Carleton University SYSC-4405 Digital Signal Processing Winter 2015

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(1)S Y S C. 4 4 0 5 D i g i t a l. S i g n a l. P r o c e s s i n g. I n t r o d u c t i o n _ W n i n t e r 2 0 1 5 . f m. Carleton University SYSC-4405 Digital Signal Processing Winter 2015. Instructor. Prof. Mohamed El-Tanany Department of Systems and Computer Engineering Room # MC7082 Tel 613-520-5739 E-mail: [email protected]. 1 / 22.

(2) S Y S C. 4 4 0 5 D i g i t a l. S i g n a l. P r o c e s s i n g. I n t r o d u c t i o n _ W n i n t e r 2 0 1 5 . f m. Signals, Systems and Signal Processing Some Definitions A signal is defined as any physical quantity that varies with time, space or any other independent variable or variables. Mathematically we describe a signal as a function of one or more independent variables. Some signals are deterministic and can be described precisely by an equation; others are random and can not be easily described in closed form. Natural signals are of the latter kind. Examples include speech, electrocardiogram (ECG) and EEG signals. This latter kind can sometimes be represented mathematically using a superposition of sine waves. Signal generation is usually associated with a system that responds to a stimulus or force. The stimulus in combination with the system is called a signal source. Thus we have audio sources, image sources and various other types of signal sources. A system may be defined as a physical device that performs an operation on a signal. Example for this is a filter used to reduce the noise corrupting an information bearing signal. When we pass the signal through a system, as in filtering, we say that we have processed the signal. In broader terms, a system may be viewed as a physical device or software realization of operations on a signal. In the latter case we have a signal processing system realized in software. This course deals with the processing of signals by digital means, either in software or hardware. Since many of the signals encountered in real life are analog in nature, we will need to consider the problem of conversion from analog to digital.. 2 / 22.

(3) S Y S C. 4 4 0 5 D i g i t a l. S i g n a l. P r o c e s s i n g. I n t r o d u c t i o n _ W n i n t e r 2 0 1 5 . f m. Basic elements of a DSP system Most of the signals encountered in science and engineering are analog in nature; The signal amplitude changes in a continuous fashion. As an example a speech signal changes as a continuous variable that is defined at all instants of time Such signals may be processed in their analog form using an analog system.. Analog input signal. Analog signal processor. Analog output signal. Analog Signal Processing Digital signal processing provides an alternative way to process the analog signal. To perform the processing digitally, there is a need for an interface between the analog source and the digital processor & between the digital processor and the end user in most cases.. 3 / 22.

(4) S Y S C. 4 4 0 5 D i g i t a l. S i g n a l. P r o c e s s i n g. A/D converter. Analog input signal. I n t r o d u c t i o n _ W n i n t e r 2 0 1 5 . f m. digital signal processor. Digital input signal. D/A converter. Digital output signal. Analog output signal. Block diagram of a digital signal processing system. The digital signal processing system may be a large programmable digital computer, a small microprocessor programmed to perform the desired digital operations or a hard wired logic system. The D/A converter is required in cases where the output has to be given to an end user in analog form as in voice communication for example. However, in some applications the D/A converter is not needed; example is the digital processing of radar signals, or processing for purposes of speaker or speech recognition.. 4 / 22.

(5) S Y S C. 4 4 0 5 D i g i t a l. S i g n a l. P r o c e s s i n g. I n t r o d u c t i o n _ W n i n t e r 2 0 1 5 . f m. Some Advantages of Digital Signal Processing Signal Storage Analog signals are stored on analog media such as tapes Digital signals are stored on digital media such as CD’s or memories. What happens if you make a copy of a copy.of a copy of a VCR tape (analog)?. Original. noise. copy3. copy2. copy1. noise. noise. Noise eventually destroys the signal What happens if you make a copy of a copy of a copy of a CD (digital)? verify. verify. verify. Error check. Error check. Error check. Perfect duplicate is possible. 5 / 22.

