Frequency-Domain FIR Filter

Filter input signal in the frequency domain

• Library:

• DSP System Toolbox / Filtering / Filter Implementations

Description

The Frequency-Domain FIR Filter block implements frequency-domain, fast Fourier transform (FFT)-based filtering to filter a streaming input signal. In the time domain, the filtering operation involves a convolution between the input and the impulse response of the finite impulse response (FIR) filter. In the frequency domain, the filtering operation involves the multiplication of the Fourier transform of the input and the Fourier transform of the impulse response. The frequency-domain filtering becomes more efficient than time-domain filtering as the impulse response grows longer. You can specify the filter coefficients directly in the frequency domain by setting Numerator domain to Frequency.

This block uses the overlap-save and overlap-add methods to perform the frequency-domain filtering. For filters with a long impulse response length, the latency inherent to these two methods can be significant. To mitigate this latency, the Frequency-Domain FIR Filter block partitions the impulse response into shorter blocks and implements the overlap-save and overlap-add methods on these shorter blocks. To partition the impulse response, select the Partition numerator to reduce latency check box. For more details on these two methods and on reducing latency through impulse response partitioning, see Algorithms.

Ports

Input

x — Data Input

vector | matrix

Data input, specified as a vector or matrix. This block supports variable-size input signals. That is, you can change the input frame size (number of rows) even after calling the algorithm. However, the number of channels (number of columns) must remain constant.

This port is unnamed until you select the Specify coefficients from input port parameter.

Data Types: single | double
Complex Number Support: Yes

NUM — Time domain FIR filter coefficients

row vector

Time domain FIR filter coefficients, specified as a row vector.

Dependencies

This port appears when you set Numerator domain to Time and select the Specify coefficients from input port parameter.

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

NUMFFT — Frequency domain FIR filter coefficients

row vector

Frequency domain FIR filter coefficients, specified as a row vector or a matrix. When you clear the Partition numerator to reduce latency parameter, the coefficients input through this port must be a row vector. The FFT length is equal to the length of the vector input. When you select the Partition numerator to reduce latency parameter, Frequency response must be a 2P-by-N matrix, where P is the partition size, and N is the number of partitions.

Dependencies

This port appears when you set Numerator domain to Frequency and select the Specify frequency response from input port parameter.

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

Output Arguments

y — Filtered output

vector | matrix

Filtered output, returned as a vector or matrix. The size, data type, and complexity of the output match those of the input.

This port is unnamed until you select the Output filter latency parameter and click Apply.

Data Types: single | double
Complex Number Support: Yes

latency — Filter latency

positive integer

Filter latency, returned as a scalar. This latency is inherent to overlap-add and overlap-save methods and does not include the group delay of the filter. This port appears only when you select the Output filter latency check box.

This port is unnamed until you select the Output filter latency check box and click Apply.

Data Types: uint32

Parameters

Frequency-domain filter method — Filtering method in frequency domain

Overlap-save (default) | Overlap-add

Filtering method in the frequency domain, specified as either Overlap-save or Overlap-add. For more details on these two methods, see Algorithms

Numerator domain — Numerator domain

Time (default) | Frequency

Domain of the filter coefficients, specified as one of the following:

• Time –– Specify the time-domain filter coefficients in the Filter coefficients parameter or through the NUM input port.

• Frequency –– Specify the filter's frequency response in the Frequency response parameter or through the NUMFFT input port.

Specify coefficients from input port — Flag to specify lowpass filter coefficients

off (default) | on

When you select this check box, the FIR filter coefficients are input through the port, NUM. When you clear this check box, the coefficients are specified on the block dialog through the Filter coefficients parameter.

To view the filter response, clear this check box, specify the coefficients on the block dialog, and click on the View Filter Response button.

Dependencies

To enable this parameter, set Numerator domain to Time.

Filter coefficients — filter coefficients

fir1(100,0.3) (default) | row vector

FIR filter coefficients, specified as a row vector.

Dependencies

To enable this parameter, set Numerator domain to Time and clear the Specify coefficients from input port parameter.

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

Specify frequency response from input port — Flag to specify frequency-domain filter coefficients

off (default) | on

When you select this check box, the FIR filter coefficients in the frequency domain are input through the port, NUMFFT. When you clear this check box, the coefficients are specified on the block dialog through the Frequency response parameter.

To view the filter response, clear this check box, specify the frequency response on the block dialog, and click on the View Filter Response button.

Dependencies

To enable this parameter, set Numerator domain to Frequency.

Frequency response — Filter coefficients

fft(fir1(100,0.3),202) (default) | row vector | matrix

Frequency response of the filter, specified as a row vector or a matrix. When you clear the Partition numerator to reduce latency parameter, Frequency response must be a row vector. The FFT length is equal to the length of the Frequency response vector. When you select the Partition numerator to reduce latency parameter, Frequency response must be a 2P-by-N matrix, where P is the partition size, and N is the number of partitions.

Dependencies

To enable this parameter, set Numerator domain to Frequency and clear the Specify frequency response from input port parameter.

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

Partition numerator to reduce latency — Flag to partition the numerator to reduce latency

off (default) | on

Flag to partition the numerator to reduce latency, specified as one of the following:

• off –– The filter uses the traditional overlap-save or overlap-add method. The latency in this case is FFT length – NumLen + 1. NumLen is the length of the numerator vector you specify in the Filter coefficients parameter.

