FIR Interpolation

Upsample and filter input signals

Library

Filtering / Multirate Filters

dspmlti4

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Description

The FIR Interpolation block upsamples an input by the integer upsampling factor L along the first dimension. The FIR interpolator (as shown in the schematic) conceptually consists of an upsampler followed by an FIR anti-imaging filter, which is usually an approximation of an ideal band-limited interpolation filter. To design an FIR anti-imaging filter, use the designMultirateFIR function.

The upsampler upsamples each channel of the input to a higher rate by inserting L–1 zeros between samples. The direct-form FIR filter that follows filters each channel of the upsampled data. The resulting discrete-time signal has a sample rate that is L times the original sample rate.

Note that the actual block algorithm implements a polyphase structure, an efficient equivalent of the combined system depicted in the diagram. For more details, see Algorithms.

You can use the FIR Interpolation block inside triggered subsystems when you set the Rate options parameter to Enforce single-rate processing.

Under specific conditions, this block also supports SIMD code generation. For more details, see Code Generation.

Specifying the Filter Coefficients

To specify the filter coefficients, select the mode you want the FIR Interpolation block to operate in. Select the mode in the Coefficient source group box.

• Dialog parameters — Enter information about the filter, such as coefficients in the block dialog box.

• Input port — Specify the filter coefficients as an input to the block. Coefficient values are tunable (can change during simulation), while their properties must remain constant.

• Filter object — Specify the filter using a dsp.FIRInterpolator System object™.

• Auto (default) — Choose the filter coefficients of an FIR Nyquist filter, predesigned for the interpolation factor specified in the block dialog box.

When you select Dialog parameters, you use the FIR filter coefficients parameter to specify the numerator coefficients of the FIR filter transfer function H(z).

$$H(z)=b_0+b_1{z}^{-1}+\mathrm{...}+b_N{z}^{-N}$$

You can generate the FIR filter coefficient vector, b = [b₀, b₁, …, b_N], using one of the DSP System Toolbox™ filter design functions such as designMultirateFIR, firnyquist, firhalfband, firgr or firceqrip.

To act as an effective anti-imaging filter, the coefficients usually correspond to a lowpass filter with a normalized cutoff frequency no greater than the reciprocal of the interpolation factor. To design such a filter, use the designMultirateFIR function.

The block internally initializes all filter states to zero.

When you select Auto, the block designs an FIR interpolator with the interpolation factor specified in Interpolation factor. The designMultirateFIR function designs the filter and returns the coefficients used by the block.

For more information on the filter design, see Orfanidis [2].

Frame-Based Processing

When you set the Input processing parameter to Columns as channels (frame based), the block resamples each column of the input over time. In this mode, the block can perform either single-rate or multirate processing. You can use the Rate options parameter to specify how the block resamples the input:

• When you set the Rate options parameter to Enforce single-rate processing, the input and output of the block have the same sample rate. To interpolate the output while maintaining the input sample rate, the block resamples the data in each column of the input such that the frame size of the output (K_o) is L times larger than that of the input (K_o = K_i*L).

  For an example of single-rate FIR Interpolation, see Example 1 — Single-Rate Processing.

• When you set the Rate options parameter to Allow multirate processing, the input and output of the FIR Interpolation block are the same size. However, the sample rate of the output is L times faster than that of the input. In this mode, the block treats a K_i-by-N matrix input as N independent channels. The block interpolates each column of the input over time by keeping the frame size constant (K_i=K_o), while making the output frame period (T_fo) L times shorter than the input frame period (T_fo = T_fi/L).

  See Example 2 — Multirate Frame-Based Processing for an example that uses the FIR Interpolation block in this mode.

Sample-Based Processing

When you set the Input processing parameter to Elements as channels (sample based), the block treats a P-by-Q matrix input as P*Q independent channels, and interpolates each channel over time. The output sample period (T_so) is L times shorter than the input sample period (T_so = T_si/L), while the input and output sizes remain identical.

