# EE 445S Real-Time Digital Signal Processing Laboratory - Lecture 14

Lecture by Prof. Brian L. Evans

## Before Lecture

• "Clementine". Sarah Jaffe, She performed at the 2011 South by Southwest Music Festival in Austin, TX.

• "Roam", B-52s, 1989.

## Announcements

• Dr. Jim Truchard, founder and CEO of National Instruments, mentioned these key challenges for translating mathematics into embedded real-time systems in his March 18, 2010, keynote talk at the IEEE International Conference on Acoustics, Speech and Signal Processing:
• Input/Output (I/O)
• Determinism (predictability)
• Timing constructs (missing in common high-level languages)

• Additional reading assignment from Communication Systems (3rd edition) by Simon Haykin
• Section 4.6 Random Processes (all)
• Section 4.9 Ergodic Processes (all)
• Section 4.10 Transmission of a Random Process Through a Linear [Time-Invariant] Filter (all)
• Section 4.11 Power Spectral Density (through page 253) especially
• Equation (4.80) on page 250 for time-averaged autocorrelation and the two limit definitions that immediately follow it.
• Equation (4.93) on page 253, which is used in the derivation of the matched filter
• Section 4.12 Gaussian Processes, but only the following parts:
• Subsection on Thermal Noise
• Subsection on White Noise
• Example 16 Ideal Low-Pass Filtered White Noise

## Supplemental

• Karagiannidis and Lioumpas, "An Improved Approximation for the Gaussian Q function", IEEE Communication Letters, August 2007. With
```       1         x
Q(x) = - erfc(-------)
2      sqrt(2)
```
the authors approximate `erfc(x)` by `g(x) h(x)`, where
```             2
-x
e
h(x) = ----------
sqrt(pi) x

-A x
1 - e
g(x) = ---------
B
```
where `A` = 1.98 and `B` = 1.135 to minimize the absolute error for `x` in [0, 20].

Last updated 07/28/17. Send comments to bevans@ece.utexas.edu