Page 14 - Analog and Digital Filter Design

Contents 1 1

Decimation 355
Interpolation 356
Digital Filtering 356
Digital Lowpass Filters 357
Truncation (Applied to FIR Filters) 36 1
Transforming the Lowpass Response 362
Bandpass FIR Filter 363
Highpass FIR Filter 363
Bandstop FIR Filter 363
DSP Implementation of an FIR Filter 364
Introduction to the Infinite Response Filter 365
DSP Mathematics 366
Binary and Hexadecimal 367
Two's Complement 367
Adding Two's Complement Numbers 369
Subtracting Two's Complement Numbers 370
Multiplication 370
Division 373
Signal Handling 373
So, Why Use a Digital Filter? 375
Reference 375
Exercises 375

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CHAPTER Digital FIR Filter Design 377
Frequency versus Time-Domain Responses 380
Denormalized Lowpass Response Coefficients 380
Denormalized Highpass Response Coefficients 38 1
Denormalized Bandpass Response Coefficients 38 1
Denormalized Bandstop Response Coefficients 382
Windows 384
Fourier Method of FIR Filter Design 384
Window Types 385
Summary of Fixed FIR Windows 390
Number of Taps Needed by Fixed Window Functions 390
FIR Filter Design Using the Remez Exchange Algorithm 392
Number of Taps Needed by Variable Window Functions 392
FIR Filter Coefficient Calculation 393
A Data-Sampling Rate-Changer 394
References 394

CHAPTER IIR Filter Design 395
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Bilinear Transformation 397
Pre-Warping 400