# MT Generate Filter Coefficients (G Dataflow)

Calculates filter coefficients for pulse-shaping and matched filters applied by the digital modulation nodes and demodulation nodes.

## pulse shaping filter

Class of filter to generate.

You must correspond the selection here with the modulation type parameter setting as shown in the following table.

Modulation Type Valid Pulse-Shaping Type
PSK, QAM, ASK, PAM none (0)
Note

The node ignores the filter length parameter and generates a filter that is always one symbol long.

Raised Cosine (1)
Root Raised Cosine (2)
MSK none (0)
Note

The node ignores the filter length parameter and generates a filter that is always one symbol long.

Raised Cosine (1)
Root Raised Cosine (2)
Gaussian (3)
FSK, CPM none (0)
Note

The node ignores the filter length parameter and generates a filter that is always one symbol long.

Raised Cosine (1)
Root Raised Cosine (2)
Gaussian (3)

Default: none

## pulse shaping samples per symbol

Number of desired samples per symbol for the pulse-shaping filter.

If you use the pulse-shaping filter for demodulation, this parameter value must match the samples per symbol element of the system parameters cluster passed to the demodulation node. Specify an even number greater than 2.

Note

If the pulse-shaping and matched filter coefficients are used by the same demodulation or modulation node, the pulse shaping samples per symbol and matched samples per symbol values must be identical.

Default: 16

## matched samples per symbol

Number of desired samples per symbol for the demodulation matched filter.

You must match this parameter value to the samples per symbol element of the system parameters cluster passed to the digital demodulation node. Specify an even number greater than 2.

Default: 16

## filter parameter

A value that indicates either alpha (rolloff for raised cosine and square root raised cosine filters), or BT (the product of the -3 dB bandwidth and the symbol period for a Gaussian filter). Ignore this parameter when you set the pulse shaping filter parameter to none.

Default: 0.5

## error in

Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

Default: no error

## filter length

The desired length, in symbols, of the pulse-shaping filter. The length of the matched filter can vary according to filter type and modulation type. Valid values are greater than 1.

Default: 8

## modulation type

Type of modulation or demodulation for which to generate filter coefficients.

Name Description
FSK

Generates FSK filter coefficients.

PSK

Generates PSK filter coefficients.

QAM

Generates QAM filter coefficients.

MSK

Generates MSK filter coefficients.

PAM

Generates PAM filter coefficients.

CPM

Generates CPM filter coefficients.

Default: FSK

## pulse shaping filter coefficients

An ordered array of filter coefficients corresponding to the desired filter response for the pulse-shaping filter used in modulation. The number of coefficients depends on the pulse-shaping filter characteristics specified in the pulse shaping filter parameter.

Number of Coefficients Size for FSK Size for MSK Size for PSK/QAM/ASK/PAM
none (samples/symbol) (samples/symbol) (samples/symbol)
raised cosine (samples/symbol) × filter length + 1 (samples/symbol) × filter length + 1 (samples/symbol) × filter length + 1
root raised cosine (samples/symbol) × filter length + 1 (samples/symbol) × filter length + 1 (samples/symbol) × filter length + 1
Gaussian (samples/symbol) × filter length + 1 (samples/symbol) × filter length + 1 N/A

## matched filter coefficients

An ordered array of filter coefficients corresponding to the desired filter response for the matched filter used in demodulation.

Number of Coefficients Size for FSK Size for MSK Size for PSK/QAM/ASK/PAM
none (samples/symbol) (samples/symbol) (samples/symbol)
raised cosine 1 1 1
root raised cosine (samples/symbol) × filter length + 1 (samples/symbol) × filter length + 1 (samples/symbol) × filter length + 1
Gaussian 14 × (samples/symbol) + 1 3 × (samples/symbol) - 1 N/A

## error out

Error information. The node produces this output according to standard error behavior.

## Filter Impulse Response Calculations

Use the calculated filter coefficients during modulation to reduce the bandwidth of the transmitted signal and during demodulation to reduce intersymbol interference. The pulse-shaping filter can be used either in transmission or for demodulation of PSK-, FSK-, MSK-, ASK-, PAM-, QAM-, and CPM-modulated signals. Use matched filter only for demodulation.

The node calculates the impulse response of the filter using the following formulas.

Filter Type Formula
Raised Cosine
$h\left(t\right)=\mathrm{sin}c\left(\frac{t}{T}\right)\frac{\mathrm{cos}\left(\frac{\pi \alpha t}{T}\right)}{1-\frac{4{\pi }^{2}{\alpha }^{2}{t}^{2}}{{\text{}}^{{T}^{2}}}}$
where T is the symbol period and α is the filter rolloff factor.
Root Raised Cosine
$h\left(t\right)=\left\{\begin{array}{c}1-\alpha +\frac{4\alpha }{\pi },\text{\hspace{0.17em}}t=0\\ \frac{\alpha }{\sqrt{2}}\left[\left(1+\frac{2}{\pi }\right)\mathrm{sin}\left(\frac{\pi }{4\alpha }\right)+\left(1+\frac{2}{\pi }\right)\mathrm{cos}\left(\frac{\pi }{4\alpha }\right)\right],\text{\hspace{0.17em}}t=±\frac{T}{4\alpha }\\ \frac{\mathrm{sin}\left(\pi \frac{t}{T}\left(1-\alpha \right)\right)+4\alpha \frac{t}{T}\mathrm{cos}\left(\pi \frac{t}{T}\left(1-\alpha \right)\right)}{\pi \frac{t}{T}\left(1-{\left(\frac{4\alpha t}{T}\right)}^{2}\right)},\text{\hspace{0.17em}}otherwise\end{array}$
where T is the symbol period and α is the filter rolloff factor.
Gaussian
$g\left(t\right)=\sqrt{\frac{BT}{\pi }{e}^{-{\left(BT\right)}^{2}{t}^{2}}}$
where T is the symbol period and B is the -3 dB bandwidth of the filter.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported