Bài giảng Digital Signal Processing - Chapter 0: Introduction - Nguyen Thanh Tuan

Nội dung text: Bài giảng Digital Signal Processing - Chapter 0: Introduction - Nguyen Thanh Tuan

1. Chapter 0 Introduction Nguyen Thanh Tuan, ClickM.Eng. to edit Master subtitle style Department of Telecommunications (113B3) Ho Chi Minh City University of Technology Email: nttbk97@yahoo.com
2. 1. Signal and System  Signal processing is to pass a signal through a system.  A digital system can be implemented as a combination of hardware and software (program, algorithm). Digital Signal Processing 3 Introduction
3. 2. Classification of Signals Continuous-time versus discrete-time signal  Signals can be classified into four different categories depending on the characteristics of the time variable and the values they take. Time Continuous Discrete Amplitude x(t) x(n) Continuous t n Analog signal Discrete signal xQ(t) 111 xQ(n) 110 101 100 Discrete 011 t 010 n 001 Quantized signal 000 Digital signal Digital Signal Processing 5 Introduction
4. 4. DSP applications-Communications  Telephony: transmission of information in digital form via telephone lines, modem technology, mobile phone.  Encoding and decoding of the information sent over physical channels (to optimize transmission, to detect or correct errors in transmission) Digital Signal Processing 7 Introduction
5. 4. DSP applications-Biomedical  Analysis of biomedical signals, diagnosis, patient monitoring, preventive health care, artificial organs.  Examples:  Electrocardiogram (ECG) signal provides information about the condition of the patient’s heart.  Electroencephalogram (EEG) signal provides information about the activity of the brain. Digital Signal Processing 9 Introduction
6. 4. DSP applications-Image Processing  Content based image retrieval: browsing, searching and retrieving images from database.  Image enhancement  Compression: reducing the redundancy in the image data to optimize transmission/storage Digital Signal Processing 11 Introduction
7. The Journey “Learning digital signal processing is not something you accomplish; it’s a journey you take”. R.G. Lyons, Understanding Digital Signal Processing Digital Signal Processing 13 Introduction
8. Course overview  Chapter 0: Introduction to Digital Signal Processing (3 periods)  Chapter 1: Sampling and Reconstruction (6 periods)  Chapter 2: Quantization (3 periods)  Chapter 3: Analysis of linear time invariant systems (LTI) (6 periods)  Chapter 4: Finite Impulse Response and convolution (3 periods)  Chapter 5: Z-transform and its applications (6 periods)  Chapter 6: Transfer function and filter realization (3 periods)  Chapter 7: Fourier transform and FFT algorithm (6 periods)  Chapter 8: FIR and IIR filter designs (6 periods)  Review and mid-term exam: 3 periods Digital Signal Processing 15 Introduction
9. Learning outcomes  Understand how to convert the analog to digital signal  Have a thorough grasp of signal processing in linear time-invariant systems.  Understand the z-transform and Fourier transforms in analyzing the signal and systems.  Be able to design and implement FIR and IIR filters. Digital Signal Processing 17 Introduction
10. Assessment Điểm ghi trên Bảng điểm kiểm tra, Bảng điểm thi và Bảng điểm tổng kết được làm tròn đến 0,5. (từ 0 đến dưới 0,25 làm tròn thành 0; từ 0,25 đến dưới 0,75 làm tròn thành 0,5; từ 0,75 đến dưới 1,0 làm tròn thành 1,0) Nếu điểm thi nhỏ hơn 3 và nhỏ hơn điểm tổng kết tính từ các điểm thành phẩn (kể cả điểm thi) thì lấy điểm thi làm điểm tổng kết. Digital Signal Processing 19 Introduction
11. Review of complex number  Rectangular form: z x iy Argand diagram Cartesian coordinates  Real part: xr cos Polar  Imaginary part: yr sin coordinates i  Euler’s formula: ei cos sin i  Polar form: z re r  22  Absolute value (modulus, magnitude): r ||z x y (−π , π] 1 y  Argument (angle):  arg(z ) tan x Digital Signal Processing 21 Introduction
