Download presentation

Presentation is loading. Please wait.

1
**ALARI/DSP INTRODUCTION-1**

Toon van Waterschoot & Marc Moonen Dept. E.E./ESAT, K.U.Leuven

2
**INTRODUCTION-1 : Who we are**

KU Leuven, Belgium Dept. of Electrical Engineering (ESAT): signal & system theory, micro- and nano-electronics, telecommunications, electrical energy, computer & document architecture, speech and image processing, … SCD (SISTA-COSIC-DOCARCH): system identification, signal processing, bio-informatics, cryptography, linear algebra, … DSP (Digital Signal Processing): digital audio and communications Research topics: acoustic echo and feedback cancellation, acoustic noise reduction, dereverberation, multicarrier communication, channel equalization, … Applications: hearing aids, public address systems, ADSL, wireless communication systems, … Toon van Waterschoot & Marc Moonen INTRODUCTION-1

3
**INTRODUCTION-1 : Course schedule**

Monday 14h h00: Introduction – Questions & Answers (Toon van Waterschoot) Tuesday 9h00 – 10h30: Lecture-1 (Marc Moonen) 11h h00: Exercise Session-1 (Toon van Waterschoot) 14h00 – 15h30: Lecture-2 (Marc Moonen) 16h h00: Exercise Session-2 (Toon van Waterschoot) Wednesday 9h00 – 10h30: Lecture-3 (Marc Moonen) 11h h00: Exercise Session-3 (Toon van Waterschoot) 14h00 – 15h30: Lecture-4 (Marc Moonen) 16h h00: Exercise Session-4 (Toon van Waterschoot) Thursday 9h00 – 10h30: Lecture-5 (Marc Moonen) 11h h00: Exercise Session-5 (Toon van Waterschoot) 14h00 – 15h30: Lecture-6 (Marc Moonen) 16h h00: Exercise Session-6 (Toon van Waterschoot) Friday 9h00 – 10h30: Lecture-7 (Marc Moonen) 11h h00: Exercise Session-7 (Toon van Waterschoot) 14h00 – 15h30: Lecture-8 (Marc Moonen) Toon van Waterschoot & Marc Moonen INTRODUCTION-1

4
**INTRODUCTION-1 : Course webpage**

Toon van Waterschoot & Marc Moonen INTRODUCTION-1

5
**INTRODUCTION-1 : Overview**

Discrete-time signals sampling, quantization, reconstruction Stochastic signal theory deterministic & random signals, (auto-)correlation functions, power spectra, … Discrete-time systems LTI, impulse response, FIR/IIR, causality & stability, convolution & filtering, … Complex number theory complex numbers, complex plane, complex sinusoids, circular motion, sinusoidal motion, … Toon van Waterschoot & Marc Moonen INTRODUCTION-1

6
**INTRODUCTION-2 : Overview**

z-transform and Fourier transform region of convergence, causality & stability, properties, frequency spectrum, transfer function, pole-zero representation, … Elementary digital filters shelving filters, presence filters, all-pass filters Discrete transforms DFT, FFT, properties, fast convolution, overlap-add/overlap-save, … Toon van Waterschoot & Marc Moonen INTRODUCTION-1

7
**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 Toon van Waterschoot & Marc Moonen INTRODUCTION-1

8
**Introduction: 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… Toon van Waterschoot & Marc Moonen INTRODUCTION-1

9
**Introduction: 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 Toon van Waterschoot & Marc Moonen INTRODUCTION-1

10
**Introduction: 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 Toon van Waterschoot & Marc Moonen INTRODUCTION-1

11
**Introduction: analog vs. digital SP**

Analog signal processing: “how things used to be” Analog world Analog electrical signal processing circuit Analog IN Analog OUT Toon van Waterschoot & Marc Moonen INTRODUCTION-1

12
**Introduction: analog vs. digital SP**

Digital signal processing in the analog world Analog world Digital world Analog world Analog-to- digital conversion Digital-to- analog conversion DSP Analog IN Digital IN Digital OUT Analog OUT Toon van Waterschoot & Marc Moonen INTRODUCTION-1

