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Significant Signals

1. t. 1. t. -1. 1. t. - T/2. T /2. 1. t. T. - T. Significant Signals. Impulse Delta Function. Definition Visualization Properties. Derivative:. Time Shift:. Time Scaling:. Convolution:. Relationship:. Signal Classification. Periodic Signals Aperiodic Signals

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Significant Signals

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  1. 1 t 1 t -1 1 t -T/2 T/2 1 t T -T Significant Signals

  2. Impulse Delta Function • Definition • Visualization • Properties Derivative: Time Shift: Time Scaling: Convolution: Relationship:

  3. Signal Classification • Periodic Signals • Aperiodic Signals • Even & Odd Signals • Even: • Odd: • Signal Energy of a deterministic signal • Signal Average Power

  4. Dirichlet Conditions Fourier Series • x(t) has a finite number of minima and maxima over one period • x(t) has a finite number of discontinuities over one period Fourier Transform • x(t) has a finite number of minima and maxima in any interval on the real line • x(t) has a finite number of discontinuities over any interval on the real line

  5. Fourier Series(Periodic Functions) • Exponential Form • Real Coefficient Trigonometric Form • Complex Coefficient Trigonometric Form

  6. Common FT Pairs

  7. FT Properties

  8. Sampling Theorem • If, signal x(t) is bandlimited to W • i.e., X( f ) = 0 for | f |≥ 0 • x(t)is sampled at multiples of some sampling interval Ts • Where Ts ≤ 1/(2W) • Yields sequence • Possible to reconstruct the original signal x(t) from the sampled values by the reconstruction formula Where is any arbitrary number that satisfies f W -W

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