
return new Dimension(500, 500);
}
public Dimension minimumLayoutSize(Container target) {
return new Dimension(100,100);
}
public void layoutContainer(Container target) {
int barwidth = 0;
int i;
for (i = 1; i < target.getComponentCount(); i++) {
Component m = target.getComponent(i);
if (m.isVisible()) {
Dimension d = m.getPreferredSize();
if (d.width > barwidth)
barwidth = d.width;
}
}
Insets insets = target.insets();
int targetw = target.size().width - insets.left - insets.right;
int cw = targetw-barwidth;
int targeth = target.size().height - (insets.top+insets.bottom);
target.getComponent(0).move(insets.left, insets.top);
target.getComponent(0).resize(cw, targeth);
cw += insets.left;
int h = insets.top;
for (i = 1; i < target.getComponentCount(); i++) {
Component m = target.getComponent(i);
if (m.isVisible()) {
Dimension d = m.getPreferredSize();
if (m instanceof Scrollbar)
d.width = barwidth;
if (m instanceof Label) {
h += d.height/5;
d.width = barwidth;
}
m.move(cw, h);
m.resize(d.width, d.height);
h += d.height;
}
}
}
};
public class Fourier extends Applet implements ComponentListener {
static FourierFrame ogf;
void destroyFrame() {
if (ogf != null)
ogf.dispose();
ogf = null;
repaint();
}
boolean started = false;
public void init() {
addComponentListener(this);
}
public static void main(String args[]) {
ogf = new FourierFrame(null);
ogf.init();
}
void showFrame() {
if (ogf == null) {
started = true;
ogf = new FourierFrame(this);
ogf.init();
repaint();
}
}
public void paint(Graphics g) {
String s = "Applet is open in a separate window.";
if (!started)
s = "Applet is starting.";
else if (ogf == null)
s = "Applet is finished.";
else if (ogf.useFrame)
ogf.triggerShow();
g.drawString(s, 10, 30);
}
public void componentHidden(ComponentEvent e){}
public void componentMoved(ComponentEvent e){}
public void componentShown(ComponentEvent e) { showFrame(); }
public void componentResized(ComponentEvent e) {}
public void destroy() {
if (ogf != null)
ogf.dispose();
ogf = null;
repaint();
}
};
class FourierFrame extends Frame
implements ComponentListener, ActionListener, AdjustmentListener,
MouseMotionListener, MouseListener, ItemListener {
PlayThread playThread;
Dimension winSize;
Image dbimage;
Random random;
public static final int sampleCount = 1024;
public static final int halfSampleCount = sampleCount/2;
public static final double halfSampleCountFloat = sampleCount/2;
final int rate = 22050;
final int playSampleCount = 16384;
public String getAppletInfo() {
return "Fourier Series by Paul Falstad";
}
FourierFrame(Fourier a) {
super("Fourier Series Applet v1.6d");
applet = a;
useFrame = true;
}
Fourier applet;
NumberFormat showFormat;
public boolean useFrame;
Container main;
Button sineButton;
Button cosineButton;
Button rectButton;
Button fullRectButton;
Button triangleButton;
Button sawtoothButton;
Button squareButton;
Button noiseButton;
Button blankButton;
Button phaseButton;
Button clipButton;
Button resampleButton;
Button quantizeButton;
Button highPassButton;
Checkbox magPhaseCheck;
Checkbox soundCheck;
Checkbox logCheck;
Scrollbar termBar;
Scrollbar freqBar;
double magcoef[];
double phasecoef[];
boolean mutes[], solos[], hasSolo;
static final double pi = 3.14159265358979323846;
static final double step = 2 * pi / sampleCount;
double func[];
int maxTerms = 160;
int selectedCoef;
static final int SEL_NONE = 0;
static final int SEL_FUNC = 1;
static final int SEL_MAG = 2;
static final int SEL_PHASE = 3;
static final int SEL_MUTES = 4;
static final int SEL_SOLOS = 5;
int selection;
int dragX, dragY;
int quantizeCount, resampleCount;
boolean dragging, freqAdjusted;
View viewFunc, viewMag, viewPhase, viewMutes, viewSolos;
FFT fft;
class View extends Rectangle {
View(int x, int y, int w, int h) {
super(x, y, w, h);
midy = y+h/2;
ymult = .6 * h/2;
periodWidth = w/3;
labely = midy - 5 - h*3/8;
}
int midy, labely;
double ymult;
int periodWidth;
}
int getrand(int x) {
int q = random.nextInt();
if (q < 0) q = -q;
return q % x;
}
FourierCanvas cv;
boolean java2;
Hashtable showTable;
boolean mustShow(String s) {
return showTable == null || showTable.containsKey(s);
}
Button doButton(String s) {
Button b = new Button(s);
if (mustShow(s))
main.add(b);
b.addActionListener(this);
return b;
}
Checkbox doCheckbox(String s) {
Checkbox b = new Checkbox(s);
if (mustShow(s))
main.add(b);
try {
String param = applet.getParameter(s);
if (param != null && param.equalsIgnoreCase("true"))
b.setState(true);
} catch (Exception e) {
e.printStackTrace();
}
b.addItemListener(this);
return b;
}
public void init() {
String jv = System.getProperty("java.class.version");
double jvf = new Double(jv).doubleValue();
if (jvf >= 48)
java2 = true;
String state = "";
try {
String param = applet.getParameter("useFrame");
if (param != null && param.equalsIgnoreCase("false"))
useFrame = false;
String show = applet.getParameter("show");
if (show != null) {
showTable = new Hashtable(10);
StringTokenizer st =
new StringTokenizer(show, ",");
while (st.hasMoreTokens()) {
String s = st.nextToken();
showTable.put(s, "");
}
showTable.put("Sound", "");
}