13
**Introduction: analog vs. digital SP**

Analog world Analog input: microphone voltage, satellite receiver voltage, … Analog output: loudspeaker voltage, antenna voltage, … VIN VOUT Toon van Waterschoot & Marc Moonen INTRODUCTION-1

14
**Introduction: analog vs. digital SP**

Digital signal processing in the analog world Analog world Digital world Analog world Analog-to- digital conversion Digital-to- analog conversion DSP Analog IN Digital IN Digital OUT Analog OUT Toon van Waterschoot & Marc Moonen INTRODUCTION-1

15
**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, … Toon van Waterschoot & Marc Moonen INTRODUCTION-1

16
**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 Toon van Waterschoot & Marc Moonen INTRODUCTION-1

17
**Introduction: design example**

Example: design of a “delay” audio effect Analog design: mixing operation Analog IN Analog OUT delay operation scaling operation Toon van Waterschoot & Marc Moonen INTRODUCTION-1

18
**Introduction: design example**

Example: design of a “delay” audio effect Digital design: x[k] y[k] y[k] = x[k] + K*y[k-D] mixing operation ADC DAC Analog IN Analog OUT delay operation write new sample buffer = {y[k], y[k-1], … y[k-D]} read delayed sample inside the DSP scaling operation K*y[k-D] Toon van Waterschoot & Marc Moonen INTRODUCTION-1

19
**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 Toon van Waterschoot & Marc Moonen INTRODUCTION-1

20
**INTRODUCTION-1 : Overview**

Discrete-time signals sampling, quantization, reconstruction Stochastic signal theory deterministic & random signals, (auto-)correlation functions, power spectra, … Discrete-time systems LTI, impulse response, FIR/IIR, causality & stability, convolution & filtering, … Complex number theory complex numbers, complex plane, complex sinusoids, circular motion, sinusoidal motion, … Toon van Waterschoot & Marc Moonen INTRODUCTION-1

21
**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 Toon van Waterschoot & Marc Moonen INTRODUCTION-1

22
**Discrete-time signals: sampling-quantization**

Analog signal processing Joseph Fourier ( ) Analog Domain (Continuous-Time Domain) Analog Signal Processing Circuit Analog IN Analog OUT (=Spectrum/Fourier Transform) Toon van Waterschoot & Marc Moonen INTRODUCTION-1 22

23
**Discrete-time signals: sampling-quantization**

Analog world Digital world Analog world Analog-to- digital conversion Digital-to- analog conversion DSP Analog IN Digital IN Digital OUT Analog OUT sampling quantization Toon van Waterschoot & Marc Moonen INTRODUCTION-1

24
**Discrete-time signals: sampling**

time-domain sampling amplitude amplitude discrete-time [k] continuous-time signal discrete-time signal impulse train continuous-time (t) It will turn out (page 27) 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 = Toon van Waterschoot & Marc Moonen INTRODUCTION-1

25
**Discrete-time signals: sampling**

spectrum replication time domain: frequency domain: magnitude magnitude frequency (f) frequency (f) Toon van Waterschoot & Marc Moonen INTRODUCTION-1

26
**Discrete-time signals: sampling**

sampling theorem the analog signal spectrum has a bandwidth of fmax Hz the spectrum replicas are separated with fs =1/Ts Hz no spectral overlap if and only if magnitude frequency Toon van Waterschoot & Marc Moonen INTRODUCTION-1

27
**Discrete-time signals: sampling**

sampling theorem: terminology: sampling frequency/rate fs Nyquist frequency fs/2 sampling interval/period Ts e.g. CD audio: fmax ¼ 20 kHz ) fs = 44,1 kHz Harry Nyquist (7 februari 1889 – 4 april 1976) 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 Toon van Waterschoot & Marc Moonen INTRODUCTION-1

28
**Discrete-time signals: quantization**

B-bit quantization quantized discrete-time signal =digital signal discrete-time signal amplitude discrete time [k] amplitude discrete time [k] Q 2Q 3Q -Q -2Q -3Q R Toon van Waterschoot & Marc Moonen INTRODUCTION-1