Latency

When you run your models in Simulink^® SingleTasking mode or set the Input processing parameter to Columns as channels (frame based) and the Rate options parameter to Enforce single-rate processing, the FIR Interpolation block always has zero-tasking latency. Zero-tasking latency means that the block propagates the first filtered input sample (received at time t=0) as the first output sample. That first output sample is then followed by L–1 interpolated values, the second filtered input sample, and so on.

The only time the FIR Interpolation block exhibits latency is when you set the Rate options parameter set to Allow multirate processing and run your models in Simulink MultiTasking mode. The amount of latency for multirate, multitasking operation depends on the setting of the Input processing parameter, as shown in the following table.

Input processing	Latency
Elements as channels (sample based)	L samples
Columns as channels (frame based)	L frames (Ki samples per frame)

When the block exhibits latency, the default initial condition is zero. Alternatively, you can use the Output buffer initial conditions parameter to specify a matrix of initial conditions containing one value for each channel or a scalar initial condition to be applied to all channels. The block scales the Output buffer initial conditions by the Interpolation factor and outputs the scaled initial conditions until the first filtered input sample becomes available.

When the block is in sample-based processing mode, the block outputs the scaled initial conditions at the start of each channel, followed immediately by the first filtered input sample, then L–1 interpolated values, and so on.

When the block is in frame-based processing mode and using the default initial condition of zero, the first K_i*L output rows contain zeros, where K_i is the input frame size. The first filtered input sample (first filtered row of the input matrix) appears in the output as sample K_i*L+1. That value is then followed by L–1 interpolated values, the second filtered input sample, and so on.

Note

For more information on latency and the Simulink tasking modes, see Excess Algorithmic Delay (Tasking Latency) and Time-Based Scheduling and Code Generation (Simulink Coder).

Fixed-Point Data Types

The following diagram shows the data types used within the FIR Interpolation block for fixed-point signals.

You can set the coefficient, product output, accumulator, and output data types in the block dialog box as discussed in Dialog Box section. This diagram shows that input data is stored in the input buffer with the same data type and scaling as the input. The block stores filtered data and any initial conditions in the output buffer using the output data type and scaling that you set in the block dialog box.

When at least one of the inputs to the multiplier is real, the output of the multiplier is in the product output data type. When both inputs to the multiplier are complex, the result of the multiplication is in the accumulator data type. For details on the complex multiplication performed by this block, see Multiplication Data Types.

Note

When the block input is fixed point, all internal data types are signed fixed point.

Examples

Example 1 — Single-Rate Processing

In the ex_firinterpolation_ref2, the FIR Interpolation block interpolates a single-channel input with a frame size of 16. Because the block is doing single-rate processing and the Interpolation factor parameter is set to 4, the output of the FIR Interpolation block has a frame size of 64. As shown in the following figure, the input, and output of the FIR Interpolation block have the same sample rate.

Example 2 — Multirate Frame-Based Processing

In the ex_firinterpolation_ref1, the FIR Interpolation block interpolates a single-channel input with a frame period of 1 second (Sample time = 1/64 and Samples per frame = 64). Because the block is doing multirate frame-based processing and the Interpolation factor parameter is set to 4, the output of the FIR Interpolation block has a frame period of 0.25 seconds. As shown in the following figure, the input and output of the FIR Interpolation block have the same frame size, but the sample rate of the output is 1/4 times that of the input.

Example 3

The ex_polyphaseinterp model illustrates the underlying polyphase implementations of the FIR Interpolation block. Run the model, and view the results on the scope. The output of the FIR Interpolation block matches the output of the Polyphase Interpolation Filter block.

Example 4

The ex_mrf_nlp model illustrates the use of the FIR Interpolation block in a number of multistage multirate filters.

Dialog Box

Coefficient Source

The FIR Interpolation block can operate in four different modes. Select the mode in the Coefficient source group box.

• Dialog parameters — Enter information about the filter, such as coefficients, in the block mask.

• Input port — Specify the filter coefficients with a Num input port. The Num input port appears when you select the Input port option. Coefficient values obtained through Num are tunable (can change during simulation), while their properties must remain constant.

