Table Of Contents

Inverse FFT (Inverse Real FFT) (G Dataflow)

Version:
    Last Modified: March 15, 2017

    Computes the inverse discrete Fourier transform (IDFT) of a sequence. You can use this node when the input sequence is the Fourier transform of a real time-domain signal.

    connector_pane_image
    datatype_icon

    reset

    A Boolean that specifies whether to reset the internal state of the node.

    True Resets the internal state of the node.
    False Does not reset the internal state of the node.

    This input is available only if you wire a complex double-precision, floating-point number to FFT{x}.

    Default: False

    datatype_icon

    FFT{x}

    Complex valued input sequence, which should be conjugated centrosymmetric except for the first element.

    This node uses only the anterior half of FFT{x}.

    This input accepts the following data types:

    • Complex double-precision, floating-point number
    • 1D array of complex double-precision, floating-point numbers
    • 2D array of complex double-precision, floating-point numbers
    datatype_icon

    sample length

    Length of each set of data. The node performs computation for each set of data.

    sample length must be greater than zero.

    This input is available only if you wire a complex double-precision, floating-point number to FFT{x}.

    Default: 100

    datatype_icon

    shift?

    A Boolean that determines whether the DC component is at the center of the FFT of the input sequence.

    True The DC component is at the center of the FFT{x}.
    False The DC component is not at the center of the FFT{x}.

    This input is available only if you wire a 1D array of complex double-precision, floating-point numbers or a 2D array of complex double-precision, floating-point numbers to FFT{x}.

    How This Input Affects 1D FFT

    The following table illustrates the pattern of the elements of FFT{x} with various length of the FFT, when shift? is False. Y is FFT{x} and n is the length of the FFT:

    n is even (k = n/2) n is odd (k = (n-1)/2)
    Array Element Corresponding Frequency Array Element Corresponding Frequency
    Y0 DC component Y0 DC component
    Y1 Δ f Y1 Δ f
    Y2 2 Δ f Y2 2 Δ f
    Y3 3 Δ f Y3 3 Δ f
    Yk-2 ( k 2 ) Δ f Yk-2 ( k 2 ) Δ f
    Yk-1 ( k 1 ) Δ f Yk-1 ( k 1 ) Δ f
    Yk Nyquist Frequency Yk k Δ f
    Yk+1 ( k 1 ) Δ f Yk+1 k Δ f
    Yk+2 ( k 2 ) Δ f Yk+2 ( k 1 ) Δ f
    Yn-3 3 Δ f Yn-3 3 Δ f
    Yn-2 2 Δ f Yn-2 2 Δ f
    Yn-1 Δ f Yn-1 Δ f

    The following table illustrates the pattern of the elements of FFT{x} with various length of the FFT, when shift? is True. Y is FFT{x} and n is the length of the FFT:

    n is even (k = n/2) n is odd (k = (n-1)/2)
    Array Element Corresponding Frequency Array Element Corresponding Frequency
    Y0 -(Nyquist Frequency) Y0 k Δ f
    Y1 ( k 1 ) Δ f Y1 ( k 1 ) Δ f
    Y2 ( k 2 ) Δ f Y2 ( k 2 ) Δ f
    Y3 ( k 3 ) Δ f Y3 ( k 3 ) Δ f
    Yk-2 2 Δ f Yk-2 2 Δ f
    Yk-1 Δ f Yk-1 Δ f
    Yk DC component Yk DC component
    Yk+1 Δ f Yk+1 Δ f
    Yk+2 2 Δ f Yk+2 2 Δ f
    Yn-3 ( k 3 ) Δ f Yn-3 ( k 2 ) Δ f
    Yn-2 ( k 2 ) Δ f Yn-2 ( k 1 ) Δ f
    Yn-1 ( k 1 ) Δ f Yn-1 k Δ f

    How This Input Affects 2D FFT

    The illustration below shows the effect of shift? on the 2D FFT result:

    2D input signals FFT without shift FFT with shift

    Default: False

    datatype_icon

    error in

    Error conditions that occur before this node runs.

    The node responds to this input according to standard error behavior.

    Standard Error Behavior

    Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

    error in does not contain an error error in contains an error
    If no error occurred before the node runs, the node begins execution normally.

    If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

    If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

    Default: No error

    datatype_icon

    x

    Inverse real FFT of the complex valued input sequence.

    This output can return a 1D array of double-precision, floating-point numbers or a 2D array of double-precision, floating-point numbers.

    datatype_icon

    error out

    Error information.

    The node produces this output according to standard error behavior.

    Standard Error Behavior

    Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

    error in does not contain an error error in contains an error
    If no error occurred before the node runs, the node begins execution normally.

    If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

    If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

    Algorithm Definition for 1D Inverse FFT

    For a 1D, N-sample, frequency domain sequence Y, the inverse discrete Fourier transform (IDFT) is defined as:

    X n = 1 N k = 0 N 1 Y k e j 2 π k n / N

    for n = 0, 1, 2, ..., N-1.

    Algorithm Definition for 2D Inverse FFT

    For a 2D, M-by-N frequency domain array Y, the inverse discrete Fourier transform (IDFT) is defined as:

    X ( m , n ) = 1 M N u = 0 M 1 v = 0 N 1 Y ( u , v ) e j 2 π m u / M e j 2 π n v / N

    for m = 0, 1, ..., M-1, n=0, 1, ..., M-1.

    Conjugated Centrosymmetric Property of 1D Inverse Real FFT

    When shift? is False and FFT{x} is the Fourier transform of a 1D real time-domain signal with length N, the posterior half part of FFT{x} can be constructed by the anterior half part. The centrosymmetric relationship between the anterior and posterior half part of FFT{x} can be written as

    f N 1 = f i * , i = 1 , 2 , ... , N 2

    where fi is the element in FFT{x}.

    This node uses only the anterior half part, from f0 to f _ N 2 to perform the inverse real FFT, where means the floor operation.

    Conjugated Centrosymmetric Property of 2D Inverse Real FFT

    When shift? is False and FFT{x} is the Fourier transform of a 2D real time-domain signal with M rows and N columns, the lower half part of FFT{x} can be constructed by the upper half part. The centrosymmetric relationship between the upper and lower half part of FFT{x} can be written as

    { f M i , j = f i , N j * i = 1 , 2 , ... , M 2 , j = 1 , 2 , ... , N 1 f M i , j = f i , j * i = 1 , 2 , ... , M 2 , j = 0

    where fi,j is the element in FFT{x}.

    This node uses only the upper half part, from f0,0 to f _ M 2 , N 1 to perform the inverse real FFT, where means the floor operation.

    Where This Node Can Run:

    Desktop OS: Windows

    FPGA: This product does not support FPGA devices


    Recently Viewed Topics