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1.2 Signal transformations involving linear transformations of the independent variable

1.2 Signal transformations involving linear transformations of the independent variable. Basic classes: Time Shift, Time Reversal, Time Scaling

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1.2 Signal transformations involving linear transformations of the independent variable

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  1. 1.2Signal transformations involving linear transformations of the independent variable Basic classes: Time Shift, Time Reversal, Time Scaling Time Shift: Signals are identical in shape, but they are shifted relative to each other. Such as x[n] and x[n-n0], x(t) and x(t-t0). x[n-n0] is a delayed version of x[n] if n0 >0 . x(t-t0) is a advanced version of x(n) if t0 <0 .

  2. A time shift occurs only when the variable t or n are substituted for t-t0 or n-n0. x(at) and x(a(t-t0))= x(at-at0) are shifted relative to each other. In applications: radar, sonar, communication and seismic signal processing.

  3. Time Reversal: Thesignal x[-n] is obtained from the signal x[n] by a reflection about n=0. Thesignal x(-t) is obtained from the signal x(t) by a reflection about t=0. Not a causal operation

  4. A time reversal occurs only when the variable t or n are substituted for -t or -n. The signal x(-at+b) is obtained from the signal x(at+b) by a reflection about t=0. The signal x[-n+b]is obtained from the signal x[n+b] by a reflection about n=0.

  5. Time Scaling: Thesignal x(at) (a>0) is obtained from the signal x(t) by linearly stretched if |a|<1,linearly compressed if |a|>1. Not a causal operation

  6. A time scaling occurs only when the variable t is substituted for at (a>0,a!=1). The signal x(at+b) (a>0) is obtained from the signal x(t+b) by linearly stretched if |a|<1,linearly compressed if |a|>1.

  7. 1.2Signal transformations involving linear transformations of the independent variable Basic classes: Time Shift, Time Reversal, Time Scaling

  8. 1.2.2 Periodic Signals Definition

  9. 1.2.2 Periodic Signals Fundamental Period

  10. 1.2.2 Periodic Signals

  11. 1.2.2 Periodic Signals

  12. 1.2.3 Even and Odd Signals

  13. The Even-Odd Decomposition of an arbitrary Signal

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