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# IFFT

Inverse fast Fourier transform (IFFT) of input

• Library:
• DSP System Toolbox / Transforms

## Description

The IFFT block computes the inverse fast Fourier transform (IFFT) across the first dimension of an N-D input array. 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 select `Auto`. For more information about the FFT implementations, see Algorithms.

When you specify an FFT length not equal to the length of the input vector (or first dimension of the input array), the block implements zero-padding, truncating, or modulo-M (FFT length) data wrapping. This occurs before the IFFT operation. For an IFFT with PM:

`y = ifft(u,M) % P ≤ M`

Wrapping:

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

Truncating:

`y (:,L) = ifft(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 IFFT output. These magnitude increases occur because the IFFT 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 IFFT block in your model.

## Ports

### Input

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Input signal for computing the IFFT. The block computes the IFFT along the first dimension of the N-D input signal. The input can be floating-point or fixed-point, real, or complex, and conjugate symmetric.

For more information on how the block computes the IFFT, 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 IFFT, computed across the first dimension of an N-D input array. For more information on how the block computes the IFFT, see Description and Algorithms.

The kth entry of the Lth output channel, y(k,L), is equal to the kth point of the M-point inverse discrete Fourier transform (IDFT) of the Lth input channel:

`$y\left(k,L\right)=\frac{1}{M}\sum _{p=1}^{P}u\left(p,L\right){e}^{j2\pi \left(p-1\right)\left(k-1\right)/M}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}k=1,\dots ,M$`

The output has the same dimensions as the input. If the input signal has a floating-point data type, the data type of the output signal uses the same floating-point data type. Otherwise, the output can be any signed fixed-point data type. The block computes scaled and unscaled versions of the IFFT.

Data Types: `single` | `double` | `int8` | `int16` | `int32` | `fixed point`

## 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 MATLAB® host computers.

Set this parameter to `Radix-2` for bit-reversed processing, fixed or floating-point data, or 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. For more information about the algorithms used by the `Radix-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.

Select or clear this check box to designate the order of the input channel elements. Select this check box when the input is in bit-reversed order, and clear it when the input is in linear order. The block yields invalid outputs when you do not set this parameter correctly.

You cannot select this check box if you have cleared the Inherit FFT length from input dimensions check box, and you are specifying the FFT length using the FFT length parameter. Also, it cannot be selected when you set the FFT implementation parameter to `FFTW`.

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

#### Dependencies

To enable this parameter, set FFT implementation to `Auto` or `Radix-2`.

Select this option when the block inputs conjugate symmetric data and you want real-valued outputs. Selecting this check box optimizes the block's computation method.

The FFT block yields conjugate symmetric output when you input real-valued data. Taking the IFFT of a conjugate symmetric input matrix produces real-valued output. Therefore, if the input to the block is both floating point and conjugate symmetric, and you select this check box, the block produces real-valued outputs.

You cannot select this check box if you have cleared the Inherit FFT length from input dimensions check box, and you are specifying the FFT length using the FFT length parameter.

If you input conjugate symmetric data to the IFFT block and do not select this check box, the IFFT block outputs a complex-valued signal with small imaginary parts. The block outputs invalid data if you select this option with non conjugate symmetric input data.

When you select this check box, the block computes its output according to the IDFT equation, discussed in the Description section.

When you clear this check box, the block computes the output using a modified version of the IDFT: $M\cdot y\left(k,l\right)$, which is defined by the following equation:

`$\begin{array}{cc}M\cdot y\left(k,l\right)=\sum _{p=1}^{P}u\left(p,l\right){e}^{j2\pi \left(p-1\right)\left(k-1\right)/M}& k=1,...,M\end{array}$`

The modified IDFT equation does not include the multiplication factor of 1/M.

Select to inherit the FFT length from the input dimensions. If you do not select this parameter, the FFT length parameter becomes available to specify the length. You cannot clear this parameter when you select either the Input is in bit-reversed order or the Input is conjugate symmetric parameter.

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

When you set the FFT implementation parameter to `Radix-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 parameter, 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:

• Product output data type is ```Inherit: Inherit via internal rule```.

• Accumulator data type is ```Inherit: Inherit via internal rule```.

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 on `saturate` 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:

• Product output data type is ```Inherit: Inherit via internal rule```.

• Accumulator data type is ```Inherit: Inherit via internal rule```.

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

Choose how you 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:

• A rule that inherits a data type, for example, ```Inherit: Same word length as input```

• An expression that evaluates to a valid data type, for example, `fixdt(1,16)`

Click the 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 and Multiplication Data Types for illustrations depicting the use of the product output data type in this block. You can set this parameter to:

• A rule that inherits a data type, for example, ```Inherit: Inherit via internal rule```. For more information on this rule, see Inherit via Internal Rule.

• An expression that evaluates to a valid data type, for example, `fixdt(1,16,0)`

Click the 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 for illustrations depicting the use of the accumulator data type in this block. You can set this parameter to:

• A rule that inherits a data type, for example, ```Inherit: Inherit via internal rule```. For more information on this rule, see Inherit via Internal Rule.

• An expression that evaluates to a valid data type, for example, `fixdt(1,16,0)`

Click the button to display the Data Type Assistant, which helps you set the Accumulator parameter.

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

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

• A rule that inherits a data type, for example, ```Inherit: Inherit via internal rule```.

When you select ```Inherit: Inherit via internal rule```, the block calculates the output word length and fraction length automatically. The equations that the block uses to calculate the ideal output word length and fraction length depend on the setting of the Divide output by FFT length check box.

• When you select the Divide output by FFT length check box, the ideal output word and fraction lengths are the same as the input word and fraction lengths.

• When you clear the Divide output by FFT length check box, the block computes the ideal output word and fraction lengths according to the following equations:

`$W{L}_{idealoutput}=W{L}_{input}+\text{floor}\left({\mathrm{log}}_{2}\left(FFTlength-1\right)\right)+1$`
`$F{L}_{idealoutput}=F{L}_{input}$`

Using these ideal results, the internal rule then selects word lengths and fraction lengths that are appropriate for your hardware. For more information, see Inherit via Internal Rule.

• An expression that evaluates to a valid data type, for example, `fixdt(1,16,0)`

Click the button to display the Data Type Assistant, which helps you set the Output 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:

• Simulation range checking (see Specify Signal Ranges (Simulink))

• Automatic scaling of fixed-point data types

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

• Simulation range checking (see Specify Signal Ranges (Simulink))

• Automatic scaling of fixed-point data types

Select this parameter to prevent the fixed-point tools from overriding the data types you specify in the block dialog box.

## 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.

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## 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.

## Version History

Introduced before R2006a