(6) S Y S C. 4 4 0 5 D i g i t a l. S i g n a l. P r o c e s s i n g. I n t r o d u c t i o n _ W n i n t e r 2 0 1 5 . f m. Analog radio versus digital radio? Analog radio: always have a signal but it may have static Digital radio: either perfect signal or completely wrong signal Digital Transmission (wired media) Normal copper phone lines only use frequencies from 0 -4000 Hz. Therefore, copper wires have been tuned for optimal transmission for 0 – 4000 Hz. Though not “crystal clear”, extra signal capacity is available past 4000 Hz. How to use this extra capacity for high speed communication? Have modem that equalizes signal powers above 4000 Hz through your old copper phone lines so that data can be transmitted reliably. Analog Solution (for equalization): Would require a custom modem (i.e., custom equalizer) to be designed and built for every phone line and would eventually have to be replaced as the copper line continued to age. DSP Solution (DSL - Digital Subscriber Line): Allows modem to measure the copper line's frequency response and perform adaptive equalization so that it will maximize the line throughput.. 6 / 22.

(7) S Y S C. 4 4 0 5 D i g i t a l. S i g n a l. P r o c e s s i n g. I n t r o d u c t i o n _ W n i n t e r 2 0 1 5 . f m. Analog & Digital Comparison The processing accuracy of analog processors is dependent on the tolerance of discrete components and electronics thermal noise, while the accuracy of digital systems is controlled by A/D resolution, word size and sampling clock frequency. Here are some details: Parameter. Analog Processing. Digital processing. Component Tolerances. 1-10%. 0.003%. Sensitivities “Drift”. Time and Temperature. None (apart from clock frequency). Noise Floor. 60 dB Typical (thermal). 90+ dB (quantization). Adaptability. Hard & Expensive. Easy & Low Cost. Volume Manufacturing. Hand Tuning. Automatic Tuning. Redesign. New Board. New Code. Layout. Noise Sensitive. Less sensitive. Advanced Functions. Hardware Intensive. Additional Software. Multi-Functions. Multiple Hardware. More MIPS & Software. Power and Size. larger. More likely to be smaller. Reliability. Lower. Higher. 7 / 22.

(8) S Y S C. 4 4 0 5 D i g i t a l. S i g n a l. P r o c e s s i n g. I n t r o d u c t i o n _ W n i n t e r 2 0 1 5 . f m. Typical DSP System. analog to digital converter. digital input. analog input ADC. LPF. analog output. XINTF. Digital Signal Processor. Lowpass filters. DAC. LPF. Ser Pt. Ser Pt. HPI. digital to analog converter digital output. Memory. Host. 8 / 22.

(9) S Y S C. 4 4 0 5 D i g i t a l. S i g n a l. P r o c e s s i n g. I n t r o d u c t i o n _ W n i n t e r 2 0 1 5 . f m. Learning Outcomes. By the end of this course students should be able to . ∙ ∙ ∙ ∙ ∙ ∙. Describe and analyze discrete time signals in the time and frequency domains. Apply digital signal processing techniques to design discrete time systems. Design digital filters, meeting given specifications, using windowing techniques. Design digital filters using transformation techniques from analog designs. Use the Discrete Fourier Transform (DFT) and the FFT for the analysis of arbitrary signals. Program digital signal processing algorithms in MATLAB. 9 / 22.

(10) S Y S C. 4 4 0 5 D i g i t a l. S i g n a l. P r o c e s s i n g. I n t r o d u c t i o n _ W n i n t e r 2 0 1 5 . f m. Some DSP Definitions. Digital Signal Processing Processing of real world signals (represented by a sequence of numbers) using mathematical techniques to perform transformations or to extract information. Digital Signal Processor A device or a system which performs digital signal processing functions. Analog Signals Real-world signals; e.g. light, sound, temperature, pressure. Digital Signal Numerical representation of the analog signal. Real-Time DSP Processing keeps pace with the input and output signals. Non-Real-Time DSP Processing is performed off-line; i.e. the data is stored and processed at a later time.. 10 / 22.

