# Complex Bandpass Decimator

Extract a frequency subband using a one-sided (complex) bandpass decimator

• Library:
• DSP System Toolbox / Filtering / Multirate Filters

## Description

The Complex Bandpass Decimator block extracts a specific subband of frequencies using a one-sided, multistage, complex bandpass decimator. The block determines the bandwidth of interest using the specified center frequency, decimator factor, and bandwidth values.

## Ports

### Input

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Data input, specified as a vector or a matrix. The number of rows in the input must be a multiple of the decimation factor.

This port is unnamed unless you select the Specify center frequency from input port parameter.

Data Types: `single` | `double`
Complex Number Support: Yes

Center frequency of the desired band in Hz, specified as a real, finite numeric scalar in the range [–Fs/2, Fs/2]. The value of Fs depends on the setting of the Inherit sample rate from input parameter. When you select this parameter, Fs is the value the block inherits from the input signal. When you clear this parameter, Fs is the value you specify in the Input sample rate (Hz) parameter.

This port is only available if you select the Specify center frequency from input port parameter.

Data Types: `single` | `double`
Complex Number Support: Yes

### Output

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Output of the complex bandpass decimator, returned as a vector or a matrix. The output contains the subband of frequencies specified by the parameters on the block dialog. The number of rows (frame size) in the output signal is 1/D times the number of rows in the input signal, where D is the decimation factor. The number of channels (columns) does not change.

The data type of the output is same as the data type of the input. The output signal is always complex.

Data Types: `single` | `double`
Complex Number Support: Yes

## Parameters

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Filter design parameters, specified as one of the following:

• `Decimation factor` –– The block specifies the decimation factor through the Decimation factor parameter. The bandwidth of interest (BW) is computed using the following equation:

`$BW=Fs/D$`

where

• Fs –– Sample rate specified through the Input sample rate (Hz) parameter.

• D –– Decimation factor.

• `Bandwidth` –– The block specifies the bandwidth through the Bandwidth (Hz) parameter. The decimation factor (D) is computed using the following equation:

`$D=\text{floor}\left(\frac{Fs}{BW+TW}\right)$`

where

• Fs –– Sample rate specified through the Input sample rate (Hz) parameter.

• BW –– Bandwidth of interest.

• TW –– Transition width specified through the Transition width (Hz) parameter.

• `Decimation factor and bandwidth` –– The decimation factor and the bandwidth of interest are specified through the Decimation factor and Bandwidth (Hz) parameters.

Factor by which to reduce the bandwidth of the input signal, specified as a positive integer. The frame size (number of rows) of the input signal must be a multiple of the decimation factor.

#### Dependencies

This parameter applies when you set Filter specification to either ```Decimation factor``` or ```Decimation factor and bandwidth```.

Width of the frequency band of interest, specified as a real positive scalar in Hz.

#### Dependencies

This parameter applies when you set Filter specification to either `Bandwidth` or ```Decimation factor and bandwidth```.

Data Types: `single` | `double`

When you select this check box, the center frequency is input through the Fc port. When you clear this check box, the center frequency is specified on the block dialog through the Center frequency (Hz) parameter.

When you select this check box, the block does not compute the filter response. To view the filter response, clear this check box, specify the center frequency on the block dialog, and click button.

Center frequency of the desired band in Hz, specified as a real, finite numeric scalar in the range [–Fs/2, Fs/2].

Tunable: Yes

Data Types: `single` | `double`

Stopband attenuation of the filter in dB, specified as a finite positive scalar.

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

Passband ripple of the filter, specified as a positive scalar in dB.

#### Dependencies

This parameter applies when you set Filter specification to either `Bandwidth` or ```Decimation factor and bandwidth```.

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

Transition width of the filter in Hz, specified as a positive scalar.

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

Minimize the number of complex coefficients. When you select this parameter, the first stage of the multistage filter is bandpass (with complex coefficients) centered at the specified center frequency. The first stage is followed by a mixing stage that heterodynes the signal to DC. The remaining filter stages, all with real coefficients, follow.

When you clear the parameter, the input signal is first passed through the different stages of the multistage filter. All stages are bandpass (complex coefficients). The signal is then heterodyned to DC if Mix signal to baseband parameter is selected and the frequency offset resulting from the decimation is nonzero.

Mix the signal to baseband. When you select this parameter, the block heterodynes the filtered, decimated signal to DC. This mixing stage runs at the output sample rate of the filter. When you clear this parameter, the block skips the mixing stage.

#### Dependencies

This parameter applies when you clear the Reduce number of complex coefficients parameter.

When you select this parameter, the block inherits its sample rate from the input signal. The block calculates the sample rate based on the sample time of the input port. When you clear this parameter, specify the sample rate in Input sample rate (Hz).

Sampling rate of the input signal in Hz, specified as a real positive scalar.

#### Dependencies

This parameter applies when you clear the Inherit sample rate from input parameter.

Data Types: `single` | `double`

## Block Characteristics

 Data Types `double` | `single` Multidimensional Signals `No` Variable-Size Signals `Yes`

## Algorithms

The complex bandpass decimator is designed by applying a complex frequency shift transformation on a lowpass prototype filter. The lowpass prototype in this case is a multirate, multistage finite impulse response (FIR) filter. The desired frequency shift applies only to the first stage. Subsequent stages scale the desired frequency shift by their respective cumulative decimation factors. For details, see Complex Bandpass Filter Design and Zoom FFT.

## Extended Capabilities

### Topics

Introduced in R2018a

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