Basics of digital signal processing ppt

block diagram of digital signal processing ppt and digital signal processing basics ppt
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Published Date:26-07-2017
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Basics on Digital Signal Processing Introduction Vassilis Anastassopoulos Electronics Laboratory, Physics Department, University of Patras Outline of the Course 1. Introduction (sampling – quantization) 2. Signals and Systems 3. Z-Transform 4. The Discreet and the Fast Fourier Transform 5. Linear Filter Design 6. Noise 7. Median Filters 2/36 Analog & digital signals Analog Digital Discrete function V of k Continuous function V Sampled discrete sampling of continuous variable t Signal variable t , with k = k (time, space etc) : V(t). integer: V V(t ). k = k 0.3 0 0..3 3 0.2 0 0..2 2 0.1 0 0..1 1 0 0 0 -0.1 t t -0.1 -0.1 s s -0.2 - -0 0..2 2 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 s sa am mp plliin ng g t tiim me e,, t t m ms s time ms k k Uniform (periodic) sampling. Sampling frequency f = 1/ t S S 3/36 Voltage V V Vo olltta ag ge e V VAnalog & digital systems 4/36 Digital vs analog processing Digital Signal Processing (DSPing) Limitations Advantages • A/D & signal processors speed: • More flexible. wide-band signals still difficult to • Often easier system upgrade. treat (real-time systems). • Data easily stored -memory. • Finite word-length effect. • Better control over accuracy requirements. • Reproducibility. • Linear phase • No drift with time and temperature 5/36 DSPing: aim & tools • Predicting a system’s output. Applications • Implementing a certain processing task. • Studying a certain signal. • General purpose processors (GPP), -controllers. Fast • Digital Signal Processors (DSP). Hardware real-time DSPing Faster • Programmable logic ( PLD, FPGA ). • Programming languages: Pascal, C / C++ ... Software • “High level” languages: Matlab, Mathcad, Mathematica… • Dedicated tools (ex: filter design s/w packages). 6/36 Related areas 7/36 Applications 8/36 Important digital signals Unit Impulse or Unit Sample. δ(n-3)Τ δ(nT ) s s The most important signal for two reasons δ(n)=1 for n=0 nΤ past s u(nT ) s Unit Step u(n)=1 for n0 δ(n)=u(n)-u(n-1) nΤ past s r(nT ) s Unit Ramp r(n)=nu(n) nΤ past s 9/36 ANALOG DIGITAL ANALOG DOMAIN DOMAIN DOMAIN Digital system example V General scheme ms Filter Filter Antialiasing V Antialiasing Sometimes steps missing ms A/D - Filter + A/D A A/D (ex: economics); k Digital - D/A + filter Processing A (ex: digital output wanted). Digital Processing k D/A V ms Topics of this Filter V lecture. Reconstruction ms 10/36 Digital system implementation KEY DECISION POINTS: ANALOG INPUT Analysis bandwidth, Dynamic range Antialiasing • Pass / stop bands. Filter 1 • Sampling rate. A/D 2 • No. of bits. Parameters. Digital 3 • Digital format. Processing What to use for processing? DIGITAL OUTPUT 11/36 AD/DA Conversion – General Scheme 12/36 AD Conversion - Details 13/36 Sampling 14/36 1 Sampling How fast must we sample a continuous signal to preserve its info content? Ex: train wheels in a movie. 25 frames (=samples) per second. Train starts wheels ‘go’ clockwise. Train accelerates wheels ‘go’ counter-clockwise. Why? Frequency misidentification due to low sampling frequency. 15/36 Rotating Disk How fast do we have to instantly stare at the disk if it rotates with frequency 0.5 Hz? 16/36 1 The sampling theorem A signal s(t) with maximum frequency f can be MAX Theo recovered if sampled at frequency f 2 f . S MAX Multiple proposers: Whittaker(s), Nyquist, Shannon, Kotel’nikov. Naming gets Nyquist frequency (rate) f = 2 f or f or f or f /2 N MAX MAX S,MIN S,MIN confusing Example s(t) 3cos(50πt)10sin(300πt)cos(100πt) Condition on f ? S F F F 1 2 3 f 300 Hz S F =25 Hz, F = 150 Hz, F = 50 Hz 1 2 3 f MAX 17/36 Sampling and Spectrum 18/36 1 Sampling low-pass signals Continuous spectrum (a) Band-limited signal: (a) frequencies in -B, B (f = B). MAX -B 0 B f Discrete spectrum (b) No aliasing (b) Time sampling frequency repetition. f 2 B no aliasing. S -B 0 B f /2 f S Discrete spectrum Aliasing & corruption (c) (c) f 2 B aliasing S Aliasing: signal ambiguity 0 f /2 f S in frequency domain 19/36 1 Antialiasing filter (a) Signal of interest (a),(b) Out-of-band noise can aliase Out of band Out of band into band of interest. Filter it before noise noise (c) Antialiasing filter -B 0 B f (b) Passband: depends on bandwidth of interest. Attenuation A : depends on MIN -B 0 B f /2 • ADC resolution ( number of bits N). S f (c) A 6.02 N + 1.76 MIN, dB • Out-of-band noise magnitude. Other parameters: ripple, stopband frequency... 20/36

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