Week 1 Introduction of Digital Signal Processing with the review of SMJE 2053 Circuits & Signals for Filter Design

Transcription

1 SMJE3163 DSP2016_Week1-04 Week 1 Introduction of Digital Signal Processing with the review of SMJE 2053 Circuits & Signals for Filter Design 1) Signals, Systems, and DSP 2) DSP system configuration 3) Applications of DAP 4) Review of Discrete-time systems 1

2 1) Signals, Systems, and DSP Signal Signals convey some information through its physical variation pattern. Signal Processing Digital Signal Processing: concerns with the representation, transformation, manipulation of signals and the extraction of the information containing signals. Processing of analog signals by digital computer/ devices. Benefits Flexibility, High Reliability, Consistency of DSP 2

3 Speech sound waveforms /a, あ / sound /I, い / sound 物理量の変化パターンを通じて 情報を担うもの

4 Amplitude Types of Signals Time Continuous-Time Discrete-Time Continuous- Value Discrete-Value

5 Amplitude Types of Signals Time Continuous-Time Discrete-Time Continuous- Value Analog Signal Discrete-Time Signal Discrete-Value Digital Signal

6 2) DSP system Configurations analog signal ADC Digital Computer DAC analog signal ADC: Analog Digital Converter DAC: Digital Analog Converter DSP System TYPE 1: Manipulate input signal to generate output signal

7 time index A-D Converter analog signal * n * During the value is hold constant, the value is quantized and converted it to binary code. [Tan-Ch.2] series of binary codes

8 Quantization and Binary Code Generation Binary code Q(x) Δ/2-5Δ/2-3Δ/2 3Δ 2Δ Δ -Δ/2 Δ/2 -Δ -2Δ -3Δ -4Δ 3Δ/2 5Δ/2 x Δ:quantization step size Characteristics of bipolar quantization (rounding)

9 D-A Converter DA Conversion Binary Code n Decoding zeroorderhold Smooth -ing filter analog signal series of binary codes DAC interpolates the values between the sampled values. Stair case reconstruction followed by the smoothing filter is most commonly used

10 Discrete-Time System Input x(n) Discrete-Time System Output y(n) Sample-by sample processing: The output sample y(n) is computed, when the input x(n) is available at the input, and the computation has to be completed before the next sample x(n+1) appears at the input port.

11 Other DSP System Configurations analog signal A/D Converter Digital Computer Processed results Send to / Display / Pattern Recognition etc. DSP TYPE 2: Manipulating signal to get (estimate) parameters which characterize the input signal. No DAC device. Digital Computer DAC analog signal DSP TYPE 3: Computer generates analog output signal No ADC system, for example?

12 3) Applications of DSP Tasks of DSP: Filtering/Separation Enhancement of target signal Noise Cancellation Spectrum Estimation Characterization of Signals for pattern recognition Data Reduction without losing signal quality 12

13 Fields of DSP Application Consumer/Commercial/Multi-Media Audio-Speech/ Image/ Video Processing Communication System Medical/Bio Science Industrial Use Scientific Analysis Military/Radar Sonar etc. Space 13

14 Separation of Speech Signals Mixed signal Microphone array system Experiment movie Separated voices by Microphone Array System

15 Processing by Microphone array

16 Mobile Robot Microphone array (Keio Univ. Hamada & Nakazawa Labs 2012)

17 Specific Speaker Tracking under Noisy environment

18 Super-resolution image reconstruction Real sequence of images Acquired 20 Images: Super Resolution Image

19 4) Review: Discrete-time Systems 4-1) Description of LTI discrete-time systems Difference equation, Block diagram Impulse (Unit-Sample) Response System function 4-2) Frequency Response Amplitude and Phase characteristics LTI: Linear Time-Invariant

20 4-1 Description of discrete-time systems Difference equation (1 st order system) Input signal (sequence) x(n) Discrete-Time System Output Signal y(n) Ex. 1) Non-recursive System y n = b 0 x n + b 1 x n 1 + b 2 x n 2 (1.1) Ex. 2) Recursive System y n = ay n 1 + b 0 x n + b 1 x n 1 (1.2)

21 Block diagram: Three basic operations: Unit delay, Multiplier (Gain), Adder (Sum) b z 1 + (a) unit delay (b) Multiplier (Gain) b (c) Adder (Sum) Σ

22 Block diagram of system (1.1) x(n) z 1 x(n-1) z 1 x(n-2) b 0 b 1 b y(n)

23 Block diagram of system (1.2) x(n) b y(n) z 1 z 1 x(n-1) y(n-1) b 1 a

24 Impulse (Unit-Sample) Response characterizes discrete-time system completely. This means that the output for any input can be computed by using solely impulse response. Unit impulse function 1, n = 0 δ n = 0, n 0 unit impulse δ(n) Discrete-Time System Impulse response h(n) Exercise 1 Compute the impulse response sequence of systems of Ex.1) and Ex.2) respectively, and then find the length of impulse responses.