29
**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 Toon van Waterschoot & Marc Moonen INTRODUCTION-1

30
**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 fmax ¼ 20 kHz ) 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 Toon van Waterschoot & Marc Moonen INTRODUCTION-1

31
**Discrete-time signals: reconstruction**

Analog world Digital world Analog world Analog-to- digital conversion Digital-to- analog conversion DSP Analog IN Digital IN Digital OUT Analog OUT reconstruction Toon van Waterschoot & Marc Moonen INTRODUCTION-1

32
**Discrete-time signals: reconstruction**

reconstructor: ‘fill the gaps’ between adjacent samples e.g. staircase reconstructor: amplitude discrete time [k] amplitude continuous time (t) discrete-time/digital signal reconstructed analog signal Toon van Waterschoot & Marc Moonen INTRODUCTION-1

33
**Discrete-time signals: reconstruction**

ideal reconstructor: ideal (rectangular) low-pass filter no distortion magnitude frequency magnitude frequency staircase reconstructor: sync-like low-pass filter with sidelobes distortion due to spurious high frequencies magnitude frequency magnitude frequency Toon van Waterschoot & Marc Moonen INTRODUCTION-1

34
**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 Toon van Waterschoot & Marc Moonen INTRODUCTION-1

35
**Discrete-time signals: conclusion**

DSP system block scheme: Digital OUT x(t) Analog IN DSP Digital IN sampler quantizer anti-aliasing prefilter anti-image postfilter reconstructor Analog OUT xp(t) x[k] xQ[k] y[k] yR(t) y(t) Toon van Waterschoot & Marc Moonen INTRODUCTION-1

36
**INTRODUCTION-1 : Overview**

Discrete-time signals sampling, quantization, reconstruction Stochastic signal theory deterministic & random signals, (auto-)correlation functions, power spectra, … Discrete-time systems LTI, impulse response, FIR/IIR, causality & stability, convolution & filtering, … Complex number theory complex numbers, complex plane, complex sinusoids, circular motion, sinusoidal motion, … Toon van Waterschoot & Marc Moonen INTRODUCTION-1

37
**Stochastic signal theory: overview**

Signal types: deterministic signals random signals Correlation functions and power spectra: autocorrelation function & power spectrum cross-correlation function & cross-spectrum (joint) wide sense stationarity White noise: Gaussian white noise uniform white noise Toon van Waterschoot & Marc Moonen INTRODUCTION-1

38
**Stochastic signal theory: signal types**

Deterministic signals a deterministic signal is an explicit function of time, e.g. Random signals a random signal is ‘unpredictable’ in a sense some information on the signal behaviour may be available, e.g. probability density function (PDF) mean variance autocorrelation function … Toon van Waterschoot & Marc Moonen INTRODUCTION-1

39
**Stochastic signal theory: corr/spectra**

Autocorrelation function measure of the dependence between successive samples (with lag ) of a random signal Power spectrum measure of the frequency content of a random signal Fourier transform of the autocorrelation function Toon van Waterschoot & Marc Moonen INTRODUCTION-1

40
**Stochastic signal theory: corr/spectra**

Cross-correlation function measure of the dependence between successive samples (with lag ) of two different random signals Cross-spectrum measure of spectral overlap between two random signals Fourier transform of the cross-correlation function Toon van Waterschoot & Marc Moonen INTRODUCTION-1

41
**Stochastic signal theory: corr/spectra**

Wide-sense stationarity (WSS): a random signal is wide-sense stationary if its mean and autocorrelation function are independent of time: Joint wide-sense stationarity (joint WSS) two random signals are jointly wide-sense stationary if their cross-correlation function is independent of time: Toon van Waterschoot & Marc Moonen INTRODUCTION-1

42
**Stochastic signal theory: white noise**

a zero-mean white noise signal has an impulse autocorrelation function and a flat power spectrum: Gaussian white noise has a Gaussian PDF (Matlab function randn) uniform white noise has a uniform PDF (Matlab function rand) power power time frequency Toon van Waterschoot & Marc Moonen INTRODUCTION-1

