INTRODUCTION TO DIGITAL SIGNAL PROCESSING Dr. Hugh Blanton ENTC 4347

Dr. Blanton - ENTC From analog to digital domain 2 / 30 TOPICS 1.Impact of DSP 2.Analog vs. digital: why, what & how 3.Digital system example 4.Sampling & aliasing 5.ADCs: performance & choice 6.Digital data formats

Dr. Blanton - ENTC From analog to digital domain 3 / 30 Digital vs Analog Digital Signal Processing More flexible. Often easier system upgrade. Data easily stored. Better control over accuracy requirements. Reproducibility. Advantages A/D & signal processors speed: wide-band signals still difficult to treat (real-time systems). Finite word-length effect. Obsolescence (analog electronics has it, too!). Limitations

Dr. Blanton - ENTC From analog to digital domain 4 / 30 Impact of DSP on Modern Living Cellular/mobile telephony Speech and channel coding Voice and data processing Power management Multipath equaliztion Digital audio Stereo and surround sound Audio equalization and mixing Electronic music Automotive Digital Audio Digital Radio Personal communication systems Active suspension Medical electronics Critical/intensive care monitors Digital X-rays ECG analyzers Cardiac monitors Medical imaging Personal computer Sound cards Data storage and retrieval Error correction/concealment Multimedia Modems

Dr. Blanton - ENTC From analog to digital domain 5 / 30 Analog & digital signals Continuous function continuous Continuous function V of continuous variable t (time, space etc) : V(t). Analog Discrete function discrete Discrete function V k of discrete sampling variable t k, with k = integer: V k = V(t k ). Digital Uniform (periodic) sampling. Sampling frequency f S = 1/ t S

Dr. Blanton - ENTC From analog to digital domain 6 / 30 DSP: aim & tools Software Programming languages: Pascal, C / C++... “High level” languages: Matlab, Mathcad, Mathematica… Dedicated tools (ex: filter design s/w packages). Applications Predicting a system’s output. Implementing a certain processing task. Studying a certain signal. General purpose processors (GPP),  -controllers. Digital Signal Processors (DSP). Programmable logic ( PLD, FPGA ). Hardware real-time DSPing FastFaster

Dr. Blanton - ENTC From analog to digital domain 7 / 30 Digital system example ANALOG DOMAIN Filter Antialiasing DIGITAL DOMAIN A/D Digital Processing ANALOG DOMAIN D/A Filter Reconstruction Sometimes steps missing - Filter + A/D (ex: economics); - D/A + filter (ex: digital output wanted). General scheme Topics of this lecture. Digital Processing Filter Antialiasing A/D

Dr. Blanton - ENTC From analog to digital domain 8 / 30 Digital system implementation Sampling rate. Pass / stop bands. KEY DECISION POINTS: Analysis bandwidth, Dynamic range No. of bits. Parameters Digital Processing A/D Antialiasing Filter ANALOG INPUT DIGITAL OUTPUT Digital format. What to use for processing? See slide “DSPing aim & tools”

Dr. Blanton - ENTC From analog to digital domain 9 / 30 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. Frequency misidentification due to low sampling frequency. Train starts wheels ‘go’ clockwise. Train accelerates wheels ‘go’ counter-clockwise. 1Why? * Sampling: independent variable (ex: time) continuous  discrete. Quantisation: dependent variable (ex: voltage) continuous  discrete. Here we’ll talk about uniform sampling.*

Dr. Blanton - ENTC From analog to digital domain 10 / 30 Sampling - 2 __ s(t) = sin(2  f 0 t) f S f 0 = 1 Hz, f S = 3 Hz __ s 1 (t) = sin(8  f 0 t) __ s 2 (t) = sin(14  f 0 t) s k (t) = sin( 2  (f 0 + k f S ) t ),  k   f S represents exactly all sine-waves s k (t) defined by: 1

Dr. Blanton - ENTC From analog to digital domain 11 / 30 The sampling theorem A signal s(t) with maximum frequency f MAX can be recovered if sampled at frequency f S > 2 f MAX. Condition on f S ? f S > 300 Hz F 1 =25 Hz, F 2 = 150 Hz, F 3 = 50 Hz F1F1 F2F2 F3F3 f MAX Example 1 Theo * * Multiple proposers: Whittaker(s), Nyquist, Shannon, Kotel’nikov. Nyquist frequency (rate) f N = 2 f MAX or f MAX or f S,MIN or f S,MIN /2 Naming gets confusing !

Dr. Blanton - ENTC From analog to digital domain 12 / 30 Frequency domain (hints)  Time & frequency  Time & frequency : two complementary signal descriptions. Signals seen as “projected’ onto time or frequency domains. Warning : formal description makes use of “negative” frequencies ! 1  Bandwidth  Bandwidth : indicates rate of change of a signal. High bandwidth signal changes fast. Ear Ear + brain act as frequency analyser: audio spectrum split into many narrow bands low-power sounds detected out of loud background. Example

Dr. Blanton - ENTC From analog to digital domain 13 / 30 Sampling low-pass signals (a) Band-limited signal: frequencies in [-B, B] (f MAX = B). (a) (b) Time sampling frequency repetition. f S > 2 B no aliasing. (b) 1 (c) aliasing ! (c) f S 2 B aliasing ! Aliasing: signal ambiguity in frequency domain

Dr. Blanton - ENTC From analog to digital domain 14 / 30 Antialiasing filter Filter it before! (a),(b) Out-of-band noise can aliase into band of interest. Filter it before! (a) (b) (c) Passband : depends on bandwidth of interest. Attenuation A MIN : depends on ADC resolution ( number of bits N). A MIN, dB ~ 6.02 N Out-of-band noise magnitude. Other parameters: ripple, stopband frequency... Antialiasing filter (c) Antialiasing filter 1

Dr. Blanton - ENTC From analog to digital domain 15 / 30 Under-sampling (hints) 1 Using spectral replications to reduce sampling frequency f S req’ments. m , selected so that f S > 2B Advantages  Slower ADCs / electronics needed.  Simpler antialiasing filters. f C = 20 MHz, B = 5MHz Without under-sampling f S > 40 MHz. With under-sampling f S = 22.5 MHz (m=1); = 17.5 MHz (m=2); = MHz (m=3).Example

Dr. Blanton - ENTC From analog to digital domain 16 / 30 Over-sampling (hints) 1 f OS = over-sampling frequency, w = additional bits required. f OS = 4 w · f S Each additional bit implies over-sampling by a factor of four. It works for: -white noise -white noise with amplitude sufficient to change the input signal randomly from sample to sample by at least LSB. -Input that can take all values between two ADC bits. Caveat Oversampling : sampling at frequencies f S >> 2 f MAX. Over-sampling & averaging may improve ADC resolution ( i.e. SNR, see ) 2