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Fundamentals of Digital Signal Processing (DSP)

Fundamentals of Digital Signal Processing (DSP). DSP is Everywhere!. Audiological equipment Hearing aids Otoacoustic systems Audiometers Aural rehabilitation programs ABRs Telecommunications Cellular phones Voice over Internet Audio CD, DVD, DAT players MP3 players

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Fundamentals of Digital Signal Processing (DSP)

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  1. Fundamentals of Digital Signal Processing (DSP)

  2. DSP is Everywhere! • Audiological equipment • Hearing aids • Otoacoustic systems • Audiometers • Aural rehabilitation programs • ABRs • Telecommunications • Cellular phones • Voice over Internet • Audio • CD, DVD, DAT players • MP3 players • Biomedical monitoring equipment • Digital Television

  3. Analog vs Digital • Analog • infinitely detailed • continuous in time • continuous in amplitude • Digital • discrete numbers • discrete in time • discrete in amplitude • Challenge: a digital representation that adequately maps the analog values.

  4. Analog Systems Electric domain Acoustic domain Acoustic domain

  5. Programmable Analog Systems Electric domain Acoustic domain Acoustic domain Digital domain

  6. Digital Systems Electrical domain Digital domain Acoustic domain Electrical domain Acoustic domain

  7. Why digital? • Flexibility • Programmability • Reproducibility and Precision (??) • Advanced Signal Processing • Multichannel compression • Precise frequency shaping • Feedback cancellation • Noise reduction • Directional processing

  8. DSP Applications • Digital signal analysis/display • Digital recording, processing, and reproduction • Digital signal synthesis

  9. DSP Buzzwords • A to D Converter • D to A Converter • Sampling • Quantization • Aliasing • Anti-aliasing filter • Algorithm • Oversampling

  10. Sampling Process Analog Signal Sampling Interval (Ts) Sampled Numbers

  11. Analog-to-Digital Conversion Analog Discrete Digital

  12. Undersampling or Aliasing Undersampling results in a form of distortion termed as aliasing. http://www.dsptutor.freeuk.com/aliasing/AliasingDemo.html

  13. How to prevent aliasing? • Nyquist Criterion: When a signal is sampled, the sampling rate must be greater than twice the highest frequency of the input signal. • What if the highest frequency is unknown? • Use a low pass filter to remove unwanted frequencies. Set the sampling rate greater than twice the bandwidth of the low pass filter. The low pass filter is called an anti-aliasing filter.

  14. Quantization • The sampled values are converted into bit representation • The process is called “Quantization” • The performance of a quantizer is dependent on the number of bits, also called bit resolution.

  15. Binary Logical Circuits Flip Flops #4 #3 #2 #1 OFF ON OFF ON 0 1 0 1 • Each of these values is called a bit. • The string of values 1010 is a binary • representation. • A string of 8 bits is called a byte.

  16. An example of binary counting Voltage Flip Flop #1 Flip Flop #2 Binary Dec 5 < V < 10 on (1) on (1) 11 3 0 < V < 5 on (1) off (0) 10 2 -5 < V < 0 off (0) on (1) 01 1 -10 < V < -5 off (0) off (0) 00 0

  17. Example (contd.) Analog – fine grain signal Voltage Digital – quantized signal Decimal number

  18. Example (contd.) Analog – fine grain signal Digital – quantized signal

  19. 3-bit Analog-to-Digital Converter Voltage #1 #2 #3 Binary Decimal 7.5 < V <= 10 on(1) on (1) on(1) 111 7 5 < V <= 7.5 on(1) on (1) off(0) 110 6 2.5 < V <= 5 on(1) off (0) on(1) 101 5 0 < V <= 2.5 on(1) off (0) off(0) 100 4 -2.5 < V <= 0 off(0) on(1) on(1) 011 3 -5 < V <= -2.5 off(0) on(1) off(0) 010 2 -7.5 < V <= -5 off(0) off(0) on(1) 001 1 -10 < V <= -7.5 off(0) off(0) off(0) 000 0

  20. 3-bit Quantization

  21. Characteristics of an A/D Converter • Input range • The voltage range that the A/D converter can handle. Can be unipolar (either +ve or –ve voltages), or bipolar (both +ve and –ve) • Resolution • Represented by the number of bits. The number of possible states is given by 2N, where N is the number of bits. • Sampling Rate • Rate at which samples are measured.

  22. Digital Signal Processing • A series of trigonometric and arithmetic operations. • Series of steps called “algorithm” • Algorithm classes • Spectral analysis • Digital filtering • Coding and compressing data • Noise reduction • Etc.

  23. Conclusions • Digital Signal Processing (DSP) is often used in modern audiological equipment. • Fundamental concepts in DSP • Sampling – discretization of the time axis • Quantization – discretization of the amplitude axis • Digital Processing – a series of instructions to manipulate the digital numbers.

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