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Lecture on Analog to Digital Conversion Definitions • Digital source produces a finite set of possible values. • Analog source produces a infinite set of possible values. • Signal is a measurable quantity (e.g., voltage) which bears information. • Noise is a measurable quantity which carries undesired interference. Why Digital? • • • • • Less expensive circuits Privacy and security Small signals (less power) Converged multimedia Error correction and reduction Why Not Digital? • More bandwidth • Synchronization in electrical circuits • Approximated information Analog to Digital Conversion • Sampling: Obtaining values at discrete points in time. • Quantization: Non-linear transformation that maps continuous values to discrete values. Analog Signal - Continuous time - Continuous value Sample Quantize - Discrete time - Continuous value Digital Signal - Discrete time - Discrete value Sampling Definition. Sampling is a process of evaluating signal w(t) at a discrete set of points, t1 ,t2 ,t3 ,t4 , .... in time. w(t) t1 t2 t3 t4 t 5 t Nyquist Sampling Theorem (in Plain Language) Signal w(t) bandlimited to B hertz may be represented over the interval - t by sampling at frequency f s where f s 2 B. If w(t) is sufficiently smooth, then w(t) can be n completely reconstructed from the samples w , n ... 3, 2, 1, 0,1, 2,3, ... . f s “sampler” ws(t) w(t) ws(t) w(t) t1 t2 t3 t4 t5 t t1 t2 t3 t4 t5 t Gated Samples Gated Sample and Hold Impulse Samples Sample and Hold Quantization V output w2(t) -V V input w1(t) -V Region of operation For M=2n levels, step size : = 2V /2n = V(2-n+1) Quantization Error, e V output w2(t) -V V input w1(t) -V /2 -/2 Error, e input w1(t) Error is symmetric around zero. 0 Average error power : 3 V 2 n 1 2 1 2 2 V 2 V 2 2n 2 2 2 e ( s )ds x dx 2 2V V 0 3 12 12 3 Suppose the input signal is a triangula r wave between V and V . 2 V2 Then the average signal power is . 3 S 22 n N out Noise Types of Noise • Quantizing noise (during A/D conversion) • Environment noise (e.g., EM interference) • Filtering noise (low pass filtering at decoder) Types of Quantization Noise • Overload noise (input too large) • Random noise (input too small) • Granular noise (non uniform error jump) • Hunting noise (too long of quite time) signal to noise ratio S 2 3M N M : quantization levels 2 S Let M 2n M 2 2n 22 n N S S 2n 10 log 10 log 2 20n log 2 6.02n N dB N out This equation states that for each bit added to the ADC scheme, about 6-dB is gained in the signal-to-noise ratio. Non-uniform Quantizer Used to reduce quantization error and increase the dynamic range when input signal is not uniformly distributed over its allowed range of values. allowed values values for most of time input time Digital to Analog Converter Circuit Analog to Digital Converter Circuit