12. Review of special functions  Rectangular (rect)  Cardinal sine (sinc)  Unnormalized:  Normalized: Digital Signal Processing 23 Introduction
13. Review of special functions  Dirac comb (impulse train, sampling function):  Properties: Digital Signal Processing 25 Introduction
14. Review of Fourier transforms 1 cos(2 F t ) FT [  ( F F )  ( F F )] 02 0 0 1 sin(2 F t ) FT j [  ( F F )  ( F F )] 02 0 0 Digital Signal Processing 27 Introduction
15. Review of trigonometric formulas 1 cos(a )cos( b ) [cos( a b ) cos( a b )] 2 1 sin(a )sin( b ) [cos( a b ) cos( a b )] 2 1 sin(a )cos( b ) [sin( a b ) sin( a b )] 2 Digital Signal Processing 29 Introduction
16. Review of convolution and correlation  Convolution:  Correlation:  Auto-correlation: Digital Signal Processing 31 Introduction
17. Review of analog filters  Decibel: |A|dB = 20log10|A|  Logarithmic scales:  Decade: decades = log10(F2/F1)  Octave: octaves = log2(F2/F1)  Cut-off (-3dB) frequency  Bandwidth Digital Signal Processing 33 Introduction
18. Bonus 1  Write a program generating tones of an 88-key piano in twelve-tone equal temperament with A440 standard. Digital Signal Processing 35 Introduction
19. Bonus 3  Write a program plotting the waveform of signal below. Digital Signal Processing 37 Introduction
20. Greek alphabet Digital Signal Processing 39 Introduction
21. Portraits of Scientists and Inventors  Heinrich Rudolf Hertz (1857-1894) was a German physicist who first conclusively proved the existence of electromagnetic waves.  Alexander Graham Bell (1847-1922) was an eminent Scottish- born scientist, inventor, engineer and innovator who is credited with inventing the first practical telephone. Digital Signal Processing 41 Introduction
22. Homework 2  For each case below, find the modulus and argument (both in radian and degree): 1) e^(i ) 2) e^(i /2) 3) e^(–i /2) 4) e^(i /4) 5) e^(i /2) + e^(i /4) 6) 1/e^(i /4) 7) e^(i /4) / e^(–i /4) 8) e^(i /4) + e^(–i /4) 9) e^(i /4) – e^(–i /4) 10) 1 + e^(i /2) 11) 1 – e^(i /2) 12) (2 – 3i). e^(i /4) Digital Signal Processing 43 Introduction
23. Homework 4  For each case below, sketch the waveform of the signal: 1) x(t) = 4sin(2t) (t:s) 2) x(t) = 4sin(2 t) (t:s) 3) x(t) = 4cos(2 t) (t:s) 4) x(t) = 4cos(10 t) (t:s) 5) x(t) = 4cos(10 t) (t:ms) 6) x(t) = 1 + 4cos(10 t) (t:s) 7) x(t) = 4cos(2 t) + 4cos(10 t) (t:s) 8) x(t) = 4sin2(2 t) (t:s) 9) x(t) = 4sinc(2t) (t:s) 10) x(t) = 4{(t – 3)/2} 11) x(t) = k{4{(t – k5 – 3)/2}} 12) x(t) = 4(t – 3) – 3(t + 4) Digital Signal Processing 45 Introduction
24. Homework 6  Suppose a filter has magnitude response as shown in figure below. Determine the expression (ignoring the phase) of the output signal and plot it’s magnitude response for each case of the input signal: 1) x(t) = 2 2) x(t) = 2cos(2 t) (t:ms) 3) x(t) = 2cos(20 t) (t:ms) 4) x(t) = 2cos(200 t) (t:ms) 5) x(t) = 2cos(400 t) (t:ms) 6) x(t) = 2cos2(400 t) (t:ms) 7) x(t) = 2cos(200 t).sin(400 t) (t:ms) 8) x(t) = 2cos(200 t) – 2cos(400 t) (t:ms) 9) x(t) = 2cos(200 t) + 2sin(400 t) (t:ms) 10) x(t) = 2cos(200 t) + 2sin(200 t) (t:ms) Digital Signal Processing 47 Introduction
25. Homework 8 2  Cho các tín hiệu tương tự x1(t) = 2cos 2πt (t: s) và x2(t) = 6sin6πt + 7cos7πt + 8sin8πt (t:s) lần lượt đi qua hệ thống tuyến tính bất biến có hàm truyền H(f) như hình: a) Xác định biểu thức (theo thời gian) của tín hiệu ngõ ra y1(t). b) Tính giá trị của tín hiệu ngõ ra y2(t = 0.125s). Digital Signal Processing 49 Introduction
26. Homework 10  Cho bộ lọc thông thấp có đáp ứng biên độ phẳng 0dB trong khoảng [0  4]KHz, suy giảm với độ dốc 12dB/octave trong khoảng [4  8]KHz và suy giảm với độ dốc 20dB/decade ngoài 8KHz. Tìm giá trị đáp ứng biên độ của bộ lọc tại các tần số sau: a) 2KHz. b) 3KHz. c) 5KHz. d) 6KHz. e) 7KHz. f) 8KHz. g) 10KHz. h) 12KHz. i) 16KHz. j) 20KHz. Digital Signal Processing 51 Introduction