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 signals Continuous function continuous Continuous function V of continuous variable t (time, space etc) : V(t). Analog Discrete function discrete Discrete function V k of discrete sampling variable t k, with k = integer: V k = V(t k ). Digital Uniform (periodic) sampling. Sampling frequency f S = 1/ t S

6. Digital vs analog proc’ing Digital Signal Processing (DSPing) More flexible. Often easier system upgrade. Data easily stored. Better control over accuracy requirements. Noise reduction. 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!). Limitations

7. DSPing: aim & tools Software Programming languages: Pascal, C / C++... “High level” languages: Matlab, Mathcad, Mathematica… Dedicated tools (ex: filter design s/w packages). Applications Predicting a system’s output. Implementing a certain processing task. Studying a certain signal. General purpose processors (GPP),  -controllers. Digital Signal Processors (DSP). Programmable logic ( PLD, FPGA ). Hardware real-time DSPing FastFaster

8. What is DSP? Digital Signal Processing – the processing or manipulation of signals using digital techniques ADCDAC Digital Signal Processor Analogue to Digital Converter Digital to Analogue Converter Input Signal Output Signal

9. 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 What is DSP?

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

11. VIDEO AUDIO DATA VOICE DSP Technology & Markets

12. Digital system example ANALOG DOMAIN Filter Antialiasing DIGITAL DOMAIN A/D Digital Processing ANALOG DOMAIN D/A Filter Reconstruction Sometimes steps missing - Filter + A/D - D/A + filter General scheme Topics of this lecture. Digital Processing Filter Antialiasing A/D

13. Digital system implementation Sampling rate. Pass / stop bands. KEY DECISION POINTS: Analysis bandwidth, Dynamic range No. of bits. Parameters. 1 23 Digital Processing A/D Antialiasing Filter ANALOG INPUT DIGITAL OUTPUT Digital format. What to use for processing? See slide “DSPing aim & tools”

14. Sampling How fast must we sample a continuous signal to preserve its info content? Ex: train wheels in a movie. 25 frames (=samples) per second. Frequency misidentification due to low sampling frequency. Train starts wheels ‘go’ clockwise. Train accelerates wheels ‘go’ counter-clockwise. 1Why? * Sampling: independent variable (ex: time) continuous  discrete. Quantisation: dependent variable (ex: voltage) continuous  discrete. Here we’ll talk about uniform sampling.*

15. Generalized Sampling Theorem Sampling rate must be greater than twice the analog signal’s bandwidth –Bandwidth is defined as non-zero extent of spectrum of the continuous-time signal in positive frequencies –Lowpass spectrum on right: bandwidth is f max –Bandpass spectrum on right: bandwidth is f 2 – f 1 Bandpass Spectrum f1f1 f2f2 f –f2–f2 –f1–f1 Lowpass Spectrum f max -f max f

16. Sampling - 2 __ s(t) = sin(2  f 0 t) s(t) @ f S f 0 = 1 Hz, f S = 3 Hz __ s 1 (t) = sin(8  f 0 t) __ s 2 (t) = sin(14  f 0 t) s k (t) = sin( 2  (f 0 + k f S ) t ),  k   s(t) @ f S represents exactly all sine-waves s k (t) defined by: 1

17. The sampling theorem A signal s(t) with maximum frequency f MAX can be recovered if sampled at frequency f S > 2 f MAX. Condition on f S ? f S > 300 Hz F 1 =25 Hz, F 2 = 150 Hz, F 3 = 50 Hz F1F1 F2F2 F3F3 f MAX Example 1 Theo * * Multiple proposers: Whittaker(s), Nyquist, Shannon, Kotel’nikov. Nyquist frequency (rate) f N = 2 f MAX or f MAX or f S,MIN or f S,MIN /2 Naming gets confusing !

18. Sampling low-pass signals Sampling low-pass signals (a) Band-limited signal: frequencies in [-B, B] (f MAX = B). (a) (b) Time sampling frequency repetition. f S > 2 B no aliasing. (b) 1 (c) aliasing ! (c) f S 2 B aliasing ! Aliasing: signal ambiguity in frequency domain

19. Antialiasing filter Filter it before! (a),(b) Out-of-band noise can aliase into band of interest. Filter it before! (a) (b) (c) Passband : depends on bandwidth of interest. Attenuation A MIN : depends on ADC resolution ( number of bits N). A MIN, dB ~ 6.02 N + 1.76 Out-of-band noise magnitude. Antialiasing filter (c) Antialiasing filter 1

20. (Some) ADC parameters (Some) ADC parameters 1.Number of bits N (~resolution) 2.Data throughput (~speed) 3.Signal-to-noise ratio (SNR) 4.Signal-to-noise-&-distortion rate (SINAD) 5.Effective Number of Bits (ENOB) 6.Spurious-free dynamic range (SFDR) 7.Integral non-linearity (INL) 8.Differential non-linearity (DNL) 9.… NB: Definitions may be slightly manufacturer-dependent! Different applications have different needs. 2 Static distortion Dynamic distortion Imaging / video Communication Radar systems

21. ADC - Number of bits N Continuous input signal digitized into 2 N levels. Uniform, bipolar transfer function (N=3) Quantisation step Quantisation step q = V FSR 2 N Ex: V FSR = 1V, N = 12 q = 244.1  V LSB Voltage ( = q) Scale factor (= 1 / 2 N ) Percentage (= 100 / 2 N ) Quantisation error 2

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. Frequency domain (hints) Frequency domain (hints)  Time & frequency  Time & frequency : two complementary signal descriptions. Signals seen as “projected’ onto time or frequency domains. 1  Bandwidth  Bandwidth : indicates rate of change of a signal. High bandwidth signal changes fast. Ear Ear + brain act as frequency analyser: audio spectrum split into many narrow bands low-power sounds detected out of loud background. Example