state = applet.getParameter("state");
} catch (Exception e) {
e.printStackTrace();
}
if (useFrame)
main = this;
else
main = applet;
selectedCoef = -1;
magcoef = new double[maxTerms];
phasecoef = new double[maxTerms];
mutes = new boolean[maxTerms];
solos = new boolean[maxTerms];
func = new double[sampleCount+1];
random = new Random();
fft = new FFT(sampleCount);
main.setLayout(new FourierLayout());
cv = new FourierCanvas(this);
cv.addComponentListener(this);
cv.addMouseMotionListener(this);
cv.addMouseListener(this);
main.add(cv);
sineButton = doButton("Sine");
cosineButton = doButton("Cosine");
triangleButton = doButton("Triangle");
sawtoothButton = doButton("Sawtooth");
squareButton = doButton("Square");
noiseButton = doButton("Noise");
phaseButton = doButton("Phase Shift");
clipButton = doButton("Clip");
resampleButton = doButton("Resample");
quantizeButton = doButton("Quantize");
rectButton = doButton("Rectify");
fullRectButton = doButton("Full Rectify");
highPassButton = doButton("High-Pass Filter");
blankButton = doButton("Clear");
soundCheck = doCheckbox("Sound");
if (!java2)
remove(soundCheck);
magPhaseCheck = doCheckbox("Mag/Phase View");
logCheck = doCheckbox("Log View");
logCheck.disable();
if (mustShow("Terms"))
main.add(new Label("Number of Terms", Label.CENTER));
termBar = new Scrollbar(Scrollbar.HORIZONTAL, 50,
1, 1, maxTerms);
termBar.addAdjustmentListener(this);
if (mustShow("Terms"))
main.add(termBar);
if (java2)
main.add(new Label("Playing Frequency", Label.CENTER));
freqBar = new Scrollbar(Scrollbar.HORIZONTAL, 251, 1, -100, 500);
freqBar.addAdjustmentListener(this);
if (java2)
main.add(freqBar);
main.add(new Label(""));
cv.setBackground(Color.black);
cv.setForeground(Color.lightGray);
showFormat = DecimalFormat.getInstance();
showFormat.setMaximumFractionDigits(5);
if (state.equalsIgnoreCase("square"))
doSquare();
else if (state.equalsIgnoreCase("sine"))
doSine();
else if (state.equalsIgnoreCase("triangle"))
doTriangle();
else if (state.equalsIgnoreCase("noise"))
doNoise();
else if (state.equalsIgnoreCase("quant")) {
doSine();
doQuantize();
} else if (state.equalsIgnoreCase("resample")) {
doSine();
doResample();
} else if (state.equalsIgnoreCase("clip")) {
doSine();
doClip();
} else if (state.equalsIgnoreCase("rect")) {
doSine();
doRect();
} else if (state.equalsIgnoreCase("fullrect")) {
doSine();
doFullRect();
} else if (state.equalsIgnoreCase("fullsaw")) {
doSawtooth();
doFullRect();
} else if (state.equalsIgnoreCase("beats"))
doBeats();
else if (state.equalsIgnoreCase("loudsoft"))
doLoudSoft();
else
doSawtooth();
if (useFrame) {
resize(800, 640);
handleResize();
Dimension x = getSize();
Dimension screen = getToolkit().getScreenSize();
setLocation((screen.width - x.width)/2,
(screen.height - x.height)/2);
show();
} else {
hide();
handleResize();
applet.validate();
}
main.requestFocus();
}
void handleResize() {
Dimension d = winSize = cv.getSize();
if (winSize.width == 0)
return;
dbimage = cv.createImage(d.width, d.height);
int margin = 20;
int pheight = (d.height-margin*2)/3;
viewFunc = new View(0, 0, d.width, pheight);
int y = pheight + margin*2;
viewMag = new View(0, y, d.width, pheight);
if (magPhaseCheck.getState()) {
viewMag.ymult *= 1.6;
viewMag.midy += (int) viewMag.ymult/2;
logCheck.enable();
} else {
logCheck.disable();
logCheck.setState(false);
}
y += pheight;
viewPhase = new View(0, y, d.width, pheight);
int pmy = viewPhase.midy + (int) viewPhase.ymult + 10;
int h = (d.height-pmy)/2;
//System.out.println("height " + h);
viewMutes = new View(0, pmy, d.width, h);
viewSolos = new View(0, pmy+h, d.width, h);
//System.out.println(viewMutes + " " + viewSolos + " " +d.height);
}
boolean shown = false;
public void triggerShow() {
if (!shown)
show();
shown = true;
}
void doBeats() {
int x;
for (x = 0; x != sampleCount; x++) {
double q = (x-halfSampleCount)*step;
func[x] = .5*(Math.cos(q*20) + Math.cos(q*21));
}
func[sampleCount] = func[0];
transform();
freqBar.setValue(-100);
}
void doLoudSoft() {
int x;
for (x = 0; x != sampleCount; x++) {
double q = (x-halfSampleCount)*step;
func[x] = Math.cos(q) + .05 * Math.cos(q*10);
}
func[sampleCount] = func[0];
transform();
}
void doSawtooth() {
int x;
for (x = 0; x != sampleCount; x++)
func[x] = (x-sampleCount/2) / halfSampleCountFloat;
func[sampleCount] = func[0];
transform();
}
void doTriangle() {
int x;
for (x = 0; x != halfSampleCount; x++) {
func[x] = (x*2-halfSampleCount) / halfSampleCountFloat;
func[x+halfSampleCount] =
((halfSampleCount-x)*2-halfSampleCount) / halfSampleCountFloat;
}
func[sampleCount] = func[0];
transform();
}
void doSine() {
int x;
for (x = 0; x != sampleCount; x++) {
func[x] = Math.sin((x-halfSampleCount)*step);
}
func[sampleCount] = func[0];
transform();
}
void doCosine() {
int x;
for (x = 0; x != sampleCount; x++) {
func[x] = Math.cos((x-halfSampleCount)*step);
}
func[sampleCount] = func[0];
transform();
}
void doRect() {
int x;
for (x = 0; x != sampleCount; x++)
if (func[x] < 0)
func[x] = 0;
func[sampleCount] = func[0];
transform();
}
void doFullRect() {
int x;
for (x = 0; x != sampleCount; x++)
