Inverse Synthetic Aperture Radar Imaging With MATLAB Algorithms. Caner Ozdemir

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Inverse Synthetic Aperture Radar Imaging With MATLAB Algorithms - Caner Ozdemir


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      1.2.3 Frequency Shifting

      If the time signal is multiplied by a phase term of

, then the FT of this time signal is shifted in frequency by fo as given below

      (1.7)

      1.2.4 Scaling

      If the time signal is scaled by a constant a, then the spectrum is also scaled with the following rule

      (1.8)

      1.2.5 Duality

      If the spectrum signal G(f) is taken as a time signal G(t), then, the corresponding frequency domain signal will be the time reversal equivalent of the original time domain signal, g(t) as

      (1.9)

      1.2.6 Time Reversal

      If the time is reversed for the time‐domain signal, then the frequency is also reversed in the frequency domain signal.

      (1.10)

      1.2.7 Conjugation

      If the conjugate of the time‐domain signal is taken, then the frequency‐domain signal conjugated and frequency‐reversed.

      (1.11)

      1.2.8 Multiplication

      If the time‐domain signals, g(t) and h(t) are multiplied in time, then their spectrum signals G(f) and H(f) are convolved in frequency.

      1.2.9 Convolution

      If the time‐domain signals, g(t) and h(t) are convolved in time, then their spectrum signals G(f) and H(f) are multiplied in the frequency domain.

      1.2.10 Modulation

      If the time‐domain signal is modulated with sinusoidal functions, then the frequency‐domain signal is shifted by the amount of the frequency at that particular sinusoidal function.

      (1.14)

      1.2.11 Derivation and Integration

      If the derivative or integration of a time‐domain signal is taken, then the corresponding frequency‐domain signal is given as below.

      (1.15)

      1.2.12 Parseval's Relationship

      A useful property that was claimed by Parseval is that since the FT (or IFT) operation maps a signal in one domain to another domain, their energies should be exactly the same as given by the following relationship.

      (1.16)

      While the FT concept can be successfully utilized for the stationary signals, there are many real‐world signals whose frequency contents vary over time. To be able to display these frequency variations over time; therefore, joint time–frequency (JTF) transforms/representations are being used.

      1.3.1 Signal in the Time Domain

      1.3.2 Signal in the Frequency Domain

Schematic illustration of time-domain signal of prince spoken by a lady. Schematic illustration of frequency-domain signal of prince.
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