| 1 |
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Introduction to the course |
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| 2 |
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Continuous and discrete time signals. Definition and some examples of signals and systems. Graphical representations of signals. Signal energy and power. Transformations of the independent variable in a signal. Periodic signals. Even and odd signals and even-odd decomposition of a signal. Continuous time exponential and sinusoidal signals and their properties. |
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| 3 |
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Discrete time exponential and sinusoidal signals and their properties. Definitions and properties of discrete time and continuous time unit impulse and unit step functions. Continuous time and discrete time systems. First and second order system examples. |
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| 4 |
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Cascade, parallel and feedback interconnections of systems. Basic system properties: Memoryless, invertibility, causality, stability, time invariance and linearity. Properties of linear systems. |
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| 5 |
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Discrete time LTI systems and the convolution sum. Continuous time LTI systems and the convolution integral. |
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| 6 |
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Properties of LTI systems. Causal LTI systems described by differential and difference equations. Block diagram representations of first-order systems. |
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| 7 |
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Fourier series representation of periodic signals. The response of LTI systems to complex exponentials. Fourier series representation of continuous time periodic signals. Convergence of the Fourier series. Properties of the CTFS. |
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| 8 |
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MID-TERM EXAM |
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| 9 |
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Fourier series representation of discrete time periodic signals. Properties of the DTFS. Fourier series and LTI systems. |
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| 10 |
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Representation of aperiodic continuous signals: The continuous time Fourier transform. Convergence of Fourier transforms. The Fourier transform for periodic signals. Properties of the CTFT. |
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| 11 |
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Convolution and multiplication properties of the CTFT. Representation of aperiodic discrete signals: The discrete time Fourier transform. Periodicity of the DTFT. |
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| 12 |
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Convergence issues associated with the DTFT. The DTFT for periodic signals. Properties of the DTFT. Convolution and multiplication properties of the DTFT. |
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| 13 |
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Representation of a continuous time signal by its samples: The Sampling Theorem. Impulse train sampling. Exact recovery by an ideal lowpass filtler. Sampling with a Zero-Order Hold. Reconstruction of a signal from its samples using interpolation. The effect of undersampling: Aliasing. |
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| 14 |
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Recapitulation |
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| 15 |
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Recapitulation |
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| 16 |
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FINAL EXAM |
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| 17 |
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FINAL EXAM |
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