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INTRODUCTION TO DIGITAL SIGNAL PROCESSING

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INTRODUCTION TO DIGITAL SIGNAL PROCESSING. Dr. Hugh Blanton ENTC 4347. TOPICS. Impact of DSP Analog vs. digital: why, what & how Digital system example Sampling & aliasing ADCs: performance & choice Digital data formats. Limitations. Advantages.

#quantization (signal processing) #sampling frequency #digital signal processing #lattice #bilinear transform #autocorrelation #kaiser window #psola
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  1. INTRODUCTION TODIGITAL SIGNAL PROCESSING Dr. Hugh Blanton ENTC 4347

  2. TOPICS • Impact of DSP • Analog vs. digital: why, what & how • Digital system example • Sampling & aliasing • ADCs: performance & choice • Digital data formats Dr. Blanton - ENTC 4347 - From analog to digital domain 2 / 30

  3. Limitations 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!). • More flexible. • Often easier system upgrade. • Data easily stored. • Better control over accuracy requirements. • Reproducibility. Digital vs Analog Digital Signal Processing Dr. Blanton - ENTC 4347 - From analog to digital domain 3 / 30

  4. 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 Medical electronics Critical/intensive care monitors Digital X-rays ECG analyzers Cardiac monitors Medical imaging Automotive Digital Audio Digital Radio Personal communication systems Active suspension Personal computer Sound cards Data storage and retrieval Error correction/concealment Multimedia Modems Dr. Blanton - ENTC 4347 - From analog to digital domain 4 / 30

  5. Analog Digital Discrete function Vk of discrete sampling variable tk, with k = integer: Vk = V(tk). Continuous function V of continuous variable t (time, space etc) : V(t). Uniform (periodic) sampling. Sampling frequency fS = 1/ tS Analog & digital signals Dr. Blanton - ENTC 4347 - From analog to digital domain 5 / 30

  6. Predicting a system’s output. • Implementing a certain processing task. • Studying a certain signal. Applications • General purpose processors (GPP), -controllers. • Digital Signal Processors (DSP). • Programmable logic ( PLD, FPGA ). Hardware Fast Faster real-time DSPing • Programming languages: Pascal, C / C++ ... • “High level” languages: Matlab, Mathcad, Mathematica… • Dedicated tools (ex: filter design s/w packages). Software DSP: aim & tools Dr. Blanton - ENTC 4347 - From analog to digital domain 6 / 30

  7. General scheme ANALOG DOMAIN FilterAntialiasing FilterAntialiasing Sometimes steps missing - Filter + A/D (ex: economics); - D/A + filter (ex: digital output wanted). A/D A/D DIGITAL DOMAIN Digital Processing Digital Processing D/A ANALOG DOMAIN Topics of this lecture. FilterReconstruction Digital system example Dr. Blanton - ENTC 4347 - From analog to digital domain 7 / 30

  8. ANALOG INPUT Antialiasing Filter 1 2 3 A/D Digital Processing • Digital format. What to use for processing? See slide “DSPing aim & tools” DIGITAL OUTPUT Digital system implementation KEY DECISION POINTS: Analysis bandwidth, Dynamic range •Sampling rate. • Pass / stop bands. • No. of bits. Parameters. Dr. Blanton - ENTC 4347 - From analog to digital domain 8 / 30

  9. 1 * Ex: train wheels in a movie. 25 frames (=samples) per second. Train starts wheels ‘go’ clockwise. Train accelerates wheels ‘go’ counter-clockwise. *Sampling: independent variable (ex: time) continuous  discrete. Quantisation: dependent variable (ex: voltage) continuous  discrete. Here we’ll talk about uniform sampling. Sampling How fast must we sample a continuous signal to preserve its info content? Why? Frequency misidentification due to low sampling frequency. Dr. Blanton - ENTC 4347 - From analog to digital domain 9 / 30

  10. 1 __ s(t) = sin(2f0t) s(t) @ fS f0 = 1 Hz, fS = 3 Hz __ s1(t) = sin(8f0t) __ s2(t) = sin(14f0t) s(t) @ fS represents exactly all sine-waves sk(t) defined by: sk (t) = sin( 2 (f0 + k fS) t ) , k  Sampling - 2 Dr. Blanton - ENTC 4347 - From analog to digital domain 10 / 30

  11. 1 Example Condition on fS? F1 F2 F3 fS > 300 Hz F1=25 Hz, F2 = 150 Hz, F3 = 50 Hz fMAX The sampling theorem A signal s(t) with maximum frequency fMAX can be recovered if sampled at frequency fS > 2 fMAX . Theo* *Multiple proposers: Whittaker(s), Nyquist, Shannon, Kotel’nikov. Naming gets confusing ! Nyquist frequency (rate) fN = 2 fMAXor fMAXor fS,MINor fS,MIN/2 Dr. Blanton - ENTC 4347 - From analog to digital domain 11 / 30

  12. 1 Example Ear + brain act as frequency analyser: audio spectrum split into many narrow bands low-power sounds detected out of loud background. • Bandwidth: indicates rate of change of a signal. High bandwidth signal changes fast. BOOM ! minus 50 Hz ?? Frequency domain (hints) • Time & frequency: two complementary signal descriptions. Signals seen as “projected’ onto time or frequency domains. Warning: formal description makes use of “negative” frequencies ! Dr. Blanton - ENTC 4347 - From analog to digital domain 12 / 30

  13. 1 (a)Band-limited signal: frequencies in [-B, B] (fMAX = B). (a) (b) (b)Time sampling frequency repetition. fS > 2 B no aliasing. (c) (c)fS 2 B aliasing ! Aliasing: signal ambiguity in frequency domain Sampling low-pass signals Dr. Blanton - ENTC 4347 - From analog to digital domain 13 / 30

  14. 1 (a) (a),(b)Out-of-band noise can aliase into band of interest. Filter it before! (c)Antialiasing filter (b) • Passband: depends on bandwidth of interest. • Attenuation AMIN : depends on • ADC resolution ( number of bits N). • AMIN, dB ~ 6.02 N + 1.76 • Out-of-band noise magnitude. • Other parameters: ripple, stopband frequency... (c) Antialiasing filter Dr. Blanton - ENTC 4347 - From analog to digital domain 14 / 30

  15. 1 m , selected so that fS > 2B Example Advantages • Slower ADCs / electronics needed. • Simpler antialiasing filters. fC = 20 MHz, B = 5MHz Without under-sampling fS > 40 MHz. With under-sampling fS = 22.5 MHz (m=1); = 17.5 MHz (m=2); = 11.66 MHz (m=3). Under-sampling (hints) Using spectral replications to reduce sampling frequency fS req’ments. Dr. Blanton - ENTC 4347 - From analog to digital domain 15 / 30

  16. 1 Oversampling : sampling at frequencies fS >> 2 fMAX . Over-sampling & averaging may improve ADC resolution ( i.e. SNR, see ) fOS = over-sampling frequency, w = additional bits required. 2 fOS = 4w· fS Each additional bit implies over-sampling by a factor of four. Caveat • It works for: • 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. Over-sampling (hints) Dr. Blanton - ENTC 4347 - From analog to digital domain 16 / 30