Computes the inverse fast Hilbert transform of the input sequence X using Fourier identities.


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Inputs/Outputs

  • c1ddbl.png X —

    X is the first input sequence.

  • i1ddbl.png Inv Hilbert {X} —

    Inv Hilbert {X} is the inverse Hilbert Transform of the input signal X.

  • ii32.png error —

    error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

    • The inverse Hilbert transform of a function h(t) is defined as

    Using the definition of the Hilbert transform

    you can obtain the inverse Hilbert transform by negating the forward Hilbert transform

    x(t) = H–1{h(t)} = –H{h(t)}

    Therefore, the Inverse Fast Hilbert Transform VI performs the discrete implementation of the inverse Hilbert transform with the aid of the Hilbert transform by taking the following steps.

    1. Hilbert transform the input sequence X

      Y = H{X}.

    2. Negate Y to obtain the inverse Hilbert transform

      H–1{X} = –Y.

    The Hilbert transform works best with AC coupled, band-limited signals.