if (func[x] < 0)
func[x] = -func[x];
func[sampleCount] = func[0];
transform();
}
void doHighPass() {
int i;
int terms = termBar.getValue();
for (i = 0; i != terms; i++)
if (magcoef[i] != 0) {
magcoef[i] = 0;
break;
}
doSetFunc();
}
void doSquare() {
int x;
for (x = 0; x != halfSampleCount; x++) {
func[x] = -1;
func[x+halfSampleCount] = 1;
}
func[sampleCount] = func[0];
transform();
}
void doNoise() {
int x;
int blockSize = 3;
for (x = 0; x != sampleCount/blockSize; x++) {
double q = Math.random() *2 - 1;
int i;
for (i = 0; i != blockSize; i++)
func[x*blockSize+i] = q;
}
func[sampleCount] = func[0];
transform();
}
void doPhaseShift() {
int i;
int sh = sampleCount/20;
double copyf[] = new double[sh];
for (i = 0; i != sh; i++)
copyf[i] = func[i];
for (i = 0; i != sampleCount-sh; i++)
func[i] = func[i+sh];
for (i = 0; i != sh; i++)
func[sampleCount-sh+i] = copyf[i];
func[sampleCount] = func[0];
transform();
}
void doBlank() {
int x;
for (x = 0; x <= sampleCount; x++)
func[x] = 0;
for (x = 0; x != termBar.getValue(); x++)
mutes[x] = solos[x] = false;
transform();
}
void doSetFunc() {
int i;
double data[] = new double[sampleCount*2];
int terms = termBar.getValue();
for (i = 0; i != terms; i++) {
int sgn = (i & 1) == 1 ? -1 : 1;
data[i*2] = sgn*magcoef[i]*Math.cos(phasecoef[i]);
data[i*2+1] = -sgn*magcoef[i]*Math.sin(phasecoef[i]);
}
fft.transform(data, true);
for (i = 0; i != sampleCount; i++)
func[i] = data[i*2];
func[sampleCount] = func[0];
updateSound();
}
void updateSound() {
if (playThread != null)
playThread.soundChanged();
}
void doClip() {
int x;
double mult = 1.2;
for (x = 0; x != sampleCount; x++) {
func[x] *= mult;
if (func[x] > 1)
func[x] = 1;
if (func[x] < -1)
func[x] = -1;
}
func[sampleCount] = func[0];
transform();
}
void doResample() {
int x, i;
if (resampleCount == 0)
resampleCount = 32;
if (resampleCount == sampleCount)
return;
for (x = 0; x != sampleCount; x += resampleCount) {
for (i = 1; i != resampleCount; i++)
func[x+i] = func[x];
}
func[sampleCount] = func[0];
transform();
resampleCount *= 2;
}
double origFunc[];
void doQuantize() {
int x;
if (quantizeCount == 0) {
quantizeCount = 8;
origFunc = new double[sampleCount];
System.arraycopy(func, 0, origFunc, 0, sampleCount);
}
for (x = 0; x != sampleCount; x++) {
func[x] = Math.round(origFunc[x]*quantizeCount)/
(double) quantizeCount;
}
func[sampleCount] = func[0];
transform();
quantizeCount /= 2;
}
int dfreq0;
double getFreq() {
// get approximate freq from slider (log scale)
double freq = 27.5*Math.exp(freqBar.getValue()*.004158883084*2);
// get offset into FFT array for frequency selected (as close as possible;
// it can't be exact because we use an FFT to generate the wave, and so the
// frequency choices must be integer multiples of a base frequency)
dfreq0 = ((int)(freq*(double) playSampleCount/rate))*2;
// get exact frequency being played
return rate*dfreq0/(playSampleCount*2.);
}
void transform() {
int x, y;
double data[] = new double[sampleCount*2];
int i;
for (i = 0; i != sampleCount; i++)
data[i*2] = func[i];
fft.transform(data, false);
double epsilon = .00001;
double mult = 2./sampleCount;
for (y = 0; y != maxTerms; y++) {
double acoef = data[y*2 ]*mult;
double bcoef = -data[y*2+1]*mult;
if ((y & 1) == 1)
acoef = -acoef;
else
bcoef = -bcoef;
//System.out.println(y + " " + acoef + " " + bcoef);
if (acoef < epsilon && acoef > -epsilon) acoef = 0;
if (bcoef < epsilon && bcoef > -epsilon) bcoef = 0;
if (y == 0) {
magcoef[0] = acoef / 2;
phasecoef[0] = 0;
} else {
magcoef[y] = Math.sqrt(acoef*acoef+bcoef*bcoef);
phasecoef[y] = Math.atan2(-bcoef, acoef);
}
// System.out.print("phasecoef " + phasecoef[y] + "\n");
}
updateSound();
}
void centerString(Graphics g, String s, int y) {
FontMetrics fm = g.getFontMetrics();
g.drawString(s, (winSize.width-fm.stringWidth(s))/2, y);
}
public void paint(Graphics g) {
cv.repaint();
}
public void updateFourier(Graphics realg) {
if (winSize == null || winSize.width == 0 || dbimage == null)
return;
Graphics g = dbimage.getGraphics();
Color gray1 = new Color(76, 76, 76);
Color gray2 = new Color(127, 127, 127);
g.setColor(cv.getBackground());
g.fillRect(0, 0, winSize.width, winSize.height);
g.setColor(cv.getForeground());
int i;
int ox = -1, oy = -1;
int midy = viewFunc.midy;
int periodWidth = viewFunc.periodWidth;
double ymult = viewFunc.ymult;
for (i = -1; i <= 1; i++) {
g.setColor((i == 0) ? gray2 : gray1);
g.drawLine(0, midy+(i*(int) ymult),
winSize.width, midy+(i*(int) ymult));
}
for (i = 2; i <= 4; i++) {
g.setColor((i == 3) ? gray2 : gray1);
g.drawLine(periodWidth*i/2, midy-(int) ymult,
periodWidth*i/2, midy+(int) ymult);
}
g.setColor(Color.white);
if (!(dragging && selection != SEL_FUNC)) {
for (i = 0; i != sampleCount+1; i++) {
int x = periodWidth * i / sampleCount;
int y = midy - (int) (ymult * func[i]);
if (ox != -1) {
g.drawLine(ox, oy, x, y);
g.drawLine(ox+periodWidth, oy, x+periodWidth, y);
g.drawLine(ox+periodWidth*2, oy, x+periodWidth*2, y);
}
ox = x;
oy = y;
}
}
int terms = termBar.getValue();
if (!(dragging && selection == SEL_FUNC)) {
g.setColor(Color.red);
ox = -1;
for (i = 0; i != sampleCount+1; i++) {
