Introduction to DSP’S - Florida Institute of Technologymy.fit.edu/~vkepuska/ece3551/Lecture...
Transcript of Introduction to DSP’S - Florida Institute of Technologymy.fit.edu/~vkepuska/ece3551/Lecture...
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Microcomputer Systems 1
Introduction to
DSP’S
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Introduction to DSP’s
Definition: DSP – Digital Signal Processing/Processor
It refers to:
Theoretical signal processing by digital means (subject of ECE3222, ECE3541),
Specialized hardware (processor) that can process signals in real-time (subject of this course ECE3551&3)
This class’s focus is on: Hardware Architecture of a real-world DSP platform
Software Development on DSPs, and
Applied Signal Processing theory and practice.
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Introduction to DSP’s
DSP’s process signals
Signal – a detectable physical quantity or impulse (as a voltage, current, or magnetic field strength) by which messages or information can be transmitted (Webster Dictionary)
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Introduction to DSP’s
Signal Characteristics: Signals are Physical Quantities: Signals are Measurable Signals are Analog Signals Contain Information.
Examples: Temperature [oC] Pressure [Newtons/m2] or [Pa] Mass [kg] Speed [m/s] Acceleration [m/s2] Torque [Newton*m] Voltage [Volts] Current [Amps] Power [Watts]
In this class, analog signals are electrical. Sensors: are devices that convert other physical quantities (temperature,
pressure, etc.) to electrical signals.
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Signal and Systems
Introduction to
Signals and
Systems
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Introduction to Signals and Systems
Introduction to Signals and Systems as related to Engineering
Modeling of physical signals by mathematical functions
Modeling physical systems by mathematical equations
Solving mathematical equations when excited by the input functions/signals.
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Modeling
Engineers model two distinct physical phenomena:
1. Signals are modeled by mathematical functions.
2. Physical systems are modeled by mathematical equations.
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What are Signals?
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Signals
Signals, x(t), are typically real
functions of one independent variable that typically represents time; t.
Time t can assume all real values: -∞ < t < ∞,
Function x(t) is typically a real
function.
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Example of Signals: Speech
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Example of Signals EKG:
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Example of Signals: EEC
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Categories of Signals
Signals can be:
1. Continuous, or
2. Discrete:
T – sampling rate
f – sampling frequency – 1/T
– radial sampling frequency – 2f= 2/T
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Signal Processing
Signals are often corrupted by noise.
s(t) = x(t)+n(t)
Want to ‘filter’ the
measured signal s(t) to
remove undesired noise
effects n(t).
Need to retrieve x(t).
Signal Processing
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Deterministic signal
Corrupting, stochastic
noise signal
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What is a System?
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Modeling Examples
Human Speech Production is driven by air (input signal) and produces sound/speech (output signal)
Voltage (signal) of a RLC circuit
Music (signal) produced by a musical instrument
Radio (system) converts radio frequency (input signal) to sound (output signal)
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Speech Production
Human vocal tract as a system:
Driven by air (as input signal)
Produces Sound/Speech (as output signal)
It is modeled by Vocal tract transfer function:
Wave equations,
Sound propagation in a uniform acoustic tube
Representing the vocal tract with simple acoustic tubes
Representing the vocal tract with multiple uniform tubes
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Anatomical Structures for Speech Production
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Uniform Tube Model
cos,
cos
sin,
cos
j t
g
j t
g
l x cu x t U e
l c
l x ccp x t j U e
A l c
Volume velocity, denoted as u(x,t), is defined as the
rate of flow of air particles perpendicularly through a specified area.
Pressure, denoted as p(x,t), and
tj
g eUtu )(),0(
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RLC Circuit
v(t)
L R
C
i(t)
Voltage, v(t) input signal Current, i(t) output signal Inductance, L (parameter of the system) Resistance, R (parameter of the system) Capacitance, C (parameter of the system)
t
tvdiC
tRidt
tdiL )()(
1)(
)(
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Newton’s Second Law in Physics
The above equation is the model of a physical system that relates an object’s motion: x(t), object’s mass: M with a force f(t) applied to it: f(t), and x(t) are models of physical signals.
The equation is the model of the physical system.
2
2 )()(
dt
txdMtf
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What is a System?
