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מכללת BITLEE

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מכללת BITLEE

קורס DSP יישומי לתעשיה

DSP-

Digital

Signal

Processing

FROM ANALOG TO DIGITAL DOMAIN

25 March 2004

- Analog vs. digital: why, what & how
- What is DSP?
- What is DSP used for?
- Speech & Audio processing
- Image & Video processing
- Adaptive filtering

- Digital system example
- Sampling & aliasing
- Frequency analysis: why? & applications
- DSP Devices and Architectures

Analog

Digital

Discrete function Vk of discrete sampling variable tk, with k = integer: Vk = V(tk).

Continuous function V of continuous variable t (time, space etc) : V(t).

Uniform (periodic) sampling. Sampling frequency fS = 1/ tS

Limitations

Advantages

- A/D & signal processors speed: wide-band signals still difficult to treat (real-time systems).
- Finite word-length effect.
- Obsolescence (analog electronics has it, too!).

- More flexible.
- Often easier system upgrade.
- Data easily stored.
- Better control over accuracy requirements.
- Noise reduction.

Digital Signal Processing (DSPing)

- Predicting a system’s output.
- Implementing a certain processing task.
- Studying a certain signal.

Applications

- General purpose processors (GPP), -controllers.
- Digital Signal Processors (DSP).
- Programmable logic ( PLD, FPGA ).

Hardware

Fast

Faster

real-time DSPing

- Programming languages: Pascal, C / C++ ...
- “High level” languages: Matlab, Mathcad, Mathematica…
- Dedicated tools (ex: filter design s/w packages).

Software

Digital Signal Processing – the processing or manipulation of signals using digital techniques

Digital Signal Processor

Input Signal

Output Signal

ADC

DAC

Analogue to Digital Converter

Digital to Analogue Converter

- Feed in analog signal
- Convert from analog to Digital
- Process mathematical representation of signal
- Convert from digital back to analog
- Output analog signal
- Real Time Processing of the mathematical representations of signals

…And much more!

DATA

VIDEO

AUDIO

DSP Technology & Markets

VOICE

General scheme

ANALOG DOMAIN

FilterAntialiasing

FilterAntialiasing

Sometimes steps missing

- Filter + A/D

- D/A + filter

A/D

A/D

DIGITAL DOMAIN

Digital Processing

Digital Processing

D/A

ANALOG DOMAIN

Topics of this lecture.

FilterReconstruction

ANALOG INPUT

Antialiasing Filter

1

2

3

A/D

Digital Processing

• Digital format.

What to use for processing?

See slide “DSPing aim & tools”

DIGITAL OUTPUT

KEY DECISION POINTS:

Analysis bandwidth, Dynamic range

•Sampling rate.

• Pass / stop bands.

• No. of bits. Parameters.

1

*

Ex: train wheels in a movie.

25 frames (=samples) per second.

Train starts wheels ‘go’ clockwise.

Train accelerates wheels ‘go’ counter-clockwise.

*Sampling: independent variable (ex: time) continuous discrete.

Quantisation: dependent variable (ex: voltage) continuous discrete.

Here we’ll talk about uniform sampling.

How fast must we sample a continuous signal to preserve its info content?

Why?

Frequency misidentification due to low sampling frequency.

Lowpass Spectrum

f

-fmax

fmax

Bandpass Spectrum

f

–f1

f2

–f2

f1

- Sampling rate must be greater than twice the analog signal’s bandwidth
- Bandwidth is defined asnon-zero extent of spectrumof the continuous-time signalin positive frequencies
- Lowpass spectrum on right:bandwidth is fmax
- Bandpass spectrum on right:bandwidth is f2 – f1

1

__ s(t) = sin(2f0t)

s(t) @ fS

f0 = 1 Hz, fS = 3 Hz

__ s1(t) = sin(8f0t)

__ s2(t) = sin(14f0t)

s(t) @ fS represents exactly all sine-waves sk(t) defined by:

sk (t) = sin( 2 (f0 + k fS) t ) , k

1

Example

Condition on fS?

F1

F2

F3

fS > 300 Hz

F1=25 Hz, F2 = 150 Hz, F3 = 50 Hz

fMAX

A signal s(t) with maximum frequency fMAX can be recovered if sampled at frequency fS > 2 fMAX .

Theo*

*Multiple proposers: Whittaker(s), Nyquist, Shannon, Kotel’nikov.

Naming gets

confusing !

Nyquist frequency (rate) fN = 2 fMAXor fMAXor fS,MINor fS,MIN/2

1

(a)Band-limited signal:

frequencies in [-B, B] (fMAX = B).

(a)

(b)

(b)Time sampling frequency repetition.

fS > 2 B no aliasing.

(c)

(c)fS 2 B aliasing !

Aliasing: signal ambiguity in frequency domain

1

(a)

(a),(b)Out-of-band noise can aliase into band of interest. Filter it before!

(c)Antialiasing filter

(b)

- Passband: depends on bandwidth of interest.
- Attenuation AMIN : depends on
- ADC resolution ( number of bits N).
- AMIN, dB ~ 6.02 N + 1.76
- Out-of-band noise magnitude.

(c)

2

Different applications have different needs.

- Number of bits N (~resolution)
- Data throughput (~speed)
- Signal-to-noise ratio (SNR)
- Signal-to-noise-&-distortion rate (SINAD)
- Effective Number of Bits (ENOB)
- Spurious-free dynamic range (SFDR)
- Integral non-linearity (INL)
- Differential non-linearity (DNL)
- …

Radar systems

Static distortion

Communication

Dynamic distortion

Imaging / video

NB: Definitions may be slightly manufacturer-dependent!

2

Continuous input signal digitized into 2N levels.

Uniform, bipolar transfer function (N=3)

Quantisation step q =

V FSR

2N

Ex: VFSR = 1V , N = 12 q = 244.1 V

Voltage ( = q)

Scale factor (= 1 / 2N )

Percentage (= 100 / 2N )

LSB

Quantisation error

- Standard telephone signal:
_ Telephone speech bandwidth 300hz-3.4khz

- Sampling Rate: 8 kHz
- 8-bit samples
- Data transfer rate = 88= 64kbits/s (64kbps)
- ATU-TI G711

- Standard music CD:
_Sound is audible in 20 Hz to 20 kHz range:

- Sampling Rate: 44.1 kHz
- 16-bit samples
- 2-channel stereo
- Data transfer rate = 21644,100 = 1.4 Mbits/s
- 1 hour of music = 1.43,600 = 635 MB

1

Example

Ear + brain act as frequency analyser: audio spectrum split into many narrow bands low-power sounds detected out of loud background.

- Bandwidth: indicates rate of change of a signal. High bandwidth signal changes fast.

- Time & frequency: two complementary signal descriptions. Signals seen as “projected’ onto time or frequency domains.