int x = periodWidth * i / sampleCount;
int j;
double dy = 0;
for (j = 0; j != terms; j++) {
dy += magcoef[j] * Math.cos(
step*(i-halfSampleCount)*j+phasecoef[j]);
}
int y = midy - (int) (ymult * dy);
if (ox != -1) {
g.drawLine(ox, oy, x, y);
g.drawLine(ox+periodWidth, oy, x+periodWidth, y);
g.drawLine(ox+periodWidth*2, oy, x+periodWidth*2, y);
}
ox = x;
oy = y;
}
}
int texty = viewFunc.height+10;
if (selectedCoef != -1) {
g.setColor(Color.yellow);
ox = -1;
double phase = phasecoef[selectedCoef];
int x;
double n = selectedCoef*2*pi/periodWidth;
int dx = periodWidth/2;
double mag = magcoef[selectedCoef];
if (!magPhaseCheck.getState()) {
if (selection == SEL_MAG) {
mag *= -Math.sin(phase);
phase = -pi/2;
} else {
mag *= Math.cos(phase);
phase = 0;
}
}
ymult *= mag;
if (!dragging) {
for (i = 0; i != sampleCount+1; i++) {
x = periodWidth * i / sampleCount;
double dy = Math.cos(
step*(i-halfSampleCount)*selectedCoef+phase);
int y = midy - (int) (ymult * dy);
if (ox != -1) {
g.drawLine(ox, oy, x, y);
g.drawLine(ox+periodWidth, oy, x+periodWidth, y);
g.drawLine(ox+periodWidth*2, oy, x+periodWidth*2, y);
}
ox = x;
oy = y;
}
}
if (selectedCoef > 0 && java2) {
int f = (int) (getFreq() * selectedCoef);
centerString(g, f +
((f > rate/2) ? " Hz (filtered)" : " Hz"),
texty);
}
if (selectedCoef != -1) {
String harm;
if (selectedCoef == 0)
harm = showFormat.format(mag) + "";
else {
String func = "cos";
if (!magPhaseCheck.getState() && selection == SEL_MAG)
func = "sin";
if (selectedCoef == 1)
harm = showFormat.format(mag) + " " + func + "(x";
else
harm = showFormat.format(mag) +
" " + func + "(" + selectedCoef + "x";
if (!magPhaseCheck.getState() || phase == 0)
harm += ")";
else {
harm += (phase < 0) ? " - " : " + ";
harm += showFormat.format(Math.abs(phase)) + ")";
}
if (logCheck.getState()) {
showFormat.setMaximumFractionDigits(2);
harm += " (" +
showFormat.format(20*Math.log(mag)/Math.log(10)) +
" dB)";
showFormat.setMaximumFractionDigits(5);
}
}
centerString(g, harm, texty+15);
}
}
if (selectedCoef == -1 && freqAdjusted && java2) {
int f = (int) getFreq();
g.setColor(Color.yellow);
centerString(g, f + " Hz", texty);
}
freqAdjusted = false;
int termWidth = getTermWidth();
ymult = viewMag.ymult;
midy = viewMag.midy;
g.setColor(Color.white);
if (magPhaseCheck.getState()) {
centerString(g, "Magnitudes", viewMag.labely);
centerString(g, "Phases", viewPhase.labely);
g.setColor(gray2);
g.drawLine(0, midy, winSize.width, midy);
g.setColor(gray1);
g.drawLine(0, midy-(int)ymult, winSize.width, midy-(int) ymult);
int dotSize = termWidth-3;
for (i = 0; i != terms; i++) {
int t = termWidth * i + termWidth/2;
int y = midy - (int) (showMag(i)*ymult);
g.setColor(i == selectedCoef ? Color.yellow : Color.white);
g.drawLine(t, midy, t, y);
g.fillOval(t-dotSize/2, y-dotSize/2, dotSize, dotSize);
}
ymult = viewPhase.ymult;
midy = viewPhase.midy;
for (i = -2; i <= 2; i++) {
g.setColor((i == 0) ? gray2 : gray1);
g.drawLine(0, midy+(i*(int) ymult)/2,
winSize.width, midy+(i*(int) ymult)/2);
}
ymult /= pi;
for (i = 0; i != terms; i++) {
int t = termWidth * i + termWidth/2;
int y = midy - (int) (phasecoef[i]*ymult);
g.setColor(i == selectedCoef ? Color.yellow : Color.white);
g.drawLine(t, midy, t, y);
g.fillOval(t-dotSize/2, y-dotSize/2, dotSize, dotSize);
}
} else {
centerString(g, "Sines", viewMag.labely);
centerString(g, "Cosines", viewPhase.labely);
g.setColor(gray2);
g.drawLine(0, midy, winSize.width, midy);
g.setColor(gray1);
g.drawLine(0, midy-(int)ymult, winSize.width, midy-(int) ymult);
g.drawLine(0, midy+(int)ymult, winSize.width, midy+(int) ymult);
int dotSize = termWidth-3;
for (i = 1; i != terms; i++) {
int t = termWidth * i + termWidth/2;
int y = midy + (int) (magcoef[i]*Math.sin(phasecoef[i])*ymult);
g.setColor(i == selectedCoef ? Color.yellow : Color.white);
g.drawLine(t, midy, t, y);
g.fillOval(t-dotSize/2, y-dotSize/2, dotSize, dotSize);
}
ymult = viewPhase.ymult;
midy = viewPhase.midy;
for (i = -2; i <= 2; i += 2) {
g.setColor((i == 0) ? gray2 : gray1);
g.drawLine(0, midy+(i*(int) ymult)/2,
winSize.width, midy+(i*(int) ymult)/2);
}
for (i = 0; i != terms; i++) {
int t = termWidth * i + termWidth/2;
int y = midy - (int) (magcoef[i]*Math.cos(phasecoef[i])*ymult);
g.setColor(i == selectedCoef ? Color.yellow : Color.white);
g.drawLine(t, midy, t, y);
g.fillOval(t-dotSize/2, y-dotSize/2, dotSize, dotSize);
}
}
double basef = getFreq();
if (viewMutes.height > 8) {
Font f = new Font("SansSerif", 0, viewMutes.height);
g.setFont(f);
FontMetrics fm = g.getFontMetrics();
for (i = 1; i != terms; i++) {
if (basef*i > rate/2)
break;
int t = termWidth * i + termWidth/2;
int y = viewMutes.y + fm.getAscent();
g.setColor(i == selectedCoef ? Color.yellow : Color.white);
if (hasSolo && !solos[i])
g.setColor(Color.gray);
String pm = "-";
if (mutes[i])
pm = "M";
int w = fm.stringWidth(pm);
g.drawString(pm, t-w/2, y);
y = viewSolos.y + fm.getAscent();
pm = "-";
if (solos[i])
pm = "S";
w = fm.stringWidth(pm);
g.drawString(pm, t-w/2, y);
}
}
realg.drawImage(dbimage, 0, 0, this);
}
double showMag(int n) {
double m = magcoef[n];