• Filter object — Specify the filter using a dsp.FIRInterpolator System object.

• Auto (default) — Choose the coefficients of an FIR Nyquist filter, predesigned for the Interpolation factor specified in the block dialog box.

Different items appear on the FIR Interpolation block dialog box depending on whether you select Dialog parameters, Input port, Filter object, or Auto in the Coefficient source group box.

 Specify Filter Characteristics in dialog box

The Main pane of the FIR Interpolation block dialog box appears as follows when you select Dialog parameters in the Coefficient source group box.

FIR filter coefficients

Specify the FIR filter coefficients, in descending powers of z. By default, designMultirateFIR(3,1) computes the filter coefficients.

Interpolation factor

Specify the integer factor, L, by which to increase the sample rate of the input sequence. The default is 3.

Input processing

Specify how the block should process the input. You can set this parameter to one of the following options:

• Columns as channels (frame based) (default) — When you select this option, the block treats each column of the input as a separate channel.

• Elements as channels (sample based) — When you select this option, the block treats each element of the input as a separate channel.

Rate options

Specify the method by which the block should interpolate the input. You can select one of the following options:

• Enforce single-rate processing — When you select this option, the block maintains the input sample rate, and interpolates the signal by increasing the output frame size by a factor of L. To select this option, you must set the Input processing parameter to Columns as channels (frame based).

• Allow multirate processing — When you select this option, the block interpolates the signal such that the output sample rate is L times faster than the input sample rate.

Output buffer initial conditions

In cases of nonzero latency, the block divides this parameter by the Interpolation factor and outputs the results at the output port until the first filtered input sample is available. The default initial condition value is 0, but you can enter a matrix containing one value for each channel, or a scalar to be applied to all signal channels. This parameter appears only when you configure the block to perform multirate processing.

Output buffer initial conditions are stored in the output data type and scaling.

See Latency for more information about latency in the FIR Interpolation block.

View filter response

This button opens the Filter Visualization Tool (fvtool) from the Signal Processing Toolbox™ product and displays the filter response of the filter defined in the block. For more information on FVTool, see the Signal Processing Toolbox documentation.

The Data Types pane of the FIR Interpolation block dialog box appears as follows when you select Dialog parameters in the Coefficient source group box.

Rounding mode

Select the rounding mode for fixed-point operations. The default is Floor. The filter coefficients do not obey this parameter; they always round to Nearest.

Note

The Rounding mode and Saturate on integer overflow settings have no effect on numerical results when all the following conditions exist:

• Product output is Inherit: Inherit via internal rule

• Accumulator is Inherit: Inherit via internal rule

• Output is Inherit: Same as accumulator

With these data type settings, the block is effectively operating in full precision mode.

Saturate on integer overflow

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.

Note

The Rounding mode and Saturate on integer overflow parameters have 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.

Coefficients

Specify the coefficients data type. See Fixed-Point Data Types and Multiplication Data Types for illustrations depicting the use of the coefficients data type in this block. You can set it 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(1,16,0)

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Coefficients parameter.

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

Coefficients Minimum

Specify the minimum value of the filter coefficients. The default value is [] (unspecified). Simulink software uses this value to perform:

• Automatic scaling of fixed-point data types

Coefficients Maximum

Specify the maximum value of the filter coefficients. The default value is [] (unspecified). Simulink software uses this value to perform:

• Automatic scaling of fixed-point data types

Product output

Specify the product output data type. See Fixed-Point Data Types and Multiplication Data Types for illustrations depicting the use of the product output data type in this block. You can set it 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 Show data type assistant 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.

Accumulator

Specify the accumulator data type. See Fixed-Point Data Types 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 Show data type assistant 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.

Output

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

• A rule that inherits a data type, for example, Inherit: Same as accumulator

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

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Output parameter.

See Control Signal Data Types (Simulink) for more information.

Output Minimum

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

Output Maximum

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

Lock data type settings against changes by the fixed-point tools

Select this parameter to prevent the fixed-point tools from overriding the data types you specify on the block mask.

