Assessment Performance Criteria
1A1 The student will recognize mathematical parameters as if they were physical variables and vice-versa.
- Determine the effect of time scaling, reversal or delay operations on the signal waveform.
- Analyze circuits described by linear, constant coefficient differential equations, with coefficients in terms of resistance, capacitance and inductance values using the convolution integral or transform methods.
- Relate the frequency response to resistance, capacitance and inductance values.
- Determine the effect of sampling rates and modulating frequency on the spectrum of a continuous-time signal.
1A2 The student will be able to follow the general mathematical concepts of the derivation of an engineering or scientific result and will possess the mathematical skills to link those concepts.
- Decompose a discrete-time or continuous-time signal in terms of impulses.
- Evaluate the impulse response of a system described by linear, constant coefficient difference or differential equations.
- Evaluate a system’s response to a given input by the convolution summation or convolution integral.
- Understand the derivation of mathematical conditions for stability and causality of an LTI system.
1A3 The student will be able to understand the relevance of the mathematical results to the physical applications.
- Understand the relevance of the signal multiplication property of Fourier Transforms to amplitude modulation and demodulation as well as to frequency division multiplexing.
- Understand the relevance of the Sampling Theorem and the Nyquist rate to signal sampling and reconstruction.
- Understand the use of Laplace and Z transforms and their singularities to determine stability of an LTI system. Use of an LTI system’s poles and zeros to determine its causality and stability.
- Understand the use of feedback to stabilize an unstable system.
- Relate the mathematical properties of the impulse response of a discrete-time or continuous-time LTI system to system stability and causality (physical realizability).
1C5 The student will be able to analyze dynamical systems in the frequency domain.
- Represent discrete-time and continuous-time signals in terms of there frequency content using Discrete-Time and Continuous-Time Fourier Transforms.
- Determine the frequency response of LTI systems described by linear, constant coefficient difference or differential equations.
- Determine the frequency response of an LTI system from its impulse response.
- Determine the frequency content of the output of an LTI system,
given the time domain or frequency domain representation of the input and system.
- Determine the effect of modulating a signal on the signal’s frequency spectrum and determine how to recover the original signal. Understand the use of modulators and filters in frequency division multiplexing.
- determine the effect of sampling a signal on the signal’s frequency spectrum and determine how to recover the original signal. Be able to determine the Nyquist rate for a band-limited signal and understand the aliasing effect of under-sampling.
- Represent a system’s frequency response in terms of its magnitude and phase response.
4A3 Students will be able to identify technical relationships between the input, output and variables and use the relationships to predict mutual changes.
- Determine the system transfer functions relating input and output of an LTI system, both in the time and frequency domains.
- Use the system transfer function to determine the system output corresponding to a given input as well as to determine the input required to achieve a desired output.
4B1 Given appropriate input and desired outputs, students will be able to specify the characteristics of the component or unit required to achieve these desired outputs.
- Determine the bandwidth of ideal filters necessary to extract a desired signal from its sampled or modulated form.
- Determine the frequency characteristics of an LTI system necessary to obtain a desired output from a given input.
4C1 The students will be able to apply standard design procedure for units connected in parallel, in series or by feedback.
- Use partial fractions expansions to decompose a rational system function and decompose a complex system function into simpler ones each corresponding to a unit of the system.
- Combine individual units in series, parallel or by feedback to achieve the overall system properties.
- Determine if a designed LTI system with feedback is stable.
|