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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.