Digital Signals-1

# Digital Signals-1 - Intro to ECE Design Drs Butera/Williams...

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Intro to ECE Design Drs. Butera/Williams Module: Digital Signals/Representations 2008, Douglas B. Williams and Robert J. Butera, Jr. Page 1 Objectives Upon completion of this module, you should be able to: understand uniform quantizers, including dynamic range and sources of error, represent numbers in two’s complement binary form, assign binary symbols to quantized signal values, and scale a signal to fit within a specified range. What are signals? As we saw in the “Volts and Amps” module, sensors typically convert observed data into time- varying voltages. In other words the sensors act as transducers that convert environmental data into a corresponding current flow that can then be observed and measured with electronics as a changing voltage. The resulting data are functions of time with units in volts and are known as ‘signals.’ What does such a voltage signal look like? Signals are commonly observed and graphed as functions of time: Such a function is known as a continuous-time signal . These signals are defined for all values of t and take on a continuous range of voltage values. Problem: Digital computers cannot store this type of data. + - Voltage sensor environment

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Intro to ECE Design Drs. Butera/Williams Module: Digital Signals/Representations 2008, Douglas B. Williams and Robert J. Butera, Jr. Page 2 Numerical quantities represented by computers have finite precision, as they must be represented by a small number of bits. We have to quantize the values in v ( t ) into the finite precision values that can be stored in however many bits are allowed per number. Quantization Assume that the observed voltage is known to range from a minimum of v min to a maximum of v max . A quantizer is a system that divides this continuous range of values into a finite number of discrete values. The most common quantizers are uniform quantizers that divide the range of values into equal-sized intervals. Here are two typical uniform quantizers for a system with 3 bits of precision. For N bits of precision a quantizer has 2 N output levels. Thus, these 3-bit quantizers have 8 levels. Midstep quantizers are generally preferred over midrise quantizers as they are less sensitive to noise at low signal levels. Let Δ denote the size of the quantization levels in these uniform quantizers. Note that for any input value of v ( t ) between −Δ /2 and Δ /2 the output of the midstep quantizer is the same, while the midrise quantizer will change output levels whenever the input crosses zero. For a small signal that is approximately zero but is varying slightly because of noise or similar observational variations, the midrise quantizer’s toggling between −Δ /2 and Δ /2 can actually magnify the effect of these small distortions. The midstep quantizer is slightly asymmetric with more negative output levels than positive, but that difference becomes insignificant as the number of bits increases. Question: The LEGO Mindstorms NXT sensors use 10 bits to encode data. How
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Digital Signals-1 - Intro to ECE Design Drs Butera/Williams...

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