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Chapter 2: Main Application 64
Transform Definition
n (optional) a b
Modern Physics 0 0 1
Pure Math 1 1 –1
Probability 2 1 1
Classical Physics 3 –1 1
Signal Processing 4 0
–2*π
Tip: The Advanced Format dialog box can be used to configure settings related to the Fourier Transform, such a Fourier
Transform definition, etc. For details, see “Advanced Format Dialog Box” on page 38.
u FFT [Action][Advanced][FFT], IFFT [Action][Advanced][IFFT]
Function: “FFT” is the command for the fast Fourier Transform, and “IFFT” is the command for the inverse fast
Fourier Transform. 2
n
data values are needed to perform FFT and IFFT. On the ClassPad, FFT and
IFFT are calculated numerically.
Syntax: FFT(list) or FFT(list,
m ) IFFT(list) or IFFT(list, m )
• Data size must be 2
n
for n = 1, 2, 3, ...
• The value for
m is optional. It can be from 0 to 2, indicating the FFT parameter to use:
0 (Signal Processing), 1 (Pure Math), 2 (Data Analysis).
The Fourier Transform is defined as the following:
∫
∞
–∞
()
2π
() =
∫
∞
–∞
()
–2π
() =
Some authors (especially physicists) prefer to write the transform in terms of angular frequency ω ≡ 2π
instead of the oscillation frequency .
However, this destroys the symmetry, resulting in the transform pair shown below.
∫
∞
–∞
()
–ω
(ω) = [()] =
∫
∞
–∞
(ω)
ω
ω
() =
–1
[(ω)] =
1
2
π
To restore the symmetry of the transforms, the convention shown below is sometimes used.
∫
∞
–∞
()
–
() = [ ()] =
1
2
π
∫
∞
–∞
()
() =
–1
[()] =
1
2
π
In general, the Fourier transform pair may be defined using two arbitrary constants a and b as shown below.
∫
∞
–∞
()
ω
(ω) =
⏐
⏐
(2
π)
1–
∫
∞
–∞
(ω)
–ω
ω
() =
⏐
⏐
(2
π)
1+
Unfortunately, a number of conventions are in widespread use for a and b . For example, (0, 1) is used in
modern physics, (1, –1) is used in pure mathematics and systems engineering, (1, 1) is used in probability
theory for the computation of the characteristic function, (–1, 1) is used in classical physics, and (0, –2π) is
used in signal processing.
Tip: The Advanced Format dialog box can be used to configure Fast Fourier Transform settings. For details, see
“Advanced Format Dialog Box” on page 38.
- ClassPad II 1
- Backing Up Data 2
- Contents 3
- About This User’s Guide 9
- Chapter 1: 10
- 1-2 Power Supply 11
- Using the Application Menu 12
- Built-in Applications 12
- Application Window 13
- Using the O Menu 14
- 1-4 Input 15
- Soft Keyboard Key Sets 16
- Input Basics 17
- Message box 19
- ( ) 22
- 1-5 ClassPad Data 25
- Main Memory Data Types 26
- Main Memory Folders 26
- Using Variable Manager 27
- Selecting a Folder 28
- Managing Application Files 30
- Creating a New Variable 31
- Variable Usage Example 32
- “library” Folder Variables 32
- Application Format Settings 34
- k Graph Format Dialog Box 36
- k Geometry Format Dialog Box 38
- k Advanced Format Dialog Box 38
- 3. Reset the ClassPad 41
- Chapter 2: 42
- Main Application 42
- Using the e Key 43
- Calculation Priority Sequence 44
- Calculation Modes 44
- Complex Mode and Real Mode 45
- Angle Conversion (° 46
- Integer Functions 50
- Angle Symbol (∠) 52
- Derivative Symbol (’) 52
- Primality Test (isPrime) 53
- “with” Operator ( 53
- ∞, const, constn) 54
- n th-Delta Function 54
- 2-4 List Calculations 55
- Inputting Matrix Data 56
- Selecting a Number Base 58
- Arithmetic Operations 58
- Bitwise Operations 58
- 2-7 Using the Action Menu 59
- Example Screenshots 60
- L[ ()] ()= 62
- Using the Complex Submenu 67
- Using the List-Create Submenu 69
- Using the Vector Submenu 77
- ∞, and upper limit = ∞ 79
- Using the Assistant Submenu 82
- ∞, upper bound value = 36 83
- ∞, df = 18 84
- ∞, df = 4 85
- Using the Financial Submenu 88
- Using the Command Submenu 88
- Other Applications 89
- Using the Stat Editor Window 90
- Using the Geometry Window 91
