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Today's lecture

Today's lecture . Continuous and discrete-time signals Distinction between discrete and digital Examples The sequence Continuous and discrete-time systems Notations Examples Transformation of the independent axis Time Shifting Time Reversal Time Scaling Example Sinusoids.

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Today's lecture

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  1. Today's lecture • Continuous and discrete-time signals • Distinction between discrete and digital • Examples • The sequence • Continuous and discrete-time systems • Notations • Examples • Transformation of the independent axis • Time Shifting • Time Reversal • Time Scaling • Example • Sinusoids

  2. Continuous-time signals • A value of signal exists at every instant of time Independent variable Independent variable

  3. Discrete-time signals • The value of signal exists only at equally spaced discrete points in time Independent variable Independent variable

  4. Discrete-time signals • Why to discretize • How to discretize • How closely spaced are the samples • Distinction between discrete & digital signals • How to denote discrete signals • Is the image a discrete or continuous signal • The image is generally considered to be a continuous variable • Sampling can however be used to obtain a discrete, two dimensional signal (sampled image)

  5. Continuous and discrete signals • A continuous-time signal is represented by enclosing the independent variable (time) in parentheses () • A discrete-time signal is represented by enclosing the independent variable (index) in square brackets []

  6. Continuous and discrete signals • Examples of continuous signals • Speech, video, image • The variation of atmospheric pressure, wind speed and temperature with altitude • Examples of discrete signal • Demographic data, weekly stock position of a company

  7. Continuous and discrete time system • Like signals we have continuous and discrete-time systems as well system system

  8. Continuous and discrete time system • Examples of continuous and discrete-time systems Squaring System Differentiator System Accumulator System

  9. Transformations • Transformations of the independent variable • Time Shift

  10. Transformations • Time reversal

  11. Transformations • Time scaling

  12. Transformations • Example

  13. Sinusoidal signals • x(t) = A cos(ωt + Φ) • A is the maximum amplitude of the sinusoidal signal • ω is the radian frequency •  is the phase shift

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