 Provide Filter Coefficients Through Input Port

The Main pane of the FIR Interpolation block dialog box appears as follows when you select Input port in the Coefficient source group box.

Interpolation factor

Specify the integer factor, L, by which to increase the sample rate of the input sequence. The default is 3.

Input processing

Specify how the block should process the input. You can set this parameter to one of the following options:

• Columns as channels (frame based) (default) — When you select this option, the block treats each column of the input as a separate channel.

• Elements as channels (sample based) — When you select this option, the block treats each element of the input as a separate channel.

Rate options

Specify the method by which the block should interpolate the input. You can select one of the following options:

• Enforce single-rate processing — When you select this option, the block maintains the input sample rate, and interpolates the signal by increasing the output frame size by a factor of L. To select this option, you must set the Input processing parameter to Columns as channels (frame based).

• Allow multirate processing — When you select this option, the block interpolates the signal such that the output sample rate is L times faster than the input sample rate.

Output buffer initial conditions

In cases of nonzero latency, the block divides this parameter by the Interpolation factor and outputs the results at the output port until the first filtered input sample is available. The default initial condition value is 0, but you can enter a matrix containing one value for each channel, or a scalar to be applied to all signal channels. This parameter appears only when you configure the block to perform multirate processing.

Output buffer initial conditions are stored in the output data type and scaling.

See Latency for more information about latency in the FIR Interpolation block.

The Data Types pane of the FIR Interpolation block dialog box appears as follows when you select Input port in the Coefficient source group box.

Rounding mode

Select the rounding mode for fixed-point operations. The default is Floor. The filter coefficients do not obey this parameter; they always round to Nearest.

Note

The Rounding mode and Saturate on integer overflow settings have no effect on numerical results when all the following conditions exist:

• Product output is Inherit: Inherit via internal rule

• Accumulator is Inherit: Inherit via internal rule

• Output is Inherit: Same as accumulator

With these data type settings, the block is effectively operating in full precision mode.

Saturate on integer overflow

When you select this check box, the block saturates the result of its fixed-point operation. When you clear this check box, the block wraps the result of its fixed-point operation. By default, this check box is cleared. For details on saturate and wrap, see overflow mode for fixed-point operations. The filter coefficients do not obey this parameter; they are always saturated.

Product output

Specify the product output data type. See Fixed-Point Data Types and Multiplication Data Types for illustrations depicting the use of the product output data type in this block. You can set it 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 Show data type assistant 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.

Accumulator

Specify the accumulator data type. See Fixed-Point Data Types 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 Show data type assistant 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.

Output

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

• A rule that inherits a data type, for example, Inherit: Same as accumulator

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

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Output parameter.

See Control Signal Data Types (Simulink) for more information.

Output Minimum

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

Output Maximum

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

Lock data type settings against changes by the fixed-point tools

Select this parameter to prevent the fixed-point tools from overriding the data types you specify on the block mask.

 Specify Multirate Filter Object

The Main pane of the FIR Interpolation block dialog box appears as follows when you select Filter object in the Coefficient source group box.

Filter object

Specify the name of the multirate filter object that you want the block to implement. You must specify the filter as a dsp.FIRInterpolator System object.

You can define the System object in the block mask or in a MATLAB^® workspace variable.

For information on creating System objects, see Define Basic System Objects.

Input processing

Specify how the block should process the input. You can set this parameter to one of the following options:

• Columns as channels (frame based) (default) — When you select this option, the block treats each column of the input as a separate channel.

• Elements as channels (sample based) — When you select this option, the block treats each element of the input as a separate channel.

Rate options

Specify the method by which the block should interpolate the input. You can select one of the following options:

• Enforce single-rate processing — When you select this option, the block maintains the input sample rate, and interpolates the signal by increasing the output frame size by a factor of L. To select this option, you must set the Input processing parameter to Columns as channels (frame based).

