FFT - Fast Fourier transform (FFT) of input - Simulink (original) (raw)

Fast Fourier transform (FFT) of input

Libraries:
DSP System Toolbox / Transforms

Description

The FFT block computes the fast Fourier transform (FFT) across the first dimension of an _N_-D input array, u. The block uses one of two possible FFT implementations. You can select an implementation based on the FFTW library or an implementation based on a collection of Radix-2 algorithms. To allow the block to choose the implementation, you can selectAuto. For more information about the FFT implementations, see Algorithms.

For user-specified FFT lengths not equal to P, zero padding or truncating, or modulo-length data wrapping occurs before the FFT operation. For an FFT with P ≤ M:

Wrapping:

y(:,L) = fft(datawrap(u(:,L),M)) % P > M; L = 1,...,N

Truncating:

y (:,L) = fft(u,M) % P > M; L = 1,...,N

Tip

When the input length, P, is greater than the FFT length,M, you may see magnitude increases in your FFT output. These magnitude increases occur because the FFT block uses modulo-M data wrapping to preserve all available input samples.

To avoid such magnitude increases, you can truncate the length of your input sample, P, to the FFT length, M. To do so, place a Pad block before the FFT block in your model.

Examples

Ports

Input

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Input signal for computing the FFT. The block computes the FFT along the first dimension of the _N_-D input signal.

For more information on how the block computes the FFT, see Description and Algorithms.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fixed point
Complex Number Support: Yes

Output

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The FFT, computed across the first dimension of an_N_-D input array. When the output of the block has an integer or fixed-point data type, it is always signed.

The _k_th entry of the _L_th output channel,y(k,L), equals the _k_th point of the_M_-point discrete Fourier transform (DFT) of the_L_th input channel:

For more information on how the block computes the FFT, see Description and Algorithms.

Data Types: single | double | int8 | int16 | int32 | fixed point
Complex Number Support: Yes

Parameters

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Main

Set this parameter to FFTW to support an arbitrary length input signal. The block restricts generated code with FFTW implementation to host computers capable of running MATLAB®.

Set this parameter to Radix-2 for bit-reversed processing, fixed or floating-point data, or portable C-code generation using theSimulink® Coder™. The dimension M of the_M_-by-N input matrix, must be a power of two. To work with other input sizes, use the Pad block to pad or truncate these dimensions to powers of two, or if possible choose the FFTW implementation. For more information about the algorithms used by theRadix-2 mode, see Radix-2 Implementation.

Set this parameter to Auto to let the block choose the FFT implementation. For floating-point inputs with non-power-of-two transform lengths, the FFTW algorithm is automatically chosen. Otherwise a Radix-2 algorithm is automatically chosen. For non-power-of-two transform lengths, the block restricts generated code to MATLAB host computers.

Designate the order of the output channel elements relative to the ordering of the input elements. When you select this check box, the output channel elements appear in bit-reversed order relative to the input ordering. If you clear this check box, the output channel elements appear in linear order relative to the input ordering.

Note

The FFT block calculates its output in bit-reversed order. Linearly ordering the FFT block output requires an extra bit-reversal operation. In many situations, you can increase the speed of the FFT block by selecting the Output in bit-reversed order check box.

For more information ordering of the output, see Linear and Bit-Reversed Output Order.

Dependencies

To enable this parameter, set FFT implementation to Auto orRadix-2.

When you select this parameter, the block divides the output of the FFT by the FFT length. This option is useful when you want the output of the FFT to stay in the same amplitude range as its input. This is particularly useful when working with fixed-point data types.

Select to inherit the FFT length from the input dimensions. When you select this check box, the input length must be a power of two.

Dependencies

When you do not select this check box, the FFT length parameter becomes available to specify the length.

Specify FFT length as an integer greater than or equal to two.

When you set the FFT implementation parameter toRadix-2, or when you check the Output in bit-reversed order check box, this value must be a power of two.

Dependencies

To enable this parameter, clear the Inherit FFT length from input dimensions check box.

Choose to wrap or truncate the input, depending on the FFT length. If you select this parameter, modulo-length data wrapping occurs before the FFT operation when the FFT length is shorter than the input length. If you clear this check box, truncation of the input data to the FFT length occurs before the FFT operation.

Dependencies

To enable this parameter, clear the Inherit FFT length from input dimensions check box.

Data Types

Select the rounding mode for fixed-point operations.

Limitations

The sine table values do not obey this parameter; instead, they always round to Nearest.

The Rounding mode parameter has no effect on numeric results when all these conditions are met:

With these data type settings, the block operates in full-precision mode.

When you select this parameter, the block saturates the result of its fixed-point operation. When you clear this parameter, the block wraps the result of its fixed-point operation. For details onsaturate and wrap, see overflow mode for fixed-point operations.

Limitations

The Saturate on integer overflow parameter has no effect on numeric results when all these conditions are met:

With these data type settings, the block operates in full-precision mode.

Choose how to specify the word length of the values of the sine table. The fraction length of the sine table values always equals the word length minus one. You can set this parameter to:

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Sine table parameter.

