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# Phase/Frequency Offset

Apply phase and frequency offsets to complex baseband signal

RF Impairments

## Description

The Phase/Frequency Offset block applies phase and frequency offsets to an incoming signal.

The block inherits its output data type from the input signal. If the input signal is u(t), then the output signal is:

$y\left(t\right)=u\left(t\right)\cdot \left(\mathrm{cos}\left(2\pi {\int }_{0}^{t}f\left(\tau \right)d\tau +\phi \left(t\right)\right)+j\mathrm{sin}\left(2\pi {\int }_{0}^{t}f\left(\tau \right)d\tau +\phi \left(t\right)\right)\right)$

where

f(t) = Frequency offset

φ(t) = Phase offset

The discrete-time output is:

$\begin{array}{l}y\left(0\right)=u\left(0\right)\left(\mathrm{cos}\left(\phi \left(0\right)\right)+j\mathrm{sin}\left(\phi \left(0\right)\right)\right)\\ y\left(i\right)=u\left(i\right)\left(\mathrm{cos}\left(2\pi f\left(i-1\right)\Delta t+\phi \left(i\right)\right)+j\mathrm{sin}\left(2\pi f\left(i-1\right)\Delta t+\phi \left(i\right)\right)\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}i\text{\hspace{0.17em}}>\text{\hspace{0.17em}}0\end{array}$

where

Δt = Sample time

This block accepts real and complex inputs of data type double or single.

### Phase Offset

The block applies a phase offset to the input signal, specified by the Phase offset parameter.

### Frequency Offset

The block applies a frequency offset to the input signal, specified by the Frequency offset parameter. Alternatively, when you select Frequency offset from port, the Frq input port provides the offset to the block. The frequency offset must be a scalar value, vector with the same number of rows or columns as the data input, or a matrix with the same size as the data input. For more information, see Interdependent Parameter-Port Dimensions.

The effects of changing the block's parameters are illustrated by the following scatter plots of a signal modulated by 16-ary quadrature amplitude modulation (QAM). The usual 16-ary QAM constellation without the effect of the Phase/Frequency Offset block is shown in the first scatter plot:

The following figure shows a scatter plot of an output signal, modulated by 16-ary QAM, from the Phase/Frequency Offset block with Phase offset set to 20 and Frequency offset set to 0:

Observe that each point in the constellation is rotated by a 20 degree angle counterclockwise.

If you set Frequency offset to 2 and Phase offset to 0, the angles of points in the constellation change linearly over time. This causes points in the scatter plot to shift radially, as shown in the following figure:

Note that every point in the scatter plot has magnitude equal to a point in the original constellation.

See Illustrate RF Impairments That Distort a Signal for a description of the model that generates this plot.

### Interdependent Parameter-Port Dimensions

Number of DimensionsData I/O DimensionFrame SizeNumber of ChannelsFrequency/Phase Offset Parameter DimensionFrequency Offset Input Port Dimension
AnyScalar11ScalarScalar
2M-by-1M1M-by-1, 1-by-M, 1-by-1M, M-by-1, 1, 1-by-1
21-by-N1NN-by-1, 1-by-N, 1-by-1N, 1-by-N, 1, 1-by-1
2M-by-NMNM-by-N, N-by-1, 1-by-N, M-by-1, 1-by-M, 1-by-1 M-by-N, N, 1-by-N, 1, 1-by-1, M, M-by-1

• When you specify a scalar offset parameter the block applies the same offset to all elements of the input signal

• When you specify a 2-by-1 offset parameter for a 2-by-3 input signal (one offset value per sample), the block applies the same sample offset across the three channels.

• When you specify a 1-by-3 offset parameter for a 2-by-3 input signal (one offset value per channel), the same channel offset is applied across the two samples of a channel.

• When you specify a 2-by-3 offset parameter for a 2-by-3 input signal (one offset value per sample for each channel), the offsets are applied element-wise to the input signal.

## Dialog Box

Frequency offset from port

Selecting this option opens a port on the block through which you can input the frequency offset information.

Frequency offset

Specifies the frequency offset in hertz.

This parameter is tunable in normal mode, Accelerator mode and Rapid Accelerator mode. If you use the Simulink® Coder™ rapid simulation (RSIM) target to build an RSIM executable, then you can tune the parameter without recompiling the model. For more information, see Tunable Parameters in the Simulink User's Guide.

Phase offset

Specifies the phase offset in degrees.

This parameter is tunable in normal mode, Accelerator mode and Rapid Accelerator mode. If you use the Simulink Coder rapid simulation (RSIM) target to build an RSIM executable, then you can tune the parameter without recompiling the model. For more information, see Tunable Parameters in the Simulink User's Guide.

If Frequency offset and Phase offset are both vectors or both matrices, their dimensions (vector lengths, or number of rows and columns) must be the same.