We call a complex-valued random variable z=x+iy a (circular symmetric) complex Gaussian variable, or it follows complex Gaussian distribution, if its real and imaginary parts, x and y, are jointly Gaussian (i.e. (x,y) follows a two-dimensional Gaussian distribution), uncorrelated (therefore also independent in this case), and they have the same variance of σ². Denoting the mean of x and y by m_x and m_y respectively, we call m_z=m_x+im_y=E[z] the mean of z, and σ²=E[(x-m_x)²]=E[(y-m_y)²]=(1/2)E[|z-m_z|²] is called z's variance per real dimension.

From above we know that the probability density function of the 2-D random variable (x,y) is

p(x,y)=(2πσ²)^-1 exp(-((x-m_x)²+(y-m_y)²)/(2σ²)). Noting that z=x+iy, the probability density function can also be represented in terms of z:

p(z)=(2πσ²)^-1 exp(-|z-m_z|²/(2σ²))

APPLICATION

To who it may concern,

 

I apply for the Teaching Instructor Position of EE238: Continuous-time Signal and Systems.

 

I have perfect reason and incomparable qualifications for such a position:

 

Firstly, I have taught “signal and systems” and “mobile communication” for 3 years in Beijing University of Posts and Telecommunications before I came to UA for PhD this September. Therefore no only do I master the content of EE238 but also have good teaching experience of this subject which can ensure my success on such an instructor position. Consider, for example, I know where lies the difficulty in understanding some knowledge points in the subject of “signal and system” and, more importantly, how to well explain and overcome the difficulties.

 

Secondly, I have a burning desire for expression, eager to impart what I have know and show my ideas to the students. That is the talent for teaching or potential to be a good teacher and it is not possessed by every person. I know precisely that I have this talent from past teaching experience. Maybe it is because I was born in a teachers’ family: my mother and my grandfather are both teachers.

 

Moreover, I have college teacher certificate (Number: 20061100170003109) awarded by Education Ministry of People’s Republic of China, which can further prove my qualification for the instructor position of EE238.

 

Finally, I hope that I have an opportunity to show my teaching talents in UA of Canada and let the undergraduates enjoy and benefit from both the teaching skill and the glamour of an energetic and outstanding Chinese college teacher, a teacher from a different country with ancient eastern culture.

 

Thank you very much!

The prosperous province of Alberta is the heart of western Canada, sandwiched between the mountains of British Columbia to the west and the prairies of Saskatchewan to the east. Edmonton, Alberta's capital, and Calgary, to the south, are Canada's fifth- and  sixth-largest cities, respectively, between them holding more than half of the province's population. These boomtowns have been Canada's fastest-growing cities since World War II, centers for the staggering oil and gas reserves that have propelled Alberta to the forefront of world energy markets and technology. Edmonton is a modern, livable city boasting some of Canada's finest cultural facilities, as well as the world's largest shopping and amusement mall. Calgary, meanwhile, is home to the world-famous Calgary Stampede--a Western wingding of epic proportions--and the city received international attention as the host of the 1988 Winter Olympic Games. Its futuristic skyline rises from the prairie like the oil derricks that put the city on the map, and cattlemen in Caddies drive past gleaming skyscrapers on their way out to the ranch.

But for most visitors to Alberta, the great outdoors, not the big cities or the fast bucks, is the main draw. The stunning mountain playgrounds of Banff, Jasper, and Waterton Lakes national parks show off the Canadian Rockies at their best, with pristine glaciers, rushing rivers, and snowcapped peaks reflected in hundreds of high-country lakes. The parks, and much of the rest of the province, are home to an abundance of wildlife such as moose, elk, bighorn sheep, wolves, bears, and an amazing array of birds; approximately 340 species of birds migrate through or nest in Alberta. And ancient wildlife thrived here, too; one of the world's greatest concentrations of dinosaur bones continues to be unearthed in the Red Deer River Valley outside Drumheller. The "Dinosaur Valley," as it's called, attracts tourist tyros and professional paleontologists alike to learn more about earth's once-dominant former tenants.

Throughout the province, wide-open spaces, endless blue skies, and accessible wilderness beckon, and big-city culture awaits when you come down from the hills. So whether your interests lean toward high peaks or high tea, you're sure to find plenty to suit you in Alberta.

My place here is very beautiful. Last Sunday I run across a small forest and arrive at the river.

Fresh air, autumn leaves, and clear water enlightened my spirit and mind.

I felt at that moment I came very nearly to the grand nature.

 

Actually, I came to a new world, different from my mathorland.

But the feeling is familiar and touching.