if (!logCheck.getState() || n == 0)
return m;
m = Math.log(m)/6.+1;
//System.out.println(magcoef[i] + " " + m);
return (m < 0) ? 0 : m;
}
double getMagValue(double m) {
if (!logCheck.getState())
return m;
if (m == 0)
return 0;
return Math.exp(6*(m-1));
}
int getTermWidth() {
int terms = termBar.getValue();
int termWidth = winSize.width / terms;
int maxTermWidth = winSize.width/30;
if (termWidth > maxTermWidth)
termWidth = maxTermWidth;
if (termWidth > 12)
termWidth = 12;
termWidth &= ~1;
return termWidth;
}
void edit(MouseEvent e) {
if (selection == SEL_NONE)
return;
int x = e.getX();
int y = e.getY();
switch (selection) {
case SEL_MAG: editMag(x, y); break;
case SEL_FUNC: editFunc(x, y); break;
case SEL_PHASE: editPhase(x, y); break;
case SEL_MUTES: editMutes(e, x, y); break;
case SEL_SOLOS: editSolos(e, x, y); break;
}
quantizeCount = resampleCount = 0;
}
void editMag(int x, int y) {
if (selectedCoef == -1)
return;
double ymult = viewMag.ymult;
double midy = viewMag.midy;
double coef = -(y-midy) / ymult;
if (magPhaseCheck.getState()) {
if (selectedCoef > 0) {
if (coef < 0)
coef = 0;
coef = getMagValue(coef);
} else if (coef < -1)
coef = -1;
if (coef > 1)
coef = 1;
if (magcoef[selectedCoef] == coef)
return;
magcoef[selectedCoef] = coef;
} else {
int c = selectedCoef;
if (c == 0)
return;
double m2 = magcoef[c]*Math.cos(phasecoef[c]);
if (coef > 1) coef = 1;
if (coef < -1) coef = -1;
double m1 = coef;
magcoef[c] = Math.sqrt(m1*m1+m2*m2);
phasecoef[c] = Math.atan2(-m1, m2);
}
updateSound();
cv.repaint();
}
void editFunc(int x, int y) {
if (dragX == x) {
editFuncPoint(x, y);
dragY = y;
} else {
// need to draw a line from old x,y to new x,y and
// call editFuncPoint for each point on that line. yuck.
int x1 = (x < dragX) ? x : dragX;
int y1 = (x < dragX) ? y : dragY;
int x2 = (x > dragX) ? x : dragX;
int y2 = (x > dragX) ? y : dragY;
dragX = x;
dragY = y;
for (x = x1; x <= x2; x++) {
y = y1+(y2-y1)*(x-x1)/(x2-x1);
editFuncPoint(x, y);
}
}
}
void editFuncPoint(int x, int y) {
int midy = viewFunc.midy;
int periodWidth = viewFunc.periodWidth;
double ymult = viewFunc.ymult;
int lox = (x % periodWidth) * sampleCount / periodWidth;
int hix = (((x % periodWidth)+1) * sampleCount / periodWidth)-1;
double val = (midy - y) / ymult;
if (val > 1)
val = 1;
if (val < -1)
val = -1;
for (; lox <= hix; lox++)
func[lox] = val;
func[sampleCount] = func[0];
cv.repaint();
}
void editPhase(int x, int y) {
if (selectedCoef == -1)
return;
double ymult = viewPhase.ymult;
double midy = viewPhase.midy;
double coef = -(y-midy) / ymult;
if (magPhaseCheck.getState()) {
coef *= pi;
if (coef < -pi)
coef = -pi;
if (coef > pi)
coef = pi;
if (phasecoef[selectedCoef] == coef)
return;
phasecoef[selectedCoef] = coef;
} else {
int c = selectedCoef;
double m1 = -magcoef[c]*Math.sin(phasecoef[c]);
if (coef > 1) coef = 1;
if (coef < -1) coef = -1;
double m2 = coef;
magcoef[c] = Math.sqrt(m1*m1+m2*m2);
phasecoef[c] = Math.atan2(-m1, m2);
updateSound();
}
cv.repaint();
}
void editMutes(MouseEvent e, int x, int y) {
if (e.getID() != MouseEvent.MOUSE_PRESSED)
return;
if (selectedCoef == -1)
return;
mutes[selectedCoef] = !mutes[selectedCoef];
cv.repaint();
}
void editSolos(MouseEvent e, int x, int y) {
if (e.getID() != MouseEvent.MOUSE_PRESSED)
return;
if (selectedCoef == -1)
return;
solos[selectedCoef] = !solos[selectedCoef];
int terms = termBar.getValue();
hasSolo = false;
int i;
for (i = 0; i != terms; i++)
if (solos[i]) {
hasSolo = true;
break;
}
cv.repaint();
}
public void componentHidden(ComponentEvent e){}
public void componentMoved(ComponentEvent e){}
public void componentShown(ComponentEvent e) {
cv.repaint();
}
public void componentResized(ComponentEvent e) {
handleResize();
cv.repaint(100);
}
public void actionPerformed(ActionEvent e) {
pressButton(e.getSource());
}
void pressButton(Object b) {
if (b == triangleButton) {
doTriangle();
cv.repaint();
}
if (b == sineButton) {
doSine();
cv.repaint();
}
if (b == cosineButton) {
doCosine();
cv.repaint();
}
if (b == rectButton) {
doRect();
cv.repaint();
}
if (b == fullRectButton) {
doFullRect();
cv.repaint();
}
if (b == squareButton) {
doSquare();
cv.repaint();
}
if (b == highPassButton) {
doHighPass();
cv.repaint();
}
if (b == noiseButton) {
doNoise();
cv.repaint();
}
if (b == phaseButton) {
doPhaseShift();
cv.repaint();
}
if (b == blankButton) {
doBlank();
cv.repaint();
}
if (b == sawtoothButton) {
doSawtooth();
cv.repaint();
}
if (b == clipButton) {
doClip();
cv.repaint();
}
if (b == quantizeButton) {
doQuantize();
cv.repaint();
} else
quantizeCount = 0;
if (b == resampleButton) {
doResample();
cv.repaint();
} else
resampleCount = 0;
}
public void itemStateChanged(ItemEvent e) {
if (e.getSource() == soundCheck && soundCheck.getState() &&
playThread == null) {
playThread = new PlayThread();
playThread.start();
}
if (e.getSource() == magPhaseCheck)
handleResize();
cv.repaint();
}
public void adjustmentValueChanged(AdjustmentEvent e) {
System.out.print(((Scrollbar) e.getSource()).getValue() + "\n");
if (e.getSource() == termBar) {
updateSound();
cv.repaint();
}
if (e.getSource() == freqBar) {