• Allow multirate processing — When you select this option, the block interpolates the signal such that the output sample rate is L times faster than the input sample rate.

View filter response

This button opens the Filter Visualization Tool (fvtool) from the Signal Processing Toolbox product and displays the filter response of the System object specified in the Filter object parameter. For more information on FVTool, see the Signal Processing Toolbox documentation.

Note

If you specify a filter in the Filter object parameter, you must apply the filter by clicking the Apply button before using the View filter response button.

The Data Types pane of the FIR Interpolation block dialog box appears as follows when you select Filter object in the Coefficient source group box.

The fixed-point settings of the filter object specified on the Main pane are displayed on the Data Types pane. You cannot change these settings directly on the block mask. To change the fixed-point settings, edit the filter object directly.

For more information on System objects, see Define Basic System Objects.

 Choose Filter Coefficients Automatically

When you select Auto in the Coefficient source group box, the block chooses the filter coefficients automatically. For more information on the filter design algorithm the block uses, see Specifying the Filter Coefficients.

The Main pane of the FIR Interpolation block dialog box appears as follows when you select Auto in the Coefficient source group box.

Interpolation factor

Specify the integer factor, L, by which to increase the sample rate of the input sequence. The default is 3.

Input processing

Specify how the block should process the input. You can set this parameter to one of the following options:

• Columns as channels (frame based) (default) — When you select this option, the block treats each column of the input as a separate channel.

• Elements as channels (sample based) — When you select this option, the block treats each element of the input as a separate channel.

Rate options

Specify the method by which the block should interpolate the input. You can select one of the following options:

• Enforce single-rate processing — When you select this option, the block maintains the input sample rate, and interpolates the signal by increasing the output frame size by a factor of L. To select this option, you must set the Input processing parameter to Columns as channels (frame based).

• Allow multirate processing — When you select this option, the block interpolates the signal such that the output sample rate is L times faster than the input sample rate.

Output buffer initial conditions

In cases of nonzero latency, the block divides this parameter by the Interpolation factor and outputs the results at the output port until the first filtered input sample is available. The default initial condition value is 0, but you can enter a matrix containing one value for each channel, or a scalar to be applied to all signal channels. This parameter appears only when you configure the block to perform multirate processing.

Output buffer initial conditions are stored in the output data type and scaling.

See Latency for more information about latency in the FIR Interpolation block.

View filter response

This button opens the Filter Visualization Tool (fvtool) from the Signal Processing Toolbox product and displays the filter response of the filter defined in the block. For more information on FVTool, see the Signal Processing Toolbox documentation.

The Data Types pane of the FIR Interpolation block dialog box appears as follows when you select Auto in the Coefficient source group box.

Rounding mode

Select the rounding mode for fixed-point operations. The default is Floor. The filter coefficients do not obey this parameter; they always round to Nearest.

Note

The Rounding mode and Saturate on integer overflow settings have no effect on numerical results when all the following conditions exist:

• Product output is Inherit: Inherit via internal rule

• Accumulator is Inherit: Inherit via internal rule

• Output is Inherit: Same as accumulator

With these data type settings, the block is effectively operating in full precision mode.

Saturate on integer overflow

When you select this check box, the block saturates the result of its fixed-point operation. When you clear this check box, the block wraps the result of its fixed-point operation. By default, this check box is cleared. For details on saturate and wrap, see overflow mode for fixed-point operations. The filter coefficients do not obey this parameter; they are always saturated.

Coefficients

Specify the coefficients data type. See Fixed-Point Data Types and Multiplication Data Types for illustrations depicting the use of the coefficients data type in this block. You can set it 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(1,16,0)

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Coefficients parameter.

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

Coefficients Minimum

Specify the minimum value of the filter coefficients. The default value is [] (unspecified). Simulink software uses this value to perform:

• Automatic scaling of fixed-point data types

Coefficients Maximum

Specify the maximum value of the filter coefficients. The default value is [] (unspecified). Simulink software uses this value to perform:

• Automatic scaling of fixed-point data types

Product output

Specify the product output data type. See Fixed-Point Data Types and Multiplication Data Types for illustrations depicting the use of the product output data type in this block. You can set it 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 Show data type assistant 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.