• on –– In this mode, the block partitions the numerator into segments of length specified by the Numerator partition length parameter. The filter performs overlap-save or overlap-add on each partition, and combines the partial results to form the overall output. The latency is now reduced to the partition length.

Numerator partition length — Partition length of numerator

32 (default) | positive integer

Partition length of the numerator, specified as a positive integer less than or equal to the length of the numerator.

Dependencies

This parameter applies only when you set Numerator domain to Time and select the Partition numerator to reduce latency parameter.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Time-domain numerator length — Time-domain numerator length

101 (default) | positive integer-valued scalar

Time-domain numerator length, specified as a positive integer-valued scalar.

Dependencies

This parameter applies only when you set Numerator domain to Frequency and clear the Partition numerator to reduce latency check box.

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32

Inherit FFT length from numerator length — Flag to inherit FFT length from the numerator length

on (default) | off

When you select this check box, the FFT length equals twice the numerator length. When you clear this check box, you specify the FFT length through the FFT length parameter.

Dependencies

This parameter applies only when you set Numerator domain to Time and clear the Partition numerator to reduce latency parameter.

FFT length — FFT length

1024 (default) | positive integer

The FFT length you specify must be greater than or equal to the length of the numerator vector you specify in the Filter coefficients parameter.

Dependencies

This parameter applies when you set Numerator domain to Time, clear the Partition numerator to reduce latency and the Inherit FFT length from numerator length parameters.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Filter is real — Flag to specify if filter is real

true (default) | false

Flag to specify if the filter is real, specified as true or false.

Dependencies

This parameter applies when Numerator domain to Frequency.

Output filter latency — Flag to output filter latency

'off' (default) | 'on'

When you select this check box and click Apply, the block outputs the filter latency through the latency port.

View Filter Response — Visualize frequency response of FIR filter

button

Opens the Filter Visualization Tool (FVTool) and displays the magnitude/phase response of the FIR filter. The response is based on the block dialog parameters. Changes made to these parameters update FVTool.

To update the magnitude response while FVTool is running, modify the block dialog parameters and click Apply.

To view the filter response when the Numerator domain is set to Time, clear the Specify coefficients from input port check box. To view the filter response when the Numerator domain is set to Frequency, clear the Specify frequency response from input port check box.

Simulate using — Type of simulation to run

Code generation (default) | Interpreted execution

• Code generation — Simulate model using generated C code. The first time you run a simulation, Simulink^® generates C code for the block. The C code is reused for subsequent simulations, as long as the model does not change. This option requires additional startup time but provides faster simulation speed than Interpreted execution.

• Interpreted execution — Simulate model using the MATLAB^®  interpreter. This option shortens startup time but has slower simulation speed than Code generation.

Model Examples

Overlap-Add/Save

Filter a sinusoid with the Overlap-Add and Overlap-Save FFT methods using the Frequency-Domain FIR filter block.

Open Model

Block Characteristics

Data Types	double | single
Direct Feedthrough	no
Multidimensional Signals	no
Variable-Size Signals	yes
Zero-Crossing Detection	no

Algorithms

Overlap-save and overlap-add are the two frequency-domain FFT-based filtering methods this algorithm uses.

Overlap-Save

The overlap-save method is implemented using the following approach:

The input stream is partitioned into overlapping blocks of size FFTLen, with an overlap factor of NumLen – 1 samples. FFTLen is the FFT length and NumLen is the length of the FIR filter numerator. The FFT of each block of input samples is computed and multiplied with the length-FFTLen FFT of the FIR numerator. The inverse fast Fourier transform (IFFT) of the result is performed, and the last FFTLen – NumLen + 1 samples are saved. The remaining samples are dropped.

The latency of overlap-save is FFTLen – NumLen + 1. The first FFTLen – NumLen + 1 samples are equal to zero. The filtered value of the first input sample appears as the FFTLen – NumLen + 2 output sample.

Note that the FFT length must be larger than the numerator length, and is typically set to a value much greater than NumLen.

Overlap-Add

The overlap-add method is implemented using the following approach:

The input stream is partitioned into blocks of length FFLen – NumLen + 1, with no overlap between consecutive blocks. Similar to overlap-save, the FFT of the block is computed, and multiplied by the FFT of the FIR numerator. The IFFT of the result is then computed. The first NumLen + 1 samples are modified by adding the values of the last NumLen + 1 samples from the previous computed IFFT.

The latency of overlap-add is FFTLen – NumLen + 1. The first FFTLen – NumLen + 1 samples are equal to zero. The filtered value of the first input sample appears as the FFTLen – NumLen + 2 output sample.

Reduce Latency Through Impulse Response Partitioning

With an FFT length that is twice the length of the FIR numerator, the latency roughly equals the length of the FIR numerator. If the impulse response is very long, the latency becomes significantly large. However, frequency domain FIR filtering is still faster than the time-domain filtering. To mitigate the latency and make the frequency domain filtering even more efficient, the algorithm partitions the impulse response into multiple short blocks and performs overlap-save or overlap-add on each block. The results of the different blocks are then combined to obtain the final output. The latency of this approach is of the order of the block length, rather than the entire impulse response length. This reduced latency comes at the cost of additional computation. For more details, see [1].

References

[1] Stockham, T. G., Jr. "High Speed Convolution and Correlation." Proceedings of the 1966 Spring Joint Computer Conference, AFIPS, 28 (1966): 229–233.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.