Having successfully completed this course, the student will be able to:
1. Identify a system and basic discrete and continuous time signals, perform scaling, addition, multiplication, and time shifting on signals.
2. Inspect a system and determine whether it is stable, memoryless, casual, invertible time invariant and linear or not. Identify series and parallel interconnections of systems to obtain the relationships between the input and the output functions.
3. Identity the Linear Time-Invariant (LTI) systems and their properties. Evaluate convolution sum and integral to obtain the output of a system given the input and the impulse response.
4. Understand the Fourier series representation of continuous-time and discrete-time periodic signals. Identify the properties of Fourier series such as time-shift, differentiation, multiplication etc.
5. Understand the continuous-time Fourier transform (CTFT) and discrete- time Fourier transform (DTFT) of aperiodic signals. Develop an understanding of properties of these transforms such as convolution, multiplication, Parseval’s relation etc.
6. Formulate impulse and frequency responses of a system described by linear constant coefficient differential and difference equations using the properties and pairs of CTFT and DTFT.
7. Identify the conditions on the sampling rate guaranteeing a bandlimited signal to be reconstructed from its samples, and formulate the reconstruction of a bandlimited continuous time signal form its samples.