freqAdjusted = true;
updateSound();
cv.repaint();
}
}
public void mouseDragged(MouseEvent e) {
dragging = true;
edit(e);
}
public void mouseMoved(MouseEvent e) {
int x = e.getX();
int y = e.getY();
dragX = x; dragY = y;
int oldCoef = selectedCoef;
selectedCoef = -1;
selection = 0;
int oldsel = selection;
if (viewFunc.contains(x, y))
selection = SEL_FUNC;
else {
int termWidth = getTermWidth();
selectedCoef = x/termWidth;
if (selectedCoef > termBar.getValue())
selectedCoef = -1;
if (selectedCoef != -1) {
if (viewMag.contains(x, y))
selection = SEL_MAG;
else if (viewMutes.contains(x, y))
selection = SEL_MUTES;
else if (viewSolos.contains(x, y))
selection = SEL_SOLOS;
else if (viewPhase.contains(x, y))
selection = SEL_PHASE;
}
}
if (selectedCoef != oldCoef || oldsel != selection)
cv.repaint();
}
public void mouseClicked(MouseEvent e) {
if (e.getClickCount() == 2 && selectedCoef != -1 &&
selection != SEL_MUTES && selection != SEL_SOLOS) {
int i;
for (i = 0; i != termBar.getValue(); i++) {
phasecoef[i] = 0;
if (selectedCoef != i)
magcoef[i] = 0;
}
magcoef[selectedCoef] = 1;
if (!magPhaseCheck.getState())
phasecoef[selectedCoef] = (selection == SEL_MAG) ? -pi/2 : 0;
doSetFunc();
cv.repaint();
}
}
public void mouseEntered(MouseEvent e) {
}
public void mouseExited(MouseEvent e) {
}
public void mousePressed(MouseEvent e) {
mouseMoved(e);
if ((e.getModifiers() & MouseEvent.BUTTON3_MASK) != 0 &&
selectedCoef != -1) {
termBar.setValue(selectedCoef+1);
cv.repaint();
}
if ((e.getModifiers() & MouseEvent.BUTTON1_MASK) == 0)
return;
dragging = true;
edit(e);
}
public void mouseReleased(MouseEvent e) {
if ((e.getModifiers() & MouseEvent.BUTTON1_MASK) == 0)
return;
dragging = false;
if (selection == SEL_FUNC)
transform();
else if (selection != SEL_NONE)
doSetFunc();
cv.repaint();
}
public boolean handleEvent(Event ev) {
if (ev.id == Event.WINDOW_DESTROY) {
if (applet == null) dispose();
else applet.destroyFrame();
return true;
}
return super.handleEvent(ev);
}
class PlayThread extends Thread {
public void soundChanged() { changed = true; }
boolean changed;
public void run() {
// this lovely code is a translation of the following, using
// reflection, so we can run on JDK 1.1:
// AudioFormat format = new AudioFormat(rate, 8, 1, true, true);
// DataLine.Info info =
// new DataLine.Info(SourceDataLine.class, format);
// SourceDataLine line = null;
// line = (SourceDataLine) AudioSystem.getLine(info);
// line.open(format, playSampleCount);
// line.start();
Object line;
Method wrmeth = null;
try {
Class afclass = Class.forName("javax.sound.sampled.AudioFormat");
Constructor cstr = afclass.getConstructor(
new Class[] { float.class, int.class, int.class,
boolean.class, boolean.class });
Object format = cstr.newInstance(new Object[]
{ new Float(rate), new Integer(16), new Integer(1),
new Boolean(true), new Boolean(true) });
Class ifclass = Class.forName("javax.sound.sampled.DataLine$Info");
Class sdlclass =
Class.forName("javax.sound.sampled.SourceDataLine");
cstr = ifclass.getConstructor(
new Class[] { Class.class, afclass });
Object info = cstr.newInstance(new Object[]
{ sdlclass, format });
Class asclass = Class.forName("javax.sound.sampled.AudioSystem");
Class liclass = Class.forName("javax.sound.sampled.Line$Info");
Method glmeth = asclass.getMethod("getLine",
new Class[] { liclass });
line = glmeth.invoke(null, new Object[] {info} );
Method opmeth = sdlclass.getMethod("open",
new Class[] { afclass, int.class });
opmeth.invoke(line, new Object[] { format,
new Integer(4096) });
Method stmeth = sdlclass.getMethod("start", null);
stmeth.invoke(line, null);
byte b[] = new byte[1];
wrmeth = sdlclass.getMethod("write",
new Class[] { b.getClass(), int.class, int.class });
} catch (Exception e) {
e.printStackTrace();
playThread = null;
return;
}
FFT playFFT = new FFT(playSampleCount);
double playfunc[] = null;
byte b[] = null;
int offset = 0;
while (soundCheck.getState() && applet.ogf != null) {
if (playfunc == null || changed) {
playfunc = new double[playSampleCount*2];
int i;
int terms = termBar.getValue();
double bstep = 2*pi*getFreq()/rate;
double mx = .2;
changed = false;
for (i = 1; i != terms; i++) {
if (hasSolo && !solos[i])
continue;
if (mutes[i])
continue;
int dfreq = dfreq0*i;
if (dfreq >= playSampleCount)
break;
int sgn = (i & 1) == 1 ? -1 : 1;
playfunc[dfreq] = sgn*magcoef[i]*Math.cos(phasecoef[i]);
playfunc[dfreq+1] = -sgn*magcoef[i]*Math.sin(phasecoef[i]);
}
playFFT.transform(playfunc, true);
for (i = 0; i != playSampleCount; i++) {
double dy = playfunc[i*2];
if (dy > mx) mx = dy;
if (dy < -mx) mx = -dy;
}
b = new byte[playSampleCount*2];
double mult = 32767/mx;
for (i = 0; i != playSampleCount; i++) {
short x = (short) (playfunc[i*2]*mult);
b[i*2] = (byte) (x/256);
b[i*2+1] = (byte) (x & 255);
}
}
try {
int ss = 4096;
if (offset >= b.length)
offset = 0;
wrmeth.invoke(line, new Object[] { b, new Integer(offset),
new Integer(ss) });
offset += ss;
} catch (Exception e) {
e.printStackTrace();
break;
}
}
playThread = null;
}
}
}
class FFT {
double wtabf[];
double wtabi[];
int size;
FFT(int sz) {
size = sz;
