1 / 56

Digital Signal Processing 2 Les 1: Inleiding 1

Digital Signal Processing 2 Les 1: Inleiding 1. Prof. dr. ir. Toon van Waterschoot Faculteit Industriële Ingenieurswetenschappen ESAT – Departement Elektrotechniek KU Leuven, Belgium. Onderzoeksafdeling.

shino
Download Presentation

Digital Signal Processing 2 Les 1: Inleiding 1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Digital Signal Processing 2Les 1: Inleiding 1 Prof. dr. ir. Toon van WaterschootFaculteit Industriële IngenieurswetenschappenESAT – Departement ElektrotechniekKU Leuven, Belgium

  2. Onderzoeksafdeling • STADIUSCentrum voorDynamischeSystemen, Signaalverwerking en Data-Analyse: • DynamischeSystemen:identificatie, optimalisatie, regeltechniek, systeemtheorie • Signaalverwerking: spraak- & audioverwerking, digitalecommunicatie, biomedischesignaalverwerking • Data-Analyse: machine learning, bio-informatica • AdvISe– Advanced Integrated Sensing Lab: • Biomedisch:biomedischetechnologie,ambient assisted living • Audio:akoestischemodellering, audio-analyse, akoestischesignaalverbetering • Chip-ontwerp:stralingshardeelektronica

  3. Onderzoekstopics • Audio signal analysis • speech recognition • event detection • source localization • audio classification • Acoustic modeling • ear modeling • room modeling • loudspeaker modeling • signal modeling • Acoustic signal enhancement • noise reduction • echo/feedback control • room equalization

  4. Contactgegevens Toon van Waterschoot • Mail: toon.vanwaterschoot@esat.kuleuven.be • Kantoor (enkel op maandag + donderdag): KU Leuven Campus Geel, lokaal P220

  5. Digital Signal Processing 2: Vakinhoud • Les 1: Inleiding 1 (Discrete signalen en systemen) • Les 2: Inleiding 2 (Wiskundige concepten) • Les 3: Spectrale analyse • Les 4: Elementair filterontwerp • Les 5: Schattingsproblemen • Les 6: Lineaire predictie • Les 7: Optimale filtering • Les 8: Adaptieve filtering • Les 9: Detectieproblemen • Les 10: Classificatieproblemen • Les 11: Codering • Les 12: Herhalingsles

  6. Digital Signal Processing 2: Lesmateriaal • Slides • slides = basis lesmateriaal • vakinhoudverschiltgrondig van vorigejaren! • slides wordenenkeledagenvoorelke les op Toledo geplaatst • Cursustekst • geenvastecursustekst • voor de meeste lessen wordtereenhoofdstukuiteen (Engelstalig) boek of eenartikel op Toledo geplaatst

  7. Digital Signal Processing 2: Labo • Doel: Implementieaspecten van DSP + implementatieproject op TMS320C5515 DSP • Docent: Peter Karsmakers (peter.karsmakers@kuleuven.be) • Uurrooster: 13 x 2u (wekelijks op woensdagochtend)

  8. Digital Signal Processing 2: Examen • Examenvormtheorie: • mondeling met schriftelijkevoorbereiding • open of geslotenboek (terbespreking met collega-docenten) • Puntenverdeling: eindcijfer= gewogengemiddelde van theorie- en praktijkexamens DSP-1 en DSP-2 • DSP-1: 34% • DSP-1 practicum: 12% • DSP-2: 34% • DSP-2: practicum: 20%

  9. Digital Signal Processing 2: Vakinhoud • Les 1: Inleiding 1 (Discrete signalen en systemen) • Les 2: Inleiding 2 (Wiskundige concepten) • Les 3: Spectrale analyse • Les 4: Elementair filterontwerp • Les 5: Schattingsproblemen • Les 6: Lineaire predictie • Les 7: Optimale filtering • Les 8: Adaptieve filtering • Les 9: Detectieproblemen • Les 10: Classificatieproblemen • Les 11: Codering • Les 12: Herhalingsles

  10. Les 1: Inleiding 1 • Introduction motivation, examples • Discrete-time signals sampling, quantization, reconstruction • Discrete-time systems LTI, impulse response, FIR/IIR, causality & stability, convolution & filtering, …

  11. Les 1: Literatuur • Introduction • Discrete-time signals S. J. Orfanidis, Introduction to Signal Processing • Ch. 1, “Sampling and Reconstruction” • Ch. 2, “Quantization” M. H. Hayes, Statistical Digital Signal Processing and Modeling • [summary] Ch. 2, Section 2.2.1 • Discrete-time systems S. J. Orfanidis, Introduction to Signal Processing • Ch. 3, “Discrete-Time Systems” • Ch. 4, “FIR Filtering and Convolution” M. H. Hayes, Statistical Digital Signal Processing and Modeling • [summary] Ch. 2, Sections 2.2.2, 2.2.3

  12. Les 1: Inleiding 1 • Introduction motivation, examples • Discrete-time signals sampling, quantization, reconstruction • Discrete-time systems LTI, impulse response, FIR/IIR, causality & stability, convolution & filtering, …