(11) S Y S C. 4 4 0 5 D i g i t a l. S i g n a l. P r o c e s s i n g. I n t r o d u c t i o n _ W n i n t e r 2 0 1 5 . f m. Some DSP Applications Consumer applications digital cellular, digital TV, digital audio broadcasting, Internet phones, music players & recorders, digital cameras etc. Military & Specialized uses secure communication, radar processing, sonar processing, beam forming, air traffic control, missile guidance, etc. Security systems finger print identification, facial and/or voice recognition, speaker identification and others. Image Processing pattern recognition, robotic vision, image enhancement, satellite weather map, animation etc. Telecommunication equipment echo cancellation, adaptive equalization, video conferencing, digital transmission etc. Biomedical patient monitoring, EEG brain mappers, ECG analysis, X-ray storage/enhancement Instrumentation & control spectrum analysis, position and rate control, noise reduction, data compression. 11 / 22.

(12) S Y S C. 4 4 0 5 D i g i t a l. S i g n a l. P r o c e s s i n g. I n t r o d u c t i o n _ W n i n t e r 2 0 1 5 . f m. Specialized Speech/audio applications speech recognition, speech synthesis, text-to-speech, digital audio, equalization, speaker verification, stereo/surround sound, 3D sound generation and localization, audio mixing Some Examples Speech Coding Sample every T seconds. Uniform Quantizer. 100010111001011. PCM data. 32 Subbands. Filter Bank. 576 freq lines. MDC T. Psychoacoustic Model. Distortion Control Loop& Bit Allocation. Huffman Encoder Coding of Side Information. Bit Stream Formatting. PCM Encoder. Bit Stream. Block Diagram of an MP3 Encoder. 12 / 22.

(13) S Y S C. 4 4 0 5 D i g i t a l. S i g n a l. P r o c e s s i n g. I n t r o d u c t i o n _ W n i n t e r 2 0 1 5 . f m. Active noise cancellation. DAC. Input MIC. Preamp. DAC. AGC. error MIC. AUDIO CODEC. Preamp. DIGITAL SIGNAL PROCESSOR. .. AGC. Active Noise Canceller. Cancelling speaker. Power amp. 13 / 22.

(14) S Y S C. 4 4 0 5 D i g i t a l. S i g n a l. P r o c e s s i n g. I n t r o d u c t i o n _ W n i n t e r 2 0 1 5 . f m. Medical imaging. Magnetic Resonance Imaging (MRI). Magnet RF COILS RF Detector and Amplifier. AMP. A/D. Digital Signal Proc.. RF COILS Magnet. Pulse Generation & Magnetic Field Control. 14 / 22.

(15) S Y S C. 4 4 0 5 D i g i t a l. S i g n a l. P r o c e s s i n g. I n t r o d u c t i o n _ W n i n t e r 2 0 1 5 . f m. DSP Supporting Algorithms Modulation, demodulation and channel equalization Data Compression + Decompression & Data encryption Rate reduction algorithms for audio and video encoding (and appropriate decoding algorithms) Voice/ image recognition algorithms Voice and audio/music synthesis Noise cancellation and noise reduction Spectral analysis/ estimation Underlying Functions FIR (Finite Impulse Response) Filters.. Xin. z-1. a0. z-1. a1. z-1. a2. z-1. a3. a4. yout y  n  = a0 x  n  + a1 x  n – 1  + a2 x  n – 2  + a3 x  n – 3  + a4 x  n – 4 . 15 / 22.

(16) S Y S C. 4 4 0 5 D i g i t a l. S i g n a l. P r o c e s s i n g. I n t r o d u c t i o n _ W n i n t e r 2 0 1 5 . f m. IIR (Infinite Impulse Response) Filters. b0. y(n). x(n). –1. -a1. z-1. -a2. z-1. b1. b2. –2. b0 + b1 z + b2 z H  z  = ---------------------------------------------- .................................................Transfer Function –1 –2 1 + a1 z + a2 z N. yn = –. M.  ak y  n – k  +  bk x  n – k  .........................Difference Equation k=1. k=0. 16 / 22.