A system can be a collection of interconnected components:
Physical Devices and/or
Processors
We typically think of a system as having terminals for access to the system:
Inputs and
Outputs
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Example:
Single Input/Single Output (SISO) System
Multiple Input/Multiple Output (MIMO) System
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Vin Vout
Electrical Network
+
-
+
-
x1 (t)
System
…
x2 (t)
xp (t)
y1 (t)
…
y2 (t)
yp (t)
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Example:
Alternate Block Diagram Representation of a Multiple Input/Multiple Output (MIMO) System
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System x(t) y(t)
1
2
1
pp tx
tx
tx
t
x
1
2
1
qq ty
ty
ty
ty
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System Modeling
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Physical System
Mathematical Model
Model Analysis
Model Simulation
Design Procedure
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Model Types
1. Input-Output Description
Frequency-Domain Representations:
Transfer Function - Typically used on ideal Linear-Time-Invariant Systems
Fourier Transform Representation
Time-Domain Representations
Differential/Difference Equations
Convolution Models
2. State-Space Description
Time-Domain Representation
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Model Types
1. Continuous Models
2. Discrete Models
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Introduction to DSP’s
Analog Continuous
DSP process digital signals:
Analog-to-Digital Converter (ADC)
Binary representation of the analog signal
Digital-to-Analog Converter (DAC)
Digital representation of the signal is converted to continuous analog signal.
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ADC
x(t)
Analog
Low-pass
Filter
Sample
and
Hold
fs
b) Amplitude Quantized Signal
xa(nT)
x[n]
Quantizer
DSP
c) Amplitude & Time Quantized – Digital Signal
a) Continuous Signal
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Example of ADC
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DAC
DSP Digital to
Analog
Converter
Analog
Low-pass
Filter y[n]
y(t)
ya(nT)
c) Continuous Low-pass filtered Signal b) Analog Signal a) Digital Output Signal
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Why Processing Signals?
Extraction of Information Amplitude Phase Frequency Spectral Content
Transform the Signal
FDMA (Frequency Division Multiple Access)
TDMA (Time Division Multiple Access)
CDMA (Code Division Multiple Access)
Compress Data ADPCM (Adaptive Differential
Pulse Code Modulation) CELP (Code Excited Linear
Prediction) MPEG (Moving Picture Experts
Group) HDTV (High Definition TV)
Generate Feedback Control Signal Robotics (ASIMOV) Vehicle Manufacturing Process Control
Extraction of Signal in
Noise Filtering Autocorrelation Convolution
Store Signals in Digital
Format for Analysis FFT …
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Digital Telephone Communication System Example:
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Typical Architecture of a DSP System
Sensor
ADC
Analog Signal Conditioning
Digital Signal Conditioning
DSP DAC
Analog Signal Processing
Digital Signal Processing
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Why Using DSP?
Low-pass Filtering example:
Chebyshev Analog Filter of Type I and Order 6, vs.
FIR 129-Tap Filter
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Chebyshev Analog Filter of Type I
Chebyshev Type I (Pass-Band Ripple)
6-Pole
1.0 dB Pass-Band Ripple
Non-liner Phase
MATLAB: fdatool Order = 6
Fs = 10,000 Hz
Fpass = 1,000 Hz
Apass = 1 [dB]
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Example of a 3-rd order Active low-pass filter implementation
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Magnitude Response of Chebyshev Filter Type I Order 6.
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Pass-Band Ripple 1.0 dB
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Digital Filter Design
FIR,
129-Tap,
Less then 0.002 dB Pass Band Ripple
Linear Phase
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FIR Filter Magnitude Response
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Less then 0.002 dB Pass-Band Ripple
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Analog vs. Digital Implementations
Analog
Cons: Approximate Filter
Coefficients
Only standard components available
Environment Temperature dependent
Less accurate
Can be used only for designed purpose
Pros: Operate in real-time
Digital (DSP)
Cons: Real-time operation is
dependent on the speed of processor and the complexity of problem at hand.
Pros: Accurate Filter
implementation to desired precision
Operation independent on the environment.
Flexible
DSP’s can be reprogrammed.
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DSP Implementation of the FIR Filter
129-tap digital filter requires 129 multiply-accumulates (MAC)
Operation must be completed within sampling interval (1/Fs) to maintain real-time. Fs=10000Hz = 10kHz ⇒ 100 s
ADSP-21xx family performs MAC process in single instruction cycle
Instruction rate > 129/100 s = 1.3 MIPS
ADSP-218x 16-bit fixed point series: 75 MIPS.
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End