Course Details

1. Categorize the various types of signals. Recognize and manipulate special signals. Understand and calculate quantities such as average value, RMS value, instantaneous power and average power of signals. Perform mathematical operations on signals such as amplitude scaling, time scaling, addition and subtraction.
2. Classify continuous time systems based on linearity, time invariance and causality. Derive the convolution integral. Use convolution to calculate the output of a system, graphically and analytically, given its impulse response and the input. Compute the impulse response of cascaded systems.
3. Compute the Fourier series of periodic waveforms and the Fourier transform of non-periodic waveforms. Employ the Fourier series and the Fourier transform to obtain the frequency spectra of signals.
4. Compute the Laplace Transform of signals. Analyze LTI systems using the Laplace transform and the Fourier transform. Obtain the transfer function, frequency response and test their stability. Derive the impulse response of LTI systems from the transfer function using partial fraction expansion.
5. Integrate the knowledge attained to compute the impulse response, the transfer function and the frequency response of simple electrical systems. Derive the impulse response of ideal filters. Specify, design and analyze simple analog filters. Classify filters in terms of their frequency response.

Signals:  Classifications.  Operations on signals: amplitude and time scaling, addition. Special signals: Unit step, Unit impulse, sinusoidal, exponential, complex exponential.

Systems: Classification of continuous-time systems and their properties. Linearity,    time invariance, causality and stability.  Description of continuous-time systems using differential equations. General forms. Impulse response. Input output description and the convolution integral. Graphical interpretation of convolution.

Fourier series: Derivation of the trigonometric Fourier series. Calculation of the  Fourier coefficients. Combined trigonometric and exponential forms of the Fourier series. Harmonics and frequency spectra. Average value, RMS value, instantaneous and average power of periodic signals.

Laplace Transform: Definition. Laplace transform of functions. Properties. Inverse Laplace transform using partial fraction expansion. Application of the Laplace transform to continuous-time linear systems analysis. Transfer function, poles and zeros, BIBO stability.

Fourier Transform: Definition. Properties. Fourier transform of functions. Frequency spectra of signals. Frequency response of LTI systems. Magnitude and phase responses.

• C. Philips, J. Parr, E. Riskin, Signals, Systems, and Transforms, Pearson Education International, 4th edition, 2008.

• L. Balmer, Signals and Systems, Prentice – Hall International, 1997.
• Leland B. Jackson, Signals, Systems and Transforms, Addison Wesley, 2001.
• Al. Oppenheim, Al. Willsky, Signals and Systems, 2nd edition, Prentice Hall, 1997.

Teaching of the course is based on lectures (3 hours per week) in a classroom, using a mixture of traditional teaching with notes on the white board and slide presentations using a projector where appropriate.