디지털신호처리 DIGITAL SIGNAL PROCESSING

1. DSP Introduction 디지털신호처리DIGITAL SIGNAL PROCESSING 전남대학교 공과대학 전자컴퓨터공학부 김진영 2010.3.

2. 왜 DSP인가? : 통신의 역사 1 1150 homing pigeon 490 BC heliograph 1790 semaphore lines 19C signal lamp

3. 왜 DSP인가? : 통신의 역사 2 정낭: 3bits • 우리나라의 통신 봉화

4. 왜 DSP인가? : 통신의 역사 2 1895년 마르코니(Marconi)는 최초의 무선 시스템을 시작하였다. 마르코니의 초기 spark-gap 송신기는 매우 낮은 주파수에서부터 단파대 이상 까지의 넓은 스펙트럼을 점유하였으며 이들 시스템은 수동으로 시간 도메인에서 모르스 부호를 사람들이 송·수신함으로써 동작하였다.

5. 왜 DSP인가? Battle against Noise All communications circuits contain some noise. This is true whether the signals are analog or digital, and regardless of the type of information conveyed. Noise is the eternal bane of communications engineers, who are always striving to find new ways to improve the signal-to-noise ratio in communications systems. Traditional methods of optimizing S/N ratio include increasing the transmitted signal power and increasing the receiver sensitivity. (In wireless systems, specialized antenna systems can also help.) Digital signal processing dramatically improves the sensitivity of a receiving unit. The effect is most noticeable when noise competes with a desired signal. A good DSP circuit can sometimes seem like an electronic miracle worker. But there are limits to what it can do. If the noise is so strong that all traces of the signal are obliterated, a DSP circuit cannot find any order in the chaos, and no signal will be received.

6. Contents • DSP definition and application • Frequency and sinusoids • Discrete time signals • BasicDSP operations • Discrete time systems • DSP system

7. DSP 정의 및 응용 Digital Signal • What is Signal? • Any physical quantities that varies with time, space or any other independent variable • Carriers of information • Classification of signals • Scalar vs. vector • Continuous-time vs. discrete-time • Continuous-valued vs. discrete-valued • Deterministic vs. random • Digital Signal=discrete-time+discrete-valued

8. DSP 정의 및 응용 System and Signal processing • System • a Physical device that performs an operation on a signal : Extracting or enhancing the useful information from a mix of conflicting information • Signal processing • Any operation on signal : software and hardware • Digital Signal Processing : any operation on digital signal

9. DSP 정의 및 응용 Why DSP • Guaranteed accuracy: better control of accuracy requirements • Perfect reproducibility • Stable processing capability: no drift in performance with temperature or age • Greater flexibility • Superior performance • Cheaper • Portability: using software running

10. DSP 정의 및 응용 Disadvantage of DSP • Speed • Bandwidths in the 100MHz range is still processed only by analogue device • Design time • Quantization error • Finite wordlength effect

11. DSP Category Digital Signal Analysis Digital filter ∙Removal of unwanted background noise ∙Removal of interference ∙Separation of frequency bands ∙Shaping of the signal spectrum ∙Spectrum analysis ∙Speech Recognition ∙Speaker verification ∙Target detection

12. DSP 정의 및 응용 Application • Image processing: pattern recognition, robotic vision, image enhancement, facsimile, satellite weather map, animation • Instrumentation/control: spectrum analysis, position and rate control, noise reduction, data compression • Speech/Audio: speech recognition, speech synthesis, digital audio, equalization • Military: secure communication, radar & sonar processing, missile guidance • Telecommunications: echo cancellation, adaptive equalization, codec, spread spectrum, video conference, data communication • Biomedical : patient monitoring, scanners, EEG brain mapers, ECG analysis, X-ray storage/enhancement • Etc

13. 주파수 개념 및 삼각함수들 Frequency? • Definition • 1. Physics: The rate at which a repeating event occurs, such as the full cycle of a wave. Frequencies are usually measured in hertz. Compare amplitude. See also period. • 2. Mathematics: The ratio of the number of occurrences of some event to the number of opportunities for its occurrence.