(17) S Y S C. 4 4 0 5 D i g i t a l. S i g n a l. P r o c e s s i n g. I n t r o d u c t i o n _ W n i n t e r 2 0 1 5 . f m. The filter coefficients {a1, a2,...} and {b0, b1, b2,....} determine the type of response to be expected. Design procedures make it possible to design IIR filters with conventional frequency responses such as Butterworth and Chebychev. Discrete Fourier Transform (DFT) N–1. Xk =. . j2kn x  n  exp  – ---------------  N . Definition. n=0. where n is a time index, and k is a frequency index Discrete Time/ discrete frequency equivalent of the Fourier transform TIME DOMAIN. FREQUENCY DOMAIN. 2 1. 0.5. 0 -1 -2. 0. 10. 20. 30. 40. 50. 60. 0.4. 1 0.5. 0.3. 0 -0.5 -1. 0. 10. 20. 30. 40. 50. 60. 0.2. 1 0.5. 0.1 0 -0.5 -1. 0. 10. 20. 30. 40. 50. 60. 0. 0. 10. 20. 30. 40. 50. 60. The DFT and other transforms such as the DCT have many uses in audio and video low-rate coding and decoding algorithms.Used extensively in instruments such as spectrum analyzers. 17 / 22.

(18) S Y S C. 4 4 0 5 D i g i t a l. S i g n a l. P r o c e s s i n g. I n t r o d u c t i o n _ W n i n t e r 2 0 1 5 . f m. Also used for modulation, demodulation and frequency domain equalization algorithms in data transmission equipment. Fast Fourier Transform (FFT) Special case of the Discrete Fourier Transform when the number of points is a power of a small integer such as 2 or 4, and has the advantage of lower computational complexity. 18 / 22.

(19) S Y S C. 4 4 0 5 D i g i t a l. S i g n a l. P r o c e s s i n g. I n t r o d u c t i o n _ W n i n t e r 2 0 1 5 . f m. How is this course organized by comparison to the prerequisite courses such as sysc-3600?. Analog vs. Discrete-time linear Systems Analog. Discrete. Signal Type. Analog. Digital. Time Domain Representation. Differential equations. Difference equations N. yn = –. M.  ak y  n – k  +  bk x  n – k  k=1. Transform Domain. k=0. Laplace Transform for system design & transient response analysis. Z-Transform to study system properties, transient responses and system design. Fourier Transform for analysis in the steady state. DFT/ FFT: analysis in the steady N–1. state. X k =. -  x  n  exp  – -------------N  ·. j2kn. n=0. Basic building blocks Applications. Integrator, differentiator, analog multiplier, adders, sign inverter. unit delay, multiplier, adder, sign inverter Digital Filters (IIR and FIR), design and implementation Spectral Analysis based on the DFT and FFT. 19 / 22.

(20) S Y S C. 4 4 0 5 D i g i t a l. S i g n a l. P r o c e s s i n g. I n t r o d u c t i o n _ W n i n t e r 2 0 1 5 . f m. Grading To pass the course, a student must pass the final examination, the term work, and obtain an overall passing average (assignments /labs plus midterm plus final exam). For students who pass the final exam, the final grade will be calculated as follows: Assignments: 20% Laboratories: 15% Midterm Test1: 7.5% Midterm Test2: 7.5% Final Examination: 50%. The final examination papers are for evaluation purposes only and will not be returned to the students. 20 / 22.

(21) S Y S C. 4 4 0 5 D i g i t a l. S i g n a l. P r o c e s s i n g. I n t r o d u c t i o n _ W n i n t e r 2 0 1 5 . f m. Main Topics Signal Representation Special sequences including unit impulse, unit step, complex exponential and sinusoidal sequences. Sampling, Shannon’s sampling theorem and the Nyquist rate signal representations in the time and frequency domains, and the relation between the continuous and discrete time versions of a signal. Modeling and analysis of linear time invariant systems Properties of Linear time invariant systems Time domain analysis based on difference equations Impulse response and frequency response Transfer functions (based on z-transform) Analysis in the transform domain. Transforms Z-transform and its applications for modeling, analysis and design of LTI systems Discrete Time Fourier Transform (DTFT), Discrete Fourier Transform (DFT) & Fast Fourier Transform (FFT) and their uses for spectral analysis. 21 / 22.

(22) S Y S C. 4 4 0 5 D i g i t a l. S i g n a l. P r o c e s s i n g. I n t r o d u c t i o n _ W n i n t e r 2 0 1 5 . f m. Finite Impulse Response Filters Structures, properties and applications Frequency responses Design procedures Infinite Impulse Response Filters Analog filter theory IIR filters structures, properties and applications Frequency responses Design procedures. 22 / 22.

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