- 2-10 Using Verify 92
- 2-11 Using Probability 92
- u To start up Probability 93
- Chapter 3: 95
- Graph & Table Application 95
- Graph window 96
- Table window 96
- 3-1 Storing Functions 97
- Graphing a Stored Function 98
- 3-2 Using the Graph Window 100
- Using View Window Memory 102
- Panning the Graph Window 103
- Scrolling the Graph Window 103
- Zooming the Graph Window 103
- Using Quick Zoom 104
- 3-3 Using Table & Graph 106
- (Link Trace) 107
- Generating a Summary Table 108
- 3-4 Using Trace 109
- 3-5 Using the Sketch Menu 110
- Using G-Solve Menu Commands 112
- 3-7 Modifying a Graph 113
- Chapter 4: 114
- Conics Application 114
- 4-1 Inputting an Equation 115
- 4-2 Drawing a Conics Graph 115
- Drawing a Circle 116
- Drawing an Ellipse 116
- Drawing a Hyperbola 116
- Drawing a General Conics 116
- Chapter 5: 118
- Function Graphs 123
- (y’, y”…, x) = 0 124
- Chapter 6: 125
- Sequence Application 125
- Generating a Number Table 126
- 6-2 Graphing a Recursion 127
- Chapter 7: 128
- Statistics Application 128
- u To create a list 129
- u To open an existing list 129
- u To close a list 129
- kPlot graphs 132
- u ClassPad Operation 135
- 1 2 63 3 4 4 4 75 137
- MSe Formulas 138
- 11 68 3 142
- 9 23 5 142
- Confidence Intervals 143
- Distributions 145
- : number of trials 146
- (x = 0, 1, 2, ...) 146
- : mean (0 < ) 146
- (x = 1, 2, 3, ...) 147
- Input and Output Terms 148
- Chapter 8: 150
- Geometry Application 150
- 8-1 Drawing Figures 151
- u To draw an ellipse 153
- u To draw a hyperbola 153
- u To draw a parabola 153
- u To draw a polygon 153
- Using the Construct Submenu 157
- u To construct a midpoint 158
- u To rotate a line segment 160
- 8-2 Editing Figures 161
- Moving and Copying Figures 162
- 8-4 Working with Animations 167
- u To trace a locus of points 168
- u To edit an animation 168
- Applications 170
- Chapter 9: 171
- Numeric Solver Application 171
- Chapter 10: 173
- u To insert a text row 174
- Expand button 175
- Tap here to display 175
- Application data strip list 176
- u To use a Geometry Link row 177
- File Compatibility 178
- Chapter 11: 179
- Financial Application 179
- Page Operations 180
- 11-3 Calculation Formulas 182
- ( ) 183
- Amortization 184
- Interest Conversion 184
- Cost/Sell/Margin 185
- Depreciation 185
- Bond Calculation 185
- (N–1+B/D ) 186
- (k–1+B/D ) 186
- Chapter 12: 189
- Program Application 189
- Creating a Program 190
- Pausing Program Execution 191
- Running a Program 192
- Terminating Program Execution 193
- Creating a Text File 193
- Using Text Files 194
- 12-2 Debugging a Program 195
- 12-3 User-defined Functions 196
- Using This Reference 198
- Syntax Conventions 198
- Command List 199
- M value, N value 205
- Chapter 13: 219
- Spreadsheet Application 219
- u Using the stylus 220
- Option Settings 221
- Selecting Cells 221
- Inputting Data into a Cell 222
- Inputting a Formula 222
- Inputting a Cell Reference 223
- Using the Cell Viewer Window 226
- 13-2 Graphing 229
- Graph Colors and Color Link 230
- MedMin MaxQ 234
- Other Graph Window Operations 236
- Distribution Calculations 240
- About DispStat Command 241
- Chapter 14: 243
- System Application 243
- Main Memory Sheet 244
- Configuring System Settings 245
- Warning! 246
- Chapter 15: 249
- Performing Data Communication 249
- Computer System Requirements 251
- Important! 251
- Auto Import of VCP Files 253
- VCP and XCP File Operations 253
- u To open a VCP file 254
- u To create a new VCP file 254
- ClassPads 255
- Communication Standby 257
- Precautions when Connecting 258
- Appendix 259
- System Variable Table 263
- Error Message Table 267
- Warning Message Table 269
- Low Memory Error Processing 270
- Number of Digits 271
- Precision 271
- Specifications 272
- CASIO COMPUTER CO., LTD 275
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