It is common in automotive situations to reserve part of the representable range to indicate error or SNA (signal not available) conditions. If you wanted to reserve the largest positive numbers for error codes, then their hex representation would look something like 0x7FFF, which can be hard to spot in a data stream. If you used the largest negative numbers, then they would look something like 0x8000, which is also not very intuitive.

By using biased representation, you can use values like 0xFFFF to indicate error values.

Of course, you could use something like bit-flags to represent errors, but that wastes a whole bit of bandwidth. Much more efficient to amortize the enumerated value over the whole signal.

You can see a real-world example of these types of signals as defined by SAE for heavy duty trucks here: https://www.scania.com/content/dam/scanianoe/market/au/produ...

The tuning fork crystal design used in wrist watches has a parabolic temperature coefficient, which means that the clock is only really accurate at room temperature. This isn't a problem for wristwatches, because, presumably your wrist is at approximately room temperature, but it does become a problem for electronics that operate with large temperature swings. (like the inside of a phone or computer, for instance).

https://www.maximintegrated.com/en/app-notes/index.mvp/id/58

This is the definition of a hard real-time system. In most of the literature, 'embedded system' is a broader term that just means there is some compute embedded in a device that performs a larger task.

1. Store embedded system state in data structure.

2. Calculate a checksum for that data structure.

3. Verify that checksum is correct.

HW Solution:

Lockstep Execution/ECC memory, etc.

In addition even the modified periodogram discussed above has asymptotically nonzero variance [2], which means no matter how many samples you take, you will still have 'noise' in your PSD estimate. If you use biased estimators of the periodogram, such as the welch-bartlett method or the blackman-tukey algorithm, you will get much better results.

[1] http://www.ni.com/white-paper/4844/en/

[2] http://www.mathworks.com/help/signal/ug/nonparametric-method...

Those analog anti-aliasing and anti-imaging filters are designed using LTI systems theory, that fundamentally rely on the Fourier tranform to reason about their transfer functions. The Nyquist-Shannon sampling theorem was proven using the fourier transform. Without the fourier transform, you need to rely entirely upon time domain representations of signals, and perform your analysis using tedious convolutions. You can't use a spectrum analyzer to examine the signal to noise ratio of your CD player. While it's true that digital music could technically exist without the fourier, there is no way in hell it would be as pervasive as it is today.

http://en.m.wikipedia.org/wiki/Linear-quadratic_regulator

Switching the output from 100% to -100% is another viable approach, known as bang-bang control, but it is not necessarily optimal

http://en.wikipedia.org/wiki/Apollo_Guidance_Computer#Softwa...

In addition, there is no way in hell that the control algorithms it was using could have been developed without the use of computers. State-space control theory was specifically developed to take advantage of discrete-time control systems.

https://www.hq.nasa.gov/alsj/ApolloDescentGuidnce.pdf

Also on the horizon is ISO26262, which mandates quality assurance for automotive embedded code in the form of paper trails. Unfortunately due to the huge amount of work required by the standard, some automakers are choosing to ignore it and hope it doesn't become mandatory.

http://www.deere.com/en_US/ProductCatalog/FR/media/pdf/8r_se...

There's no incentive for companies to publish information on their vehicle bus interfaces, since it would basically give away trade secrets to competitors.

Suddenly your "inexpensive" adc had become a $200 ecu that merely tells the driver wheat part of the car isn't functioning, right before they check the most common cause of the problem.

For example, this appnote[0] uses a Delta-Sigma converter to digitize a load cell, with the ability to "detect one sheet of copier paper dropped on a stack of 20 reams". In order to do this, it relies on an intrumentation amplifier and custom correlated-double sampling to get a measurement accurate to 200,000 counts.

And even if your input signal can be directly input to your ADC, you'll still need an analog anti-aliasing filter.

Signal conditioning is an important part of signal processing that has to happen in the analog domain.

[0] http://cds.linear.com/docs/en/application-note/an96fa.pdf

http://www.freescale.com/webapp/sps/site/application.jsp?cod...

http://youtu.be/N_195d7bP9M?t=3m10s

Before a digital circuit can process a signal, it must first be quantized, an inherently analog process. Your digital data is only as good as your analog signal, plus inherent quantization noise[1]. In addition, any mixed-signal IC represents a design compromise between digital and analog constraints.

Any signal processing system is inherently limited by the SNR of its source signal. There is no point in building a more accurate converter than the noisiest component of your input data. In fact, when metrologists are trying achieve the maximum accuracy in their measurements, it is not uncommon to leave a test circuit on for days at a time, in order to reach a thermal equilibrium to minimize the seebeck effect[2].

And when engineers to need to make the most accurate of measurements, what do they turn to? Analog circuits. The world's most accurate voltage reference, the Kelvin-Varley Divider, dates back to the late 19th century[3]. For a modern example of a precision reference, see Jim William's excellent white paper, "Quantifying Silence"[4].

[1] http://en.wikipedia.org/wiki/Quantization_(signal_processing...

[2] http://www.keithley.com/knowledgecenter/knowledgecenter_pdf/...

[3] http://en.wikipedia.org/wiki/Kelvin%E2%80%93Varley_divider

[4] http://cds.linear.com/docs/en/application-note/an124f.pdf