IFFT
Inverse Fast Fourier Transform (IFT) of the input signal.
blockType: SubSystem
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Path in the library: |
Description
Block IFFT calculates the inverse fast Fourier transform (FFT) on the first dimension of a multidimensional input array, -D.
The block uses one of two possible implementations of the FFT. You can choose the implementation based on the FFTW library or the implementation based on the Radix-2 algorithm.
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When the length of the input signal, , is greater than the length of the OPF, , you can observe an increase in the amplitude of the output signal. This is because the block IFFT uses length modulo data reset , to preserve all available input samples. To avoid this increase in amplitude, you can truncate the input sample length to the OPF length . To do this, place a block Pad before the block in the model IFFT. |
Ports
Input
#
Port_1
—
input signal
vector | matrix| multidimensional array
Details
Input signal for OPF calculation as a vector, matrix or multidimensional array.
The unit calculates the OPF by the first measurement of the multidimensional input signal.
| Data types |
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| Complex numbers support |
Yes |
Output
#
Port_1
—
OPF of the input signal
vector | matrix| multidimensional array
Details
An output signal returned as a vector, matrix or multidimensional array.
OPF calculated from the first dimension of the multidimensional input array.
The -th entry of the -th output channel, , is equal to the -point -point inverse discrete Fourier transform (ODPF) of the -th input channel:
| Data types |
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| Complex numbers support |
Yes |
Parameters
Parameters
#
FFT implementation —
FFT realisation
Radix-2 | FFTW
Details
FFT Implementation:
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FFTW- support input signal of arbitrary length. -
Radix-2- implementation of bitwise processing of floating point data. The dimensionality of the input matrix with the size to must be equal to the power of two. To work with other input data dimensions, use the block Pad, to flatten or truncate these dimensions to powers of two, or if possible, choose theFFTWimplementation.
| Values |
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| Default value |
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| Program usage name |
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| Tunable |
No |
| Evaluatable |
Yes |
# Input is in bit-reversed order — bit-reverse input
Details
Specifies the order of the input channel elements relative to the order of the output channel elements. When this check box is selected, the input channel items are displayed in bit-reverse order relative to the output sequence order. When unchecked, the input channel items are displayed in linear order relative to the output sequence order.
| The IFFT block computes its input in bit-reverse order. The linear ordering of the IFFT block’s input data requires an additional bit-reverse operation. In many situations it is possible to increase the speed of the IFFT block by checking the Input in bit-reversed order checkbox. |
Dependencies
To use this parameter, set the FFT implementation parameters to Radix-2.
| Default value |
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| Program usage name |
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| Tunable |
No |
| Evaluatable |
Yes |
# Divide output by FFT length — divide the output by the FFT length
Details
When this parameter is selected, the unit divides the OPF output by the FFT length. This option is useful when you want the OPF output to remain in the same amplitude range as the input.
| Default value |
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| Program usage name |
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| Tunable |
No |
| Evaluatable |
Yes |
# Inherit FFT length from input dimensions — inherit the FFT length from the input dimensions
Details
Select this check box to inherit FFT length from input dimensions.
Dependencies
If this checkbox is not selected, the FFT length parameters become available for specifying the length.
| Default value |
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| Program usage name |
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| Tunable |
No |
| Evaluatable |
Yes |
# FFT length — FFT length
Details
Specify the FFT length as an integer, .
If the FFT implementation parameters are set to Radix-2 or the Intput in bit-reversed order checkbox is selected, this value must be two.
Dependencies
To use this parameter, uncheck Inherit FFT length from input dimensions.
| Default value |
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| Program usage name |
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| Tunable |
No |
| Evaluatable |
Yes |
# Wrap input data when FFT length is shorter than input length — convolution or truncation input data
Details
Selects whether to convolve or truncate the input data depending on the FFT length. If this parameter is selected, modulo convolution is performed before the FFT operation when the FFT length is less than the input length. If unchecked, the input data is truncated to the FFT length before the FFT operation.
Dependencies
To use this parameter, clear the Inherit FFT length from input dimensions checkbox.
| Default value |
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| Program usage name |
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| Tunable |
No |
| Evaluatable |
Yes |
Algorithms
FFTW implementation
The FFTW implementation provides an optimised FFT calculation, including support for transform lengths equal to and not equal to powers of two, as in simulation. The input data type must be floating point.
Radix-2 implementation
The Radix-2 implementation supports bit-reverse processing and allows the block to perform C code generation. The dimensionality of the input matrix of size to must be equal to a power of two. To work with other input dimensions, use the Pad block to augment or truncate those dimensions to a power of two.
When Radix-2 is selected, the block implements one or more of the following algorithms:
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Butterfly operation
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Double signal algorithm
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Half length algorithm
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Radix-2’s time-invariant thinning (DIT) algorithm
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Radix-2 Frequency (DIF) Thinning Algorithm
Radix-2 algorithms for real and complex signals
| Complexity of input data | Order of output data | Algorithms used for FFT calculation |
|---|---|---|
Complex |
Linear |
Bit-reversal operation and Radix-2 DIT algorithm |
Complex |
Bit-reversal |
Radix-2 DIF |
Real |
Linear |
Bit-reversal operation and Radix-2 DIT combined with half-length and double-signal algorithms |
Real |
Bit-reverse |
Radix-2 DIF combined with half-length and double-signal algorithms |
The efficiency of the FFT algorithm can be improved for real input signals by forming complex sequences from the real sequences before computing the DIF. If there are real input channels, the FFT unit generates these complex sequences by applying the double signal algorithm to the first input channels and the half length algorithm to the last odd channel.
Optimising Radix-2 for a table of trigonometric values
In some situations, the Radix-2 block algorithm calculates all possible trigonometric values of the twiddle factor (twiddle factor)
,
where
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- is the larger of the two values: or ,
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.
The block stores these values in a table and retrieves them during the simulation. The number of entries in the table for floating point is shown in the following table:
| Number of entries in the table for N-point FFT | |
|---|---|
floating point |
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Literature
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Orfanidis, S. J. "Introduction to Signal Processing." Upper Saddle River, NJ: Prentice Hall, 1996, p. 497.
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Proakis, John G. and Dimitris G. Manolakis. "Digital Signal Processing, 3rd ed." Upper Saddle River, NJ: Prentice Hall, 1996.
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FFTW (https://www.fftw.org)
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Frigo, M. and S. G. Johnson, "FFTW: An Adaptive Software Architecture for the FFT," Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, Vol. 3, 1998, pp. 1381-1384.