25 The Impulse (Unit-Sample) Response δ n : unit sample h(n): Impulse (unit-sample) response n = 0 n n = 0 n Due to linearity property, if one knows the unitsample response of an LTI system one can compute system s response to any input. Copyright 2014 McGraw-Hill Education. Permission required for reproduction or display

26 Q.1 Find the impulse Response from the difference eq. (1.1) n<0 h(n)=0, n=0 h(0)=b 0, n=1 h(1)=b 1, n=2 h(2)=b 2, n 3 h(n)=0 Since the length of above response is finite, this type of system is referred to as finite impulse response (FIR) system/filter. Q.2 Find the impulse Response from the difference eq. (1.2) n<0 h(n)=0, n=0 h(0)=b 0, n=1 h(1)=a b 0 + b 1 n=2 h(2)=a(ab 0 + b 1 ), n=3 h(3)=a 2 (a b 0 + b 1 ),. endless, Since the length of this impulse is finite, this type of system is referred to as infinite impulse response (IIR) system/filter.

27 System/Transfer function: The ratio of input and output in the z-domain z-transform: X z = n= n= x n z n System function: Y z H z = X z System functions of Ex.1) and Ex.2) are given by: Ex1) H z = b 0 + b 1 z 1 + b 2 z 2 (1.3) Ex2) H z = b 0+b 1 z 1 1 az 1 (1.4)

28 4-2 Frequency Response Definition: The complex-valued gain H e jω input e jωn of the system for the e jωn Discrete-Time System H e jω e jωn Frequency response can be found from the system function H z by H e jω = H z z=e jω (1.5)

29 The polar form of frequency response gives the magnitude response A Ω and the phase response θ Ω. H e jω = A Ω e jθ Ω (1.6) Q. 3 Compute the frequency response of system (1.1) with the parameters, b 0 =1, b 1 =2, b 2 =1. Solution: Substituting the parameters into (1.3) gives H z = 1 + 2z 1 + z 2 (1.7) and H e jω = 1 + 2e jω + e j2ω (1.8) = e jω e jω +2 + e jω = e jω 2 + 2cosΩ (1.9)

30 18.3 The Frequency Response H(ω) Definition LTI system x n = e jωn H(ω) y n = H(ω)e jωn H ω : frequency response of the system. DTFT of the unit-sample response h(n) of the system, It can be found from the system function H(z)

31 18.3 The Frequency Response H(e jω ) Definition LTI system x n = e jωn H(e jω ) y n = H(e jω )e jωn H ω : frequency response of the system. DTFT of the unit-sample response h(n) of the system, It can be found from the system function H(z)

32 The magnitude of H e jω is A Ω = H e jω = cosω (1.10), and the phase response of H e jω is θ Ω = H e jω = Ω (1.11) Q. 4 Compute the frequency response of system (1.1) with the parameters, b 0 = -1, b 1 =2, b 2 =-1. Solution: Substituting the parameters into (1.3) gives H z = 1 + 2z 1 z 2 (1.12) and H e jω = 1 + 2e jω e j2ω (1.13) = e jω e jω +2 e jω = e jω 2 2cosΩ (1.14)

33 Magnitude Response π 0 Ω Ω Phase Response[rad] System (1.1) with b 0 = 1, b 1 = 2, b 2 = 1

34 5 Magnitude Response 4 3 Phase Response[rad] π Ω Ω System (1.1) with b 0 = 1, b 1 = 2, b 2 = 1

35 4 グラフタイトル : input sequence : output sequence

36 Output Response by Frequency Response Graph Q. 5 Find a rough output signal of the system (1.1) with b 0 = 1, b 1 = 2, b 2 = 1 when the input is: x n = cos 2π 3 n

37 What s Next (week2 class)? In Week 2 & 3, we focus Filter Design Methods in the discrete-time domain. Relationship between characteristics of discrete-time signal processing and overall analog system 37

38 Summary of Week 1 Course Outline, Weekly Schedule We discussed: what is DSP, what benefits it brings, Broad fields of DSP application Review of Discrete-time System for Filter Design 38