  13. Introduction: overview • Digital signal processing? • Analog vs. digital signal processing • Example: design of a delay audio effect • in the analog world • in the digital world

  14. Introduction: digital signal processing? Digital signal processing? • Signal: a physical quantity which varies as a function of some independent variable(s) • 1-dimensional: sound signal (mechanical/electrical), electromagnetic signal (wired/wireless), chemical concentration, … • 2-dimensional: image • … • N-dimensional: … • Independent variable: time, position, frequency, … here…

  15. Introduction: digital signal processing? Digital signal processing? • Processing: altering the signal characteristics to improve signal quality • equalization: to undo the (frequency-selective) effect of passing the signal through a system (channel) • noise reduction: to remove noise/interference • signal separation: to separate multiple signals which are present in one measurement • modulation: to prepare a signal for being transmitted through a frequency-selective channel • … • Processing ~ Filtering

  16. Introduction: digital signal processing? Digital signal processing? • Digital: the signal processing is performed by a finite number of operations using a finite number of digits • discretization of independent variable: the signal is sampled w.r.t. the (continuous) independent variable (e.g., discrete time, discrete frequency, …) • discretization of signal value: the signal value (amplitude) is approximated on a discrete scale (quantization) • Bits: digital signals are often represented using binary digits = bits

  17. Introduction: analog vs. digital SP Analogsignal processing: “how things used to be” Analog world Analog electrical signal processing circuit Analog IN Analog OUT

  18. Introduction: analog vs. digital SP Digital signal processing in the analog world Analog world Digital world Analog world Digital-to- analog conversion Analog-to- digital conversion 0110100101 1001100010 DSP Analog IN Digital IN Digital OUT Analog OUT

  19. Introduction: analog vs. digital SP • Analog world • Analog input: microphone voltage, satellite receiver voltage, … • Analog output: loudspeaker voltage, antenna voltage, … VIN 0 VOUT 0

  20. Introduction: analog vs. digital SP Digital signal processing in the analog world Analog world Digital world Analog world Digital-to- analog conversion Analog-to- digital conversion 0110100101 1001100010 DSP Analog IN Digital IN Digital OUT Analog OUT

  21. Introduction: analog vs. digital SP • Digital world • Digital signal processor (DSP): microprocessor designed particularly for signal processing operations, incorporated in sound card, modem, mobile phone, mp3 player, digital camera, digital tv, hearing aid, …

  22. Introduction: design example • Goal: design and implement an audio effect which mixes a scaled and delayed version of an audio signal to the original signal Example: design of a “delay” audio effect mixing operation Analog IN Analog OUT scaling operation delay operation

  23. Introduction: design example Example: design of a “delay” audio effect • Analog design: mixing operation Analog IN Analog OUT delay operation scaling operation

  24. Introduction: design example Example: design of a “delay” audio effect • Digital design: y[k] x[k] mixing operation y[k] = x[k] + K*y[k-D] ADC DAC Analog IN Analog OUT write new sample  buffer = {y[k], y[k-1], … y[k-D]}  read delayed sample delay operation • inside • the DSP scaling operation K*y[k-D]

  25. Introduction: design example Example: design of a “delay” audio effect • Analog design: • design of analog circuits • manufacturing of print board • assembly of analog components • Digital design: • design of digital algorithm • compilation on digital signal processor circuit design  algorithm design application-specific hardware  re-usable hardware

  26. Les 1: Inleiding 1 • Introduction motivation, examples • Discrete-time signals sampling, quantization, reconstruction • Discrete-time systems LTI, impulse response, FIR/IIR, causality & stability, convolution & filtering, …

  27. Discrete-time signals: overview • A/D conversion: sampling and quantization • time-domain sampling & spectrum replication • sampling theorem • anti-aliasing prefilters • quantization • oversampling and noise shaping • D/A conversion: reconstruction • ideal vs. realistic reconstructors • anti-image postfilters • Conclusion: DSP system block scheme

  28. Discrete-time signals: sampling-quantization Analogsignal processing Joseph Fourier (1768-1830) Analog Domain (Continuous-Time Domain) Analog Signal Processing Circuit Analog IN Analog OUT (=Spectrum/Fourier Transform)

  29. Discrete-time signals: sampling-quantization Analog world Digital world Analog world Digital-to- analog conversion Analog-to- digital conversion 0110100101 1001100010 DSP Analog IN Digital IN Digital OUT Analog OUT sampling quantization

  30. amplitude impulse train discrete-time [k] Discrete-time signals: sampling • time-domain sampling amplitude continuous-time signal discrete-time signal 0 1 2 3 4 continuous-time (t) It will turn out that a spectrum can be computed from x[k], which (remarkably) will be equal to the spectrum (Fourier transform) of the (continuous-time) sequence of impulses =

  31. Discrete-time signals: sampling • spectrum replication • time domain: • frequency domain: magnitude magnitude frequency (f) frequency (f)

