Difference between revisions of "ECE 280/Fall 2021/Test 1"
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\(
\begin{align*}
r_{xy}&=\int_{-\infty}^{\infty}x(\tau)\,y(t+\tau)\,d\tau=x(-t)*y(t)=x_m(t)*y(t) \\
\phi_{xy}&=\int_{-\infty}^{\infty}x(t+\tau)\,y(t)\,d\tau=x(t)*y(-t)=x(t)*y_{m}(t)=r_{xy}(-t)=r_{yx}(t)
\end{align*}
\)
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| − | This page lists the topics covered on the first test for [[ECE 280/Fall 2021|ECE 280]]. The test will cover material through Homework 4 and Lecture 8. The tests will be different for the two lecture sections. | + | DRAFT 9/25/21: This page lists the topics covered on the first test for [[ECE 280/Fall 2021|ECE 280]]. The test will cover material through Homework 4 and Lecture 8. The tests will be different for the two lecture sections. |
==Test I Fall 2021 Coverage== | ==Test I Fall 2021 Coverage== | ||
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# Correlation | # Correlation | ||
#* Autocorrelation, autocorrelation function, cross-correlation, cross-correlation function, measure of correlation | #* Autocorrelation, autocorrelation function, cross-correlation, cross-correlation function, measure of correlation | ||
| + | <!-- | ||
| + | |||
# Using transfer functions | # Using transfer functions | ||
#* Obtaining transfer function from differential equation | #* Obtaining transfer function from differential equation | ||
#* Obtaining differential equation from transfer function | #* Obtaining differential equation from transfer function | ||
#* Solving for magnitude and phase in the AC steady state | #* Solving for magnitude and phase in the AC steady state | ||
| + | --> | ||
==Previous Tests== | ==Previous Tests== | ||
| Line 38: | Line 41: | ||
\end{align*} | \end{align*} | ||
</math></center> | </math></center> | ||
| − | meaning the interpretation of the independent variable is different. For $$r_{xy}(t)$$, the "t" is "How far to the ''left'' do I slide $$y$$ for the area of the product of the signals to be $$r_{xy}(t)$$"; alternately, it could be interpreted as | + | meaning the interpretation of the independent variable is different. For $$r_{xy}(t)$$, the "t" is "How far to the ''left'' do I slide $$y$$ for the area of the product of the signals to be $$r_{xy}(t)$$?"; alternately, it could be interpreted as "How far to the ''right'' do I slide $$x$$ for the area of the product of the signals to be equal to $$r_{xy}(t)$$?" |
==Specifically Not On The Test== | ==Specifically Not On The Test== | ||
# Maple | # Maple | ||
Latest revision as of 15:24, 25 September 2021
DRAFT 9/25/21: This page lists the topics covered on the first test for ECE 280. The test will cover material through Homework 4 and Lecture 8. The tests will be different for the two lecture sections.
Test I Fall 2021 Coverage
- Signal properties
- Aperiodic or periodic (and if periodic, what is the period?)
- Energy (and if so, the total energy), power (and if so, the average power), or neither
- Even or odd (and regardless, be able to find even part and odd part for any signal)
- Independent and dependent variable transformations
- Scaling, time shift, time scaling, time reversal
- Elementary signals
- Impulse function $$\delta(t)$$ and its first four integrals ($$u(t)$$, $$r(t)$$, $$q(t)$$, and $$c(t)$$)
- Quickly write a formula for piecewise functions made up of straight lines (i.e. accumulations of value and slope changes)
- Impulse and step response and their relationship to each other
- Convolution
- Using the integral
- Using graphical convolution
- Using convolution properties for elementary signals
- System properties (from system equation, impulse response, or step response)
- Memoryless
- Causal
- BIBO stable
- Linear
- Time Invariant
- We will not ask about Invertible
- Correlation
- Autocorrelation, autocorrelation function, cross-correlation, cross-correlation function, measure of correlation
Previous Tests
Dr. G's previous tests for ECE 280 (and ECE 54/64) are at the Test Bank; note that in previous semesters a different version of the correlation function was used - that version is labeled $$\phi_{xy(t)}$$ versus this semester's notation of $$r_{xy}(t)$$.
meaning the interpretation of the independent variable is different. For $$r_{xy}(t)$$, the "t" is "How far to the left do I slide $$y$$ for the area of the product of the signals to be $$r_{xy}(t)$$?"; alternately, it could be interpreted as "How far to the right do I slide $$x$$ for the area of the product of the signals to be equal to $$r_{xy}(t)$$?"
Specifically Not On The Test
- Maple
- MATLAB
- Python
- Fourier Series
