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

• Biomedical monitoring equipment• Digital Television

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.

Analog SystemsAcousticdomain

Electricdomain

Acousticdomain

Programmable Analog SystemsAcousticdomain

Acousticdomain

Electricdomain

Digital domain

Digital SystemsAcousticdomain

Electricaldomain

Electricaldomain

Acousticdomain

Digital domain

Why digital?

• Flexibility• Programmability• Reproducibility and Precision (??)• Advanced Signal Processing

– Multichannel compression– Precise frequency shaping– Feedback cancellation– Noise reduction– Directional processing

DSP Applications

• Digital signal analysis/display

• Digital recording, processing, and reproduction

• Digital signal synthesis

DSP Buzzwords

• A to D Converter• D to A Converter• Sampling• Quantization• Aliasing• Anti-aliasing filter• Algorithm• Oversampling

Sampling Process

Analog Signal

Sampling Interval (Ts)

Sampled Numbers

Analog-to-Digital Conversion

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-5

0

5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-5

0

5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-5

0

5

Analog

Discrete

Digital

Undersampling or Aliasing

Undersampling results in a form of distortion termed as aliasing.

http://www.dsptutor.freeuk.com/aliasing/AliasingDemo.html

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.

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.

Binary Logical Circuits Flip Flops

ON OFF ON OFF

#1 #2 #3 #4

1 0 1 0

Each of these values is called a bit. The string of values 1010 is a binaryrepresentation. A string of 8 bits is called a byte.

0 0.2 0.4 0.6 0.8 1-20

-15

-10

-5

0

5

10

15

20

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

Example (contd.)

0 0.2 0.4 0.6 0.8 1-20

-15

-10

-5

0

5

10

15

20

0 0.2 0.4 0.6 0.8 1-2

-1

0

1

2

3

4

5

Vol

tage

Dec

imal

num

ber

Analog – fine grain signal

Digital – quantized signal

Example (contd.)

0 0.2 0.4 0.6 0.8 1

-10

-5

0

5

10

0 0.2 0.4 0.6 0.8 1-2

-1

0

1

2

3

4

5

Analog – fine grain signal

Digital – quantized signal

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

3-bit Quantization

0 0.2 0.4 0.6 0.8 1-2

0

2

4

6

8

0 0.2 0.4 0.6 0.8 1

-10

-5

0

5

10

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.

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.

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.