See Specify Data Types Using Data Type Assistant (Simulink) for more information.

Limitations

The sine table values do not obey the Rounding mode and Saturate on integer overflow parameters; instead, they are always saturated and rounded to Nearest.

Specify the product output data type. See Fixed-Point Data Types andMultiplication Data Types for illustrations depicting the use of the product output data type in this block. You can set this parameter to:

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Product output parameter.

See Specify Data Types Using Data Type Assistant (Simulink) for more information.

Specify the accumulator data type. See Fixed-Point Data Types for illustrations depicting the use of the accumulator data type in this block. You can set this parameter to:

Click the Show data type assistant button to display the Data Type Assistant, which helps you set theAccumulator parameter.

See Specify Data Types Using Data Type Assistant (Simulink) for more information.

Specify the output data type. See Fixed-Point Data Types for illustrations depicting the use of the output data type in this block. You can set this parameter to:

Click the Show data type assistant button to display the Data Type Assistant, which helps you set theOutput parameter.

See Control Data Types of Signals (Simulink) for more information.

Specify the minimum value that the block should output. The default value is [] (unspecified). Simulink software uses this value to perform:

Specify the maximum value that the block should output. The default value is [] (unspecified). Simulink software uses this value to perform:

Block Characteristics

Data Types double | fixed point integer single
Direct Feedthrough no
Multidimensional Signals yes
Variable-Size Signals yesa
Zero-Crossing Detection no
a Variable-size signals are only supported when the Inherit FFT length from input dimensions checkbox is selected.

More About

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The following diagrams show the data types used in the FFT block for fixed-point signals. You can set the Sine table,Accumulator, Product output, andOutput data types displayed in the diagrams in the FFT dialog box as discussed in Parameters.

Inputs to the FFT block are first cast to the output data type and stored in the output buffer. Each butterfly stage then processes signals in the accumulator data type, with the final output of the butterfly being cast back into the output data type. The block multiplies in a twiddle factor before each butterfly stage in a decimation-in-time FFT and after each butterfly stage in a decimation-in-frequency FFT.

The output of the multiplier appears in the accumulator data type because both of the inputs to the multiplier are complex. For details on the complex multiplication performed, see Multiplication Data Types.

Note

When the block input is fixed point, all internal data types are signed fixed point.

Algorithms

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The FFTW implementation provides an optimized FFT calculation including support for power-of-two and non-power-of-two transform lengths in both simulation and code generation. Generated code using the FFTW implementation can only run on computers capable of running MATLAB. The input data type must be floating-point.

The Radix-2 implementation supports bit-reversed processing, fixed or floating-point data, and allows the block to provide portable C-code generation using the Simulink Coder. The dimension M of the_M_-by-N input matrix must be a power of two. To work with other input sizes, use the Pad block to pad or truncate these dimensions to powers of two, or if possible choose the FFTW implementation.

With Radix-2 selected, the block implements one or more of the following algorithms:

Radix-2 Algorithms for Real and Complex Signals

Complexity of Input Output Ordering Algorithms Used for FFT Computation
Complex Linear Bit-reversed operation and radix-2 DIT
Complex Bit-reversed Radix-2 DIF
Real Linear Bit-reversed operation and radix-2 DIT in conjunction with the half-length and double-signal algorithms
Real Bit-reversed Radix-2 DIF in conjunction with the half-length and double-signal algorithms

The efficiency of the FFT algorithm can be enhanced for real input signals by forming complex-valued sequences from the real-valued sequences prior to the computation of the DFT. When there are 2_N_+1 real input channels, the FFT block forms these complex-valued sequences by applying the double-signal algorithm to the first 2_N_ input channels, and the half-length algorithm to the last odd-numbered channel.

For real input signals with fixed-point data types, different numerical results might appear in the output of the last odd-numbered channel, even when all input channels are identical. This numerical difference results from differences in the double-signal algorithm and the half-length algorithm.

You can eliminate this numerical difference in two ways:

For more information on the double-signal algorithm, see [2], “Efficient Computation of the DFT of Two Real Sequences” on page 475. For more information on the half-length algorithm, see [2], “Efficient Computation of the DFT of a 2N-Point Real Sequence” on page 476.

Radix-2 Optimization for the Table of Trigonometric Values

In certain situations, the block’s Radix–2 algorithm computes all the possible trigonometric values of the twiddle factor

where K is the greater value of either_M_ or N and k=0,⋯,K−1. The block stores these values in a table and retrieves them during simulation. The number of table entries for fixed-point and floating-point is summarized in the following table:

Number of Table Entries for N-Point FFT
floating-point 3_N_/4
fixed-point N

References

[1] Orfanidis, S. J.Introduction to Signal Processing. Upper Saddle River, NJ: Prentice Hall, 1996, p. 497.

[2] Proakis, John G. and Dimitris G. Manolakis. Digital Signal Processing, 3rd ed. Upper Saddle River, NJ: Prentice Hall, 1996.

[4] 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.

Extended Capabilities

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Usage notes and limitations:

Version History

Introduced before R2006a