43
**INTRODUCTION-1 : Overview**

Discrete-time signals sampling, quantization, reconstruction Stochastic signal theory deterministic & random signals, (auto-)correlation functions, power spectra, … Discrete-time systems LTI, impulse response, FIR/IIR, causality & stability, convolution & filtering, … Complex number theory complex numbers, complex plane, complex sinusoids, circular motion, sinusoidal motion, … Toon van Waterschoot & Marc Moonen INTRODUCTION-1

44
**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 Toon van Waterschoot & Marc Moonen INTRODUCTION-1

45
**Discrete-time systems: introduction**

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 … DSP sampler quantizer anti-aliasing prefilter anti-image postfilter reconstructor xp(t) x[k] xQ[k] y[k] yR(t) y(t) x(t) Toon van Waterschoot & Marc Moonen INTRODUCTION-1

46
**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 system output Toon van Waterschoot & Marc Moonen INTRODUCTION-1

47
**Discrete-time systems: LTI systems**

Linear time-invariant (LTI) systems: linearity: time-invariance: Toon van Waterschoot & Marc Moonen INTRODUCTION-1

48
**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 amplitude time 1 time 1 amplitude the impulse response length – 1 is equal to the order of the system Toon van Waterschoot & Marc Moonen INTRODUCTION-1

49
**Discrete-time systems: LTI systems**

Impulse response: if the impulse response is known, the system response to an arbitrary input signal can be calculated amplitude time 1 1 1 1 = + + 1 time 1 1 1 = + + Toon van Waterschoot & Marc Moonen INTRODUCTION-1

50
**Discrete-time systems: LTI systems**

FIR/IIR: FIR: finite impulse response IIR: infinite impulse response amplitude 1 time amplitude 1 time Toon van Waterschoot & Marc Moonen INTRODUCTION-1

51
**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 time time Toon van Waterschoot & Marc Moonen INTRODUCTION-1

52
**Discrete-time systems: LTI systems**

Stability: a system is said to be stable if a bounded input signal always generates a bounded output signal: a necessary and sufficient condition for stability is that the system impulse response be absolutely summable: instability can only occur with IIR systems Toon van Waterschoot & Marc Moonen INTRODUCTION-1

53
**Discrete-time systems: convolution**

amplitude 1 1 1 = + + 1 time 1 time 1 1 1 = + + Toon van Waterschoot & Marc Moonen INTRODUCTION-1

54
**Discrete-time systems: convolution**

the expression can be written in a more general form: this operation is called convolution of the system impulse response with the input signal shorthand notation: Toon van Waterschoot & Marc Moonen INTRODUCTION-1

55
**Discrete-time systems: convolution**

if we define: the impulse response length (with the system order) the input sequence length then the output sequence has length Toon van Waterschoot & Marc Moonen INTRODUCTION-1

56
**Discrete-time systems: convolution**

Direct form convolution: one way to perform the convolution of and is to directly calculate the summation this is done for all time indices an appropriate choice for the summation limits is: Toon van Waterschoot & Marc Moonen INTRODUCTION-1

57
**Discrete-time systems: convolution**

Matrix form convolution: another way to perform the convolution of and is by rewriting the summation as a matrix product the signal vectors and the impulse response matrix are defined as follows (with e.g. M=2 and L=4) Toon van Waterschoot & Marc Moonen INTRODUCTION-1

58
**INTRODUCTION-1 : Overview**

Discrete-time signals sampling, quantization, reconstruction Stochastic signal theory deterministic & random signals, (auto-)correlation functions, power spectra, … Discrete-time systems LTI, impulse response, FIR/IIR, causality & stability, convolution & filtering, … Complex number theory complex numbers, complex plane, complex sinusoids, circular motion, sinusoidal motion, … Toon van Waterschoot & Marc Moonen INTRODUCTION-1

59
**Complex number theory: overview**

Complex numbers: roots of a quadratic polynomial equation fundamental theorem of algebra complex numbers complex plane Complex sinusoids complex numbers complex sinusoids circular motion positive and negative frequencies sinusoidal motion Toon van Waterschoot & Marc Moonen INTRODUCTION-1

