מכללת BITLEE. קורס DSP יישומי לתעשיה. DSP- D igital S ignal P rocessing. FROM ANALOG TO DIGITAL DOMAIN. 25 March 2004. TOPICS. Analog vs. digital: why, what & how What is DSP? What is DSP used for? Speech & Audio processing Image & Video processing Adaptive filtering
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קורס DSP יישומי לתעשיה
FROM ANALOG TO DIGITAL DOMAIN
25 March 2004
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
Digital Signal Processing (DSPing)
Digital Signal Processing – the processing or manipulation of signals using digital techniques
Digital Signal Processor
Analogue to Digital Converter
Digital to Analogue Converter
…And much more!
DSP Technology & Markets
Sometimes steps missing
- Filter + A/D
- D/A + filter
Topics of this lecture.
• Digital format.
What to use for processing?
See slide “DSPing aim & tools”
KEY DECISION POINTS:
Analysis bandwidth, Dynamic range
• Pass / stop bands.
• No. of bits. Parameters.
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?
Frequency misidentification due to low sampling frequency.
__ 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
Condition on fS?
fS > 300 Hz
F1=25 Hz, F2 = 150 Hz, F3 = 50 Hz
A signal s(t) with maximum frequency fMAX can be recovered if sampled at frequency fS > 2 fMAX .
*Multiple proposers: Whittaker(s), Nyquist, Shannon, Kotel’nikov.
Nyquist frequency (rate) fN = 2 fMAXor fMAXor fS,MINor fS,MIN/2
frequencies in [-B, B] (fMAX = B).
(b)Time sampling frequency repetition.
fS > 2 B no aliasing.
(c)fS 2 B aliasing !
Aliasing: signal ambiguity in frequency domain
(a),(b)Out-of-band noise can aliase into band of interest. Filter it before!
Different applications have different needs.
Imaging / video
NB: Definitions may be slightly manufacturer-dependent!
Continuous input signal digitized into 2N levels.
Uniform, bipolar transfer function (N=3)
Quantisation step q =
Ex: VFSR = 1V , N = 12 q = 244.1 V
Voltage ( = q)
Scale factor (= 1 / 2N )
Percentage (= 100 / 2N )
_ Telephone speech bandwidth 300hz-3.4khz
_Sound is audible in 20 Hz to 20 kHz range:
Ear + brain act as frequency analyser: audio spectrum split into many narrow bands low-power sounds detected out of loud background.