14. 주파수 개념 및 삼각함수들 Why sinusoids? • The most basic signals in the theory of signals and systems • Sinusoidal function is an eigen-function of the linear system

15. 주파수 개념 및 삼각함수들 Continuous/discrete-time sinusoidal signal • Continuous-time • Discrete-time

16. 주파수 개념 및 삼각함수들 Continuous/discrete-time sinusoidal signal

17. 주파수 개념 및 삼각함수들 Phasor 1 • Phasor vector: a representation of a sine wave whose amplitude(A), phase(θ) and frequency(ω) • Rotating phasor interpretation • Phasor addition

18. 주파수 개념 및 삼각함수들 Phasor 2 • Phasor arithmetic • Scalar multiplication • Differentiation and integration • addition

19. 주파수 개념 및 삼각함수들 Phasor 3 http://en.wikipedia.org/wiki/Phasor_(electronics)

20. 이산-시간 신호 Types of Sequence • Unit sample sequence • Unit step function • Real-valued exponential sequence • (Geometric series) • Complex-valued exponential sequence • Sinusoidal sequence • Random sequence • Periodic sequence

21. 이산-시간 신호 Some useful sequence • Unit sample synthesis • Even and odd synthesis

22. 주요 DSP 조작 DSP Operation 1 • Signal addition • Signal multiplication • Scaling • Time shifting and advancing • Sample summation • Sample product • Signal energy and power (signal measure)

23. 주요 DSP 조작 DSP Operation 2 • Convolution • Correlation • Digital filter • Discrete transform: discrete Fourier transform • Modulation: digital modulation

24. Discrete time system Properties of discrete time system1 • Static v.s dynamic systems • Static: memoryless • Dynamic: memory • Time-invariant vs. time-variant systems • (Def) Time-invariant(shift invariant) iff x(n)→y(n) implies that x(n-k) →y(n-k) for every input signal x(n) and every time shift • (test) y(n,k)=H[x(n-k)] if y(n,k)=y(n-k) for all possible k: time invariant

25. Discrete time system Properties of discrete time system 2 • (Ex) time-multiplier • Linear vs. nonlinear systems • (Def) A system H is linear iff H[a1x1 (n)+a2x2 (n)]=a1H[x1 (n)]+a2H[x2 (n)]

26. Discrete time system Properties of discrete time system 3 • Causal vs. noncausal systems • (Def) causal if the output of the system at any time n depends only on present and post inputs; y(n)=F[x(n),x(n-1),x(n-2),….] • (ex) y(n)=x(-n): noncausal • Stable vs. unstable system • (Def) Bounded input-bound output(BIBO) iff every bounded input produces a bounded output;

27. Discrete time system Properties of discrete time system 4 • Invertible linear system • (TH) L:X→Y be an invertible linear transformation of X onto Y, where X, Y are linear spaces, then L-1 is linear • (proof)

28. Discrete time system Linear System 1 • General linear system • Linear time-invariant (LTI) system: an input-output pair, x(n) and y(n), is invariant to shift in time n.

29. Discrete time system Linear System 2 • Why difference equations: • Difference equations: An LTI system can be described by a linear constant coefficient difference equation of the form.

30. Digital signal processing system Block diagram of DSP system • A/D conversion • DSP • DA conversion Block diagram of a simplified, generalized real-time digital signal processing system

31. Digital signal processing system Analog-to-digital conversion process 1 • A/D process • The (band limited) signal is first sampled in time (t=nT, x(nT)→x(n)) • The amplitude of each signal sample is quantized into one of 2B levels • The discrete amplitude levels are represented or encoded into distinct binary words each of length B bits

32. Digital signal processing system Sampling 1 • Sampling • Sampling theorem: If the highest frequency contained in an analog signal xa(t) is Fmax=B and the signal is sampled at a rate Fs≥2fmax=2B, then xa(t) can be exactly recovered from its sample values using the interpolation function g(t)=(sin2πBT)/(2πBT). Thus xa(t) may be expressed as where xa(n/Fs)=xa(nT)=x(n) are the samples of xa(t). http://en.wikipedia.org/wiki/File:Sinc_function_(normalized).svg

33. Digital signal processing system Sampling 2 • Xs(f)=XaⓧP(f) where P(f) is periodic signal in frequency domain with period Fs, because • If Fs<Fmax, aliasing occurs. • If Fs<Fmax, anti-aliasing filters are necessary.

34. Digital signal processing system Sampling 3

35. Digital signal processing system Sampling 4 205x250 pixels (Moire pattern of bricks) 622x756 pixels

36. Digital signal processing system Quantization and encoding 1 • Linear quantization • v(t)=(Vfs/2)sinωt=Asinωt • Quantization step=q=Vfs(2B-1)≈Vfs/2B=2A/2B • Quantization error • Signal-to-quantization noise power ratio(SQNR)

37. Digital signal processing system Quantization and encoding 2 Quantization of a signal for 4bit PCM

38. Digital signal processing system Digital-to-analog conversion process: Signal recovery 1 • Basic idea: Because there is no ideal low pass filter, the perfect reconstruction is impossible and the impulse signal is not possible in real world • (참조) • Real implementation • Anti-imaging filter: Attenuate the high frequency image spectrum(post-filter)

39. Digital signal processing system Digital signal processing system Digital-to-analog conversion process: Signal recovery 2 • (참조) • Zero-order hold(ZOH) interpolation

40. Digital-to-analog conversion process: Signal recovery 3 • First-order-hold(FOH) interpolation