Frequency analysis: why?

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Frequency analysis why?

• Fast efficient insight on signals building
  blocks.
• Simplifies original problem - ex. solving Part.
  Diff. Eqns. (PDE).
• Powerful complementary to time domain analysis
  techniques.
• Several transforms in DSPing Fourier, Laplace,
  z, etc.

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Fourier analysis - applications

• Applications wide ranging and ever present in
  modern life
• Telecomms - GSM/cellular phones,
• Electronics/IT - most DSP-based applications,
• Entertainment - music, audio, multimedia,
• Imaging, image processing,
• Industry/research - X-ray spectrometry, chemical
  analysis (FT spectrometry), radar design,
• Medical - EGG, heart malfunction diagnosis,
• Speech analysis (voice activated devices,
  biometry, ).

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Fourier analysis - tools
Input Time Signal Frequency spectrum
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Fourier Series (FS)
synthesis
analysis
Note cos(k?t), sin(k?t) k form orthogonal
base of function space.
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FS synthesis
Square wave reconstruction from spectral terms
Convergence may be slow (1/k) - ideally need
infinite terms. Practically, series truncated
when remainder below computer tolerance (?
error). BUT Gibbs Phenomenon.
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Gibbs phenomenon
Overshoot exist _at_ each discontinuity
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Fourier Integral (FI)
Fourier analysis tools for aperiodic signals.
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FT - example
FT of 2?-wide square window
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Digital data formats
Positional number system with base b
.. a2 a1 a0 . a-1 a-2 .. b .. a2 b 2 a1
b 1 a0 b 0 a-1 b -1 a-2 b -2 ..
Important bases 10 (decimal), 2 (binary), 8
(octal), 16 (hexadecimal).
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Fixed-point binary
Represent integer or fractional binary numbers.
NB Constant gap between numbers.
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Floating-point binary - 2
IEEE 754 standard
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Finite word-length effects
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DSP Devices Architectures

• Selecting a DSP several choices
• Fixed-point
• Floating point
• Application-specific devices(e.g. FFT
  processors, speech recognizers,etc.).
• Main DSP Manufacturers
• Texas Instruments (http//www.ti.com)
• Motorola (http//www.motorola.com)
• Analog Devices (http//www.analog.com)

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Typical DSP Operations

• Filtering
• Energy of Signal
• Frequency transforms

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Traditional DSP Architecture
X RAM
Y RAM
a
x(n-i)
Multiply/Accumulate
Accumulator
y(n)
Most modern DSPs have more advanced features.
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TIs DSP Portfolio
C6000 (C62x, C67x)

• Power Efficient Performance
• Wireless Telephones/IADs
• Modems / Telephony
• VoIP
• .32ma/MIPS to sub 1V parts
• 5 / 100 MIPS

C3x C4x C8x

• Control Efficient
• Storage
• Brushless Motor Control
• Flash Memory
• A/D
• PWM Generators

• High Performance
• Multi-Channel / Function
• Comm Infrastructure
• xDSL
• Imaging, Video
• VLIW architecture
• 2400 MIPS
• Roadmap to 1 GHZ

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Personal and Portable Applications
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C67x Architecture
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DSP STARTER KIT (DSK)
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C6711 DSK OVERVIEW
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