Digital Signal Processing (DSP)

SIGNAL

mathematical model of phenomena

DIGITALIZING

translate a physical quantity into numbers

SIGNAL → FUNCTION → NUMBERS

FILTER DESIGN

remove all we don't want from the signal

SYSTEM

mathematical formal model that transforms the signal in input (ex: filter)

ex: transformfrom the time domaininto frequency domain (Fourier transform)

SCHEMA: blocchi in successione

SENSORS

transform a non-electrical quantity into an elect. quantity (ex: temperature, encoder)

The signal can be analog or digital (just converted by the sensor)

INPUT

SIGNAL CONDITIONING

adapt the signal → ex: improveAND INTERFACING the signal

clean up the signal... amplification, ADC

SIGNAL —> mathematical model of phenomena

DIGITALIZING —> translate a physical quantity into numbers.

SIGNAL —> FUNCTION —> NUMBERS

FILTER DESIGN —> remove all we don't want from the signal

SYSTEM —> mathematical formal model that transform the signal in input. (ex: filter)

ex: transform from the time domain into frequency domain (Fourier transform)

SCHEMA: blocchi in successione

SENSORS: transform a non-electrical quantity into an electrical quantity (ex: temperature encoder)

(The signal can be analog or digital (just converted by the sensor))

INPUT

SIGNAL CONDITIONING: adapt the signal —> ex: improve the signal, clean up the signal... amplification, ADC

AND INTERFACING

DSP:

• digital control
• digital filtering
• transform
• parameter estimation (ex: estimation of position in a drone)
• feature extraction
• optimization

"Embedded Systems"

(MCU, MP, PLC, FPGA, DSP)

OUTPUT SIGNAL CONDITIONING & INTERFACING:

• D/A Conversion
• PWM modulation
• Amplification

DIGITAL ADVANTAGE:

• flexibility
• robustness
• predictability
• performance
• development time
• Known (numerical) precision

y = (1 + ^R₂⁄_R1) x

R₁ & R₂ are affected by tolerance

gain G' is G + ΔG

R₁ & R₂ change with temperature & age

There's an offset in operational amplifier

_y = G_dcx,

x

is a number which represent a finite set

not depend of nothing is just a number

ni ottengono le qualitá

elencate prima più controllo rispetto all’analogico

basta cambiare di

interno del MP

rescanlare Guadacnio

Si commette un errore mo ni tiene sotto controllo

ni sa quant’è (banda finita, risoluazione ecc..)

SIGNAL

Function (usually of time) associated to a physical quantity

• DETERMINISTIC: the shape of the signal is given
• RANDOM (STOCHASTIC) PROCESSES:
  • Set of signals with common statistical features

Differences between analog and digital are domain and co-domain.

CONTINOUS TIME (CT)

CONTINUOUS-TIME (CT)

• ℝ ⟷ ℝ
• ℝ ⟷ ℤ

DISCRETE-TIME (DT)

• ℤ ⟷ ℝ
• ℤ ⟷ ℤ

difficile da avere nella realtà

x(t)

SEQUENCE

= SAMPLING :

(pick the signal every constant time)

Associcating a giving value to the finite quantity is called QUANTIZATION

approximation error

Quindi ADC → 2 operations :

• SAMPLING → domain
• QUANTIZATION → codomain

Sequences

X(m)

The distance of the pulse depends on sampling time

m - adimensional index

amplitude of the pulse

1) Kronecker Delta

X(m) = δ(m) = { 1 m = 00 m ≠ 0

δ(t) is a distribution

δ_DIRAC(t) è diversa da δ(m)

2) Unit Step:

X(m) = U(m) = { 1 m > 00 m < 0

3) Exponential Sequence:

X(m) = A α^mU(m) =

• if 0 < α < 1 - va a zero
• if -1 < α < 0 - si alterna e va a zero
• if α > 1 - diverge
• if α < -1 - diverge alternando

Ogni sistema lineare può essere scomposto in segnali elementari

se stabile converge

se instabile diverge

COMPLEX

If L = |L| e^jφ_L

A = |A| e^jφ₀

4)

X(m) = |A| |α|^m e^{j(ω₀m + φ₀)} =

= |A| |α|^m cos(ω₀m + φ₀) + j |A| |α|^m sin(ω₀m + φ₀)

Re

Re