Signal Analysis & Systems
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Signal and system model and classification. Continuous time signals. Signals and vectors.
Generalized Fourier series representation. Amplitude and phase spectra of signals. Energy
and power content of signals. Bandwidth of signals. The Fourier transform and its applications.
Sampling of signals. Convolution of signals. Power and energy spectral densities. Correlation
functions. Time-domain analysis of continuous time systems. The system impulse response.
Communication channels
1. Signals and system classification into continuous-time and discrete-time. Continuous-time
signal characteristics (even, odd, periodic, aperiodic, etc). Properties of continuous-time
systems (stability, linearity, etc).
2. Impulse representation of continuous-time signals. Convolution and its properties. Properties
of Linear Time-Invariant (LTI) systems. Impulse response.
3. Generalized, complex exponential, and trigonometric Fourier series representation of periodic
signals. Frequency spectra. Properties of Fourier series.
4. The Fourier transform and its properties (linearity, time scaling, time shifting, time
transformation, duality, convolution, frequency shifting, differentiation, integration, etc).
5. The Fourier transform of some typical time domain signals.
6. Sampling and digitizing of continuous-time signals and their spectra.
7. Line, power and energy spectra of signals. Bandwidth of signals.
8. Applications of the Fourier transform. Filters (ideal and practical).
9. Discrete-time signals. Discrete-time Fourier transform. Fast Fourier transform. Introduction to
the z-transform.