  32. Discrete-time signals: sampling • sampling theorem • the analog signal spectrum has a bandwidth of fmaxHz • the spectrum replicas are separated with fs=1/Ts Hz • no spectral overlap if and only if magnitude frequency

  33. Discrete-time signals: sampling • sampling theorem: • terminology: • sampling frequency/rate fs • Nyquist frequency fs/2 • sampling interval/period Ts • e.g. CD audio: • anti-aliasing prefilters: • if then frequencies above the Nyquist frequency will be ‘folded back’ to lower frequencies = aliasing • to avoid aliasing, the sampling operation is usually preceded by a low-pass anti-aliasing filter Harry Nyquist (7 februari 1889 – 4 april 1976)

  34. amplitude amplitude 3Q 2Q Q R 0 -Q -2Q -3Q discrete time [k] discrete time [k] Discrete-time signals: quantization • B-bit quantization quantized discrete-time signal =digital signal discrete-time signal

  35. Discrete-time signals: quantization • B-bit quantization: • the quantization error can only take on values between and • hence can be considered as a random noise signal with range • the signal-to-noise ratio (SNR) of the B-bit quantizer can then be defined as the ratio of the signal range and the quantization noise range : = the “6dB per bit” rule

  36. Discrete-time signals: quantization • oversampling: • it is possible to make a trade-off between sampling rate and quantization noise • using a ‘coarse’ quantizer may be compensated by sampling at a higher rate = oversampling • e.g. an increasing number of audio recordings is done at a sampling rate of 96 kHz (while ) • noise shaping: • the quantization noise is typically assumed to be white • the noise spectrum may be altered to decrease its disturbing effect = noise shaping • e.g. psycho-acoustic noise shaping in audio quantizing

  37. Discrete-time signals: reconstruction Analog world Digital world Analog world Digital-to- analog conversion Analog-to- digital conversion 0110100101 1001100010 DSP Analog IN Digital IN Digital OUT Analog OUT reconstruction

  38. amplitude amplitude discrete time [k] continuous time (t) Discrete-time signals: reconstruction • reconstructor: • ‘fill the gaps’ between adjacent samples • e.g. staircase reconstructor: discrete-time/digital signal reconstructed analog signal

  39. magnitude magnitude magnitude magnitude frequency frequency frequency frequency Discrete-time signals: reconstruction • ideal reconstructor: • ideal (rectangular) low-pass filter • no distortion • staircase reconstructor: • sync-like low-pass filter • with sidelobes • distortion due to • spurious high • frequencies

  40. Discrete-time signals: reconstruction • anti-image postfilter: • low-pass filter to remove spurious high frequency components due to imperfect reconstruction • comparable to the anti-aliasing prefilter

  41. Analog IN Analog OUT x(t) y(t) xp(t) x[k] xQ[k] y[k] yR(t) anti-aliasing prefilter anti-image postfilter DSP sampler quantizer reconstructor Digital IN Digital OUT Discrete-time signals: conclusion DSP system block scheme:

  42. Les 1: Inleiding 1 • Introduction motivation, examples • Discrete-time signals sampling, quantization, reconstruction • Discrete-time systems LTI, impulse response, FIR/IIR, causality & stability, convolution & filtering, …

  43. Discrete-time systems: overview • Introduction: • discrete-time systems • I/O behaviour • LTI systems: • linear time-invariant systems • impulse response • FIR/IIR • causality • stability • Convolution: • direct form • matrix form

  44. x(t) y(t) xp(t) x[k] xQ[k] y[k] yR(t) anti-aliasing prefilter anti-image postfilter DSP sampler quantizer reconstructor Discrete-time systems: introduction • discrete-time systems: • any system implemented on a digital signal processor: • discrete-time model of continuous-time system, e.g. • wireless channel in mobile communications • twisted pair telephone line • acoustic echo channel between loudspeaker and microphone • …

  45. system Discrete-time systems: introduction • input/output (I/O) behaviour: • mapping of input sequence on output sequence: • the output signal is a function of the input signal: input output

  46. system Discrete-time systems: LTI systems • Linear time-invariant (LTI) systems: • linearity: • time-invariance: input output

  47. amplitude amplitude 1 1 0 time 0 time Discrete-time systems: LTI systems • Impulse response: • LTI systems are characterized uniquely by their impulse response = the system output in response to a unit impulse input signal • the impulse response length – 1 is equal to the order of the system

  48. amplitude 1 1 1 1 0 time 0 0 0 1 1 1 1 0 time 0 0 0 Discrete-time systems: LTI systems • Impulse response: • if the impulse response is known, the system response to an arbitrary input signal can be calculated = + + = + +

  49. Discrete-time systems: LTI systems • FIR/IIR: • FIR: finite impulse response • IIR: infinite impulse response amplitude 1 time 0 amplitude 1 time 0

  50. Discrete-time systems: LTI systems • Causality: • a causal system has an impulse response that is zero for all negative time indices • a non-causal system has an impulse response that has some non-zero coefficients on the negative time axis, i.e. the system output depends on future input values amplitude amplitude 1 1 0 time 0 time

More Related