if ((size & (size-1)) != 0)
System.out.println("size must be power of two!");
calcWTable();
}
void calcWTable() {
// calculate table of powers of w
wtabf = new double[size];
wtabi = new double[size];
int i;
for (i = 0; i != size; i += 2) {
double pi = 3.1415926535;
double th = pi*i/size;
wtabf[i ] = (double)Math.cos(th);
wtabf[i+1] = (double)Math.sin(th);
wtabi[i ] = wtabf[i];
wtabi[i+1] = -wtabf[i+1];
}
}
void transform(double data[], boolean inv) {
int i;
int j = 0;
int size2 = size*2;
if ((size & (size-1)) != 0)
System.out.println("size must be power of two!");
// bit-reversal
double q;
int bit;
for (i = 0; i != size2; i += 2) {
if (i > j) {
q = data[i]; data[i] = data[j]; data[j] = q;
q = data[i+1]; data[i+1] = data[j+1]; data[j+1] = q;
}
// increment j by one, from the left side (bit-reversed)
bit = size;
while ((bit & j) != 0) {
j &= ~bit;
bit >>= 1;
}
j |= bit;
}
// amount to skip through w table
int tabskip = size << 1;
double wtab[] = (inv) ? wtabi : wtabf;
int skip1, skip2, ix, j2;
double wr, wi, d1r, d1i, d2r, d2i, d2wr, d2wi;
// unroll the first iteration of the main loop
for (i = 0; i != size2; i += 4) {
d1r = data[i];
d1i = data[i+1];
d2r = data[i+2];
d2i = data[i+3];
data[i ] = d1r+d2r;
data[i+1] = d1i+d2i;
data[i+2] = d1r-d2r;
data[i+3] = d1i-d2i;
}
tabskip >>= 1;
// unroll the second iteration of the main loop
int imult = (inv) ? -1 : 1;
for (i = 0; i != size2; i += 8) {
d1r = data[i];
d1i = data[i+1];
d2r = data[i+4];
d2i = data[i+5];
data[i ] = d1r+d2r;
data[i+1] = d1i+d2i;
data[i+4] = d1r-d2r;
data[i+5] = d1i-d2i;
d1r = data[i+2];
d1i = data[i+3];
d2r = data[i+6]*imult;
d2i = data[i+7]*imult;
data[i+2] = d1r-d2i;
data[i+3] = d1i+d2r;
data[i+6] = d1r+d2i;
data[i+7] = d1i-d2r;
}
tabskip >>= 1;
for (skip1 = 16; skip1 <= size2; skip1 <<= 1) {
// skip2 = length of subarrays we are combining
// skip1 = length of subarray after combination
skip2 = skip1 >> 1;
tabskip >>= 1;
for (i = 0; i != 1000; i++);
// for each subarray
for (i = 0; i < size2; i += skip1) {
ix = 0;
// for each pair of complex numbers (one in each subarray)
for (j = i; j != i+skip2; j += 2, ix += tabskip) {
wr = wtab[ix];
wi = wtab[ix+1];
d1r = data[j];
d1i = data[j+1];
j2 = j+skip2;
d2r = data[j2];
d2i = data[j2+1];
d2wr = d2r*wr - d2i*wi;
d2wi = d2r*wi + d2i*wr;
data[j] = d1r+d2wr;
data[j+1] = d1i+d2wi;
data[j2 ] = d1r-d2wr;
data[j2+1] = d1i-d2wi;
}
}
}
}
}
A far higher place must be assigned to Judaism among the competitors for the allegiance of Europe. The cosmopolitan importance at one time assumed by this religion has been considerably obscured, owing to the subsequent devolution of its part to Christianity. It is, however, by no means impossible that, but for the diversion created by the Gospel, and the disastrous consequences of their revolt against Rome, the Jews might have won the world to a purified form of their own monotheism. A few significant circumstances are recorded showing how much influence they had acquired, even in Rome, before the first preaching of Christianity. The first of these is to be found in Cicero¡¯s defence of Flaccus. The latter was accused of appropriating part of the annual contributions sent to the temple at Jerusalem; and, in dealing with this charge, Cicero speaks of the Jews, who were naturally prejudiced against his client, as a powerful faction the hostility of which he is anxious not to provoke.330 Some twenty years later, a great advance has been made. Not only must the material interests of the Jews be respected, but a certain conformity to their religious prescriptions is considered a mark of good breeding, In one of his most amusing satires, Horace tells us how, being anxious to shake off a bore, he appeals for help to his friend Aristius Fuscus, and reminds him of217 some private business which they had to discuss together. Fuscus sees his object, and being mischievously determined to defeat it, answers: ¡®Yes, I remember perfectly, but we must wait for some better opportunity; this is the thirtieth Sabbath, do you wish to insult the circumcised Jews?¡¯ ¡®I have no scruples on that point,¡® replies the impatient poet. ¡®But I have,¡¯ rejoins Fuscus,¡ª¡®a little weak-minded, one of the many, you know¡ªexcuse me, another time.¡®331 Nor were the Jews content with the countenance thus freely accorded them. The same poet elsewhere intimates that whenever they found themselves in a majority, they took advantage of their superior strength to make proselytes by force.¡¯332 And they pursued the good work to such purpose that a couple of generations later we find Seneca bitterly complaining that the vanquished had given laws to the victors, and that the customs of this abominable race were established over the whole earth.333 Evidence to the same effect is given by Philo Judaeus and Josephus, who inform us that the Jewish laws and customs were admired, imitated, and obeyed over the whole earth.334 Such assertions might be suspected of exaggeration, were they not, to a certain extent, confirmed by the references already quoted, to which others of the same kind may be added from later writers showing that it was a common practice among the Romans to abstain from work on the Sabbath, and even to celebrate it by praying, fasting, and lighting lamps, to visit the synagogues, to study the law of Moses, and to pay the yearly contribution of two drachmas to the temple at Jerusalem.335 Jeff¡¯s hand was quietly coming down. ¡°What happened to you?