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.
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
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 |
Y 0 | DC component | Y 0 | DC component |
Y 1 | Y 1 | ||
Y 2 | Y 2 | ||
Y 3 | Y 3 | ||
Y k-2 | Y k-2 | ||
Y k-1 | Y k-1 | ||
Y k | Nyquist Frequency | Y k | |
Y k+1 | Y k+1 | ||
Y k+2 | Y k+2 | ||
Y n-3 | Y n-3 | ||
Y n-2 | Y n-2 | ||
Y n-1 | Y n-1 |
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 |
Y 0 | -(Nyquist Frequency) | Y 0 | |
Y 1 | Y 1 | ||
Y 2 | Y 2 | ||
Y 3 | Y 3 | ||
Y k-2 | Y k-2 | ||
Y k-1 | Y k-1 | ||
Y k | DC component | Y k | DC component |
Y k+1 | Y k+1 | ||
Y k+2 | Y k+2 | ||
Y n-3 | Y n-3 | ||
Y n-2 | Y n-2 | ||
Y n-1 | Y n-1 |
How This Input Affects 2D FFT
Default: False
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.
Default: No error
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.
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.
For a 1D, N-sample, frequency domain sequence Y, the inverse discrete Fourier transform (IDFT) is defined as:
for n = 0, 1, 2, ..., N-1.
For a 2D, M-by-N frequency domain array Y, the inverse discrete Fourier transform (IDFT) is defined as:
for m = 0, 1, ..., M-1, n=0, 1, ..., M-1.
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
where f i is the element in FFT{x}.
This node uses only the anterior half part, from f 0 to to perform the inverse real FFT, where means the floor operation.
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
where f i,j is the element in FFT{x}.
This node uses only the upper half part, from f 0,0 to to perform the inverse real FFT, where means the floor operation.
Where This Node Can Run:
Desktop OS: Windows
FPGA: Not supported
Web Server: Not supported in VIs that run in a web application