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מכללת BITLEE

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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מכללת BITLEE

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  1. מכללת BITLEE קורס DSP יישומי לתעשיה

  2. DSP- Digital Signal Processing

  3. FROM ANALOG TO DIGITAL DOMAIN 25 March 2004

  4. TOPICS • 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

  5. 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 Analog & digital signals

  6. 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 vs analog proc’ing Digital Signal Processing (DSPing)

  7. 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 DSPing: aim & tools

  8. What is DSP? 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

  9. What is DSP? • 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

  10. What is DSP Used For? …And much more!

  11. DATA VIDEO AUDIO DSP Technology & Markets VOICE

  12. 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 Digital system example

  13. 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 Digital system implementation KEY DECISION POINTS: Analysis bandwidth, Dynamic range •Sampling rate. • Pass / stop bands. • No. of bits. Parameters.

  14. 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. Sampling How fast must we sample a continuous signal to preserve its info content? Why? Frequency misidentification due to low sampling frequency.

  15. Lowpass Spectrum f -fmax fmax Bandpass Spectrum f –f1 f2 –f2 f1 Generalized Sampling Theorem • 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

  16. 1 __ s(t) = sin(2f0t) s(t) @ fS f0 = 1 Hz, fS = 3 Hz __ s1(t) = sin(8f0t) __ s2(t) = sin(14f0t) s(t) @ fS represents exactly all sine-waves sk(t) defined by: sk (t) = sin( 2 (f0 + k fS) t ) , k  Sampling - 2

  17. 1 Example Condition on fS? F1 F2 F3 fS > 300 Hz F1=25 Hz, F2 = 150 Hz, F3 = 50 Hz fMAX The sampling theorem 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

  18. 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 Sampling low-pass signals

  19. 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) Antialiasing filter

  20. 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! (Some) ADC parameters

  21. 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 ADC - Number of bits N

  22. Digital Telephony PCM (Pulse Code Modulation) • Standard telephone signal: _ Telephone speech bandwidth 300hz-3.4khz • Sampling Rate: 8 kHz • 8-bit samples • Data transfer rate = 88= 64kbits/s (64kbps) • ATU-TI G711

  23. Digital Audio • 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 = 21644,100 = 1.4 Mbits/s • 1 hour of music = 1.43,600 = 635 MB

  24. 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. Frequency domain (hints) • Time & frequency: two complementary signal descriptions. Signals seen as “projected’ onto time or frequency domains.

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