60
**Complex number theory: complex numbers**

“imaginary” roots of a polynomial equation Toon van Waterschoot & Marc Moonen INTRODUCTION-1

61
**Complex number theory: complex numbers**

roots of a quadratic polynomial equation: consider a quadratic polynomial, describing a parabola: the roots of the polynomial correspond to the points where the parabola crosses the horizontal -axis Toon van Waterschoot & Marc Moonen INTRODUCTION-1

62
**Complex number theory: complex numbers**

roots of a quadratic polynomial equation: if the polynomial has 2 real roots, and the parabola has 2 distinct intercepts with the -axis if the polynomial has 1 real root (with multiplicity 2), and the parabola has 1 intercept (tangent point) with the -axis if the polynomial has no real roots, and the parabola has no intercepts with the -axis p(x) x p(x) x p(x) x Toon van Waterschoot & Marc Moonen INTRODUCTION-1

63
**Complex number theory: complex numbers**

roots of a quadratic polynomial equation: alternatively, if we could say that the polynomial has 2 “imaginary roots”, and the parabola has 2 “imaginary” intercepts with the -axis these imaginary roots are represented as complex numbers: with p(x) x Toon van Waterschoot & Marc Moonen INTRODUCTION-1

64
**Complex number theory: complex numbers**

fundamental theorem of algebra: every n-th order polynomial has exactly n complex roots Toon van Waterschoot & Marc Moonen INTRODUCTION-1

65
**Complex number theory: complex numbers**

complex conjugate: modulus: argument: the complex numbers form a field, and all algebraic rules for real numbers also apply for complex numbers Toon van Waterschoot & Marc Moonen INTRODUCTION-1

66
**Complex number theory: complex numbers**

complex plane: the modulus and argument naturally lead to a radial representation in the complex plane Im Re complex plane Toon van Waterschoot & Marc Moonen INTRODUCTION-1

67
**Complex number theory: complex sinusoids**

complex variable complex sinusoid: from the radial representation we obtain replacing using Euler’s identity we get Toon van Waterschoot & Marc Moonen INTRODUCTION-1

68
**Complex number theory: complex sinusoids**

circular motion: a complex sinusoid can be seen as a vector which describes a circular trajectory in the z-plane Im z-plane Re Toon van Waterschoot & Marc Moonen INTRODUCTION-1

69
**Complex number theory: complex sinusoids**

positive and negative frequencies: for positive frequencies the circular motion is in counterclockwise direction for negative frequencies the circular motion is in clockwise direction Im Im Re Re Toon van Waterschoot & Marc Moonen INTRODUCTION-1

70
**Complex number theory: complex sinusoids**

sinusoidal motion: sinusoidal motion is the projection of circular motion onto any straight line in the z-plane, e.g., is the projection of onto the Re-axis is the projection of onto the Im-axis Im Re Toon van Waterschoot & Marc Moonen INTRODUCTION-1

71
**INTRODUCTION-2 : Overview**

z-transform and Fourier transform region of convergence, causality & stability, properties, frequency spectrum, transfer function, pole-zero representation, … Elementary digital filters shelving filters, presence filters, all-pass filters Discrete transforms DFT, FFT, properties, fast convolution, overlap-add/overlap-save, … Toon van Waterschoot & Marc Moonen INTRODUCTION-1

Similar presentations

OK

EE313 Linear Systems and Signals Fall 2010 Initial conversion of content to PowerPoint by Dr. Wade C. Schwartzkopf Prof. Brian L. Evans Dept. of Electrical.

EE313 Linear Systems and Signals Fall 2010 Initial conversion of content to PowerPoint by Dr. Wade C. Schwartzkopf Prof. Brian L. Evans Dept. of Electrical.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on dth service free download Ppt on bank lending limit Ppt on game theory five nights Ppt on arc welding process Free download ppt on modern periodic table Ppt on vegetarian and non vegetarian relationships Ppt on ram and rom history Display ppt online Ppt on business plan for nurse Ppt on introduction to object-oriented programming language