¡± begged Sandy. ¡°Something new has come up, sir. I was waiting there by my ship a good while back, and I heard another one cruising and spiraling, shooting the field, I guess, because he came in and set down. My crate, just the way you ordered, was down by the grove, not in plain sight in the middle of the course. But Jeff set his ship down, left the engine running, and went off. I stayed hid to see what would happen, but when he didn¡¯t come back, I thought I¡¯d better go and find you¡ªand see if it meant anything to you.¡± She stood alone, with the sticky, wet knife in her hand, catching her breath, coming out of the madness. Then she stooped, and pushing the branches aside felt about for her pistol. It lay at the root of a tree, and[Pg 80] when she had picked it up and put it back in the holster, there occurred to her for the first time the thought that the shot in the dead stillness must have roused the camp. And now she was sincerely frightened. If she were found here, it would be more than disagreeable for Landor. They must not find her. She started at a swift, long-limbed run, making a wide detour, to avoid the sentries, bending low, and flying silently among the bushes and across the shadowy sands. The year 1756 opened with menaces to England of the most serious nature. The imbecility of the Ministry was beginning to tell in the neglect of its colonies and its defences. France threatened to invade us, and a navy of fifty thousand men was suddenly voted, and an army of thirty-four thousand two hundred and sixty-three of native troops; but as these were not ready, it was agreed to bring over eight thousand Hessians and Hanoverians. To pay for all this it was necessary to grant excessive supplies, and lay on new duties and taxes. In presenting the money bills in the month of May, Speaker Onslow could not avoid remarking that there were two circumstances which tended to create alarm¡ªforeign subsidies and foreign troops introduced, and nothing but their confidence in his Majesty could allay their fears, or give them confidence that their burdens would be soon reduced. There was, in fact, no chance for any such reduction, for wars, troubles, and disgraces were gathering around from various quarters. The first reverse came from the Mediterranean. MUCH to their amazement, the boys waked up the next morning in Nashville, and found that they had passed through the "dark and bloody ground" of Kentucky absolutely without adventure. After drawing and dividing the rations and cartridges. Si gave the boys the necessary instruction about having their things ready so that they could get them in the dark the next morning, and ordered them to disregard the bonfires and mirth-making, and lie down to get all the sleep they could, in preparation for the hard work of the next day. Then, like the rest of the experienced men, who saw that the campaign was at length really on, and this would be the last opportunity for an indefinite while to write, he sat down to write short letters to his mother and to Annabel. "Bully for the Wild Wanderers of the Wabash," Shorty joined in. "They're the boss regiment in the army o' the Cumberland, and the Army o' the Cumberland's the boss army on earth. Hooray for US Co. Le's have a speech. Where's Monty Scruggs?" "Bring a light, do¡ªI can't abide this dark." Albert suddenly began to look uneasy. After all he was not really drunk, only a little fuddled. He walked straight, and his roll was natural to him, while though he was exceedingly cheerful, and often burst into song, his words were not jumbled, and he generally seemed to have a fair idea of what he was saying. "But I heard what the doctor said to you." "A purty accident¡ªwud them stacks no more dry than a ditch. 'Twas a clear case of 'bustion¡ªfireman said so to me; as wicked and tedious a bit o' wark as ever I met in my life." Calverley stept from the shadow of the cliff, and beheld a meteor in the sky, brightening and expanding, as the clouds opened, until it assumed the appearance of a brilliant star, of astonishing magnitude, encircled by dazzling rays, which, in a singular manner, were all inclined in one direction, and pointing to that part of the horizon where lay the rival of England¡ªFrance. The foreman's face assumed a deeper hue than usual: he looked fiercely at the galleyman, but there was a determination in the weather-beaten face that made him pause ere he spoke. "Galleyman," he at length said, "you knew the business before you came: if you be so fond of saving old witches' lives, why didn't you say so, that I might not now be in this dilemma?" "No, no, not the boy," replied Merritt, rather impatiently. HoMEÁíÀàС˵ߣɫ
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