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...
Microcomputer Systems 1
Introduction to
DSP’S
12 December 2014 Veton Këpuska 2
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.
12 December 2014 Veton Këpuska 3
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)
12 December 2014 Veton Këpuska 4
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.
Signal and Systems
Introduction to
Signals and
Systems
12 December 2014 Veton Këpuska 6
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.
12 December 2014 Veton Këpuska 7
Modeling
Engineers model two distinct physical phenomena:
1. Signals are modeled by mathematical functions.
2. Physical systems are modeled by mathematical equations.
What are Signals?
12 December 2014 Veton Këpuska 8
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.
12 December 2014 Veton Këpuska 9
Example of Signals: Speech
12 December 2014 Veton Këpuska 10
Example of Signals EKG:
12 December 2014 Veton Këpuska 11
Example of Signals: EEC
12 December 2014 Veton Këpuska 12
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
12 December 2014 Veton Këpuska 13
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
12 December 2014 Veton Këpuska 14
Deterministic signal
Corrupting, stochastic
noise signal
What is a System?
12 December 2014 Veton Këpuska 15
12 December 2014 Veton Këpuska 16
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)
12 December 2014 Veton Këpuska 17
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
12 December 2014 Veton Këpuska 18
Anatomical Structures for Speech Production
12 December 2014 Veton Këpuska 19
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(
12 December 2014 Veton Këpuska 20
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)(
)(
12 December 2014 Veton Këpuska 21
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
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
12 December 2014 Veton Këpuska 22
Example:
Single Input/Single Output (SISO) System
Multiple Input/Multiple Output (MIMO) System
12 December 2014 Veton Këpuska 23
Vin Vout
Electrical Network
+
-
+
-
x1 (t)
System
…
x2 (t)
xp (t)
y1 (t)
…
y2 (t)
yp (t)
Example:
Alternate Block Diagram Representation of a Multiple Input/Multiple Output (MIMO) System
12 December 2014 Veton Këpuska 24
System x(t) y(t)
1
2
1
pp tx
tx
tx
t
x
1
2
1
qq ty
ty
ty
ty
System Modeling
12 December 2014 Veton Këpuska 25
Physical System
Mathematical Model
Model Analysis
Model Simulation
Design Procedure
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
12 December 2014 Veton Këpuska 26
Model Types
1. Continuous Models
2. Discrete Models
12 December 2014 Veton Këpuska 27
12 December 2014 Veton Këpuska 28
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.
12 December 2014 Veton Këpuska 29
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
12 December 2014 Veton Këpuska 30
Example of ADC
12 December 2014 Veton Këpuska 31
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
12 December 2014 Veton Këpuska 32
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 …
12 December 2014 Veton Këpuska 33
Digital Telephone Communication System Example:
12 December 2014 Veton Këpuska 34
Typical Architecture of a DSP System
Sensor
ADC
Analog Signal Conditioning
Digital Signal Conditioning
DSP DAC
Analog Signal Processing
Digital Signal Processing
12 December 2014 Veton Këpuska 35
Why Using DSP?
Low-pass Filtering example:
Chebyshev Analog Filter of Type I and Order 6, vs.
FIR 129-Tap Filter
12 December 2014 Veton Këpuska 36
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]
12 December 2014 Veton Këpuska 37
Example of a 3-rd order Active low-pass filter implementation
12 December 2014 Veton Këpuska 38
Magnitude Response of Chebyshev Filter Type I Order 6.
12 December 2014 Veton Këpuska 39
Pass-Band Ripple 1.0 dB
12 December 2014 Veton Këpuska 40
Digital Filter Design
FIR,
129-Tap,
Less then 0.002 dB Pass Band Ripple
Linear Phase
12 December 2014 Veton Këpuska 41
FIR Filter Magnitude Response
12 December 2014 Veton Këpuska 42
Less then 0.002 dB Pass-Band Ripple
12 December 2014 Veton Këpuska 43
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.
12 December 2014 Veton Këpuska 44
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.
End