Accumulator

Specify the accumulator data type. See Fixed-Point Data Types 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 Show data type assistant 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.

Output

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

• A rule that inherits a data type, for example, Inherit: Same as accumulator

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

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Output parameter.

See Control Signal Data Types (Simulink) for more information.

Output Minimum

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

Output Maximum

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

Lock data type settings against changes by the fixed-point tools

Select this parameter to prevent the fixed-point tools from overriding the data types you specify on the block mask.

References

[1] Fliege, N. J. Multirate Digital Signal Processing: Multirate Systems, Filter Banks, Wavelets. West Sussex, England: John Wiley & Sons, 1994.

[2] Orfanidis, Sophocles J. Introduction to Signal Processing. Upper Saddle River, NJ: Prentice-Hall, 1996.

Supported Data Types

Port	Supported Data Types
Input	Double-precision floating point Single-precision floating point Fixed point 8-, 16-, and 32-bit signed integers 8-, 16-, and 32-bit unsigned integers
Output	Double-precision floating point Single-precision floating point Fixed point 8-, 16-, and 32-bit signed integers 8-, 16-, and 32-bit unsigned integers

Algorithms

The FIR interpolation filter is implemented efficiently using a polyphase structure.

To derive the polyphase structure, start with the transfer function of the FIR filter:

$$H(z)=b_0+b_1{z}^{-1}+\mathrm{...}+b_N{z}^{-N}$$

N+1 is the length of the FIR filter.

You can rearrange this equation as follows:

$$H(z)=\begin{array}{c}\left(b_0+b_L{z}^{-L}+b_{2L}{z}^{-2L}+\mathrm{..}+b_{N-L+1}{z}^{-(N-L+1)}\right)+\\ z^{-1}\left(b_1+b_{L+1}{z}^{-L}+b_{2L+1}{z}^{-2L}+\mathrm{..}+b_{N-L+2}{z}^{-(N-L+1)}\right)+\\ \begin{array}{c}⋮\\ z^{-(L-1)}\left(b_{L-1}+b_{2L-1}{z}^{-L}+b_{3L-1}{z}^{-2L}+\mathrm{..}+b_N{z}^{-(N-L+1)}\right)\end{array}\end{array}$$

L is the number of polyphase components, and its value equals the interpolation factor that you specify.

You can write this equation as:

$$H(z)=E_0(z^L)+z^{-1}{E}_1(z^L)+\mathrm{...}+z^{-(L-1)}{E}_{L-1}(z^L)$$

E₀(z^L), E₁(z^L), ..., E_L-1(z^L) are polyphase components of the FIR filter H(z).

Conceptually, the FIR interpolation filter contains an upsampler followed by an FIR lowpass filter H(z).

Replace H(z) with its polyphase representation.

Here is the multirate noble identity for interpolation.

Applying the noble identity for interpolation moves the upsampling operation to after the filtering operation. This move enables you to filter the signal at a lower rate.

You can replace the upsampling operator, delay block, and adder with a commutator switch. The switch starts on the first branch 0 and moves in the counter clockwise direction, each time receiving one sample from each branch. The interpolator effectively outputs L samples for every one input sample it receives. Hence the sample rate at the output of the FIR interpolation filter is Lfs.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using Simulink® Coder™.

Generated code relies on memcpy or memset functions (string.h) under certain conditions.

The FIR Interpolation block supports SIMD code generation using Intel AVX2 technology under these conditions:

• Input processing is set to Columns as channels (frame based).

• Rate options is set to Enforce single-rate processing.

• Input signal is real-valued with real filter coefficients.

• Input signal is complex-valued with real or complex filter coefficients.

• Input signal has a data type of single or double.

The SIMD technology significantly improves the performance of the generated code.

HDL Code Generation

Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

HDL Coder™ provides additional configuration options that affect HDL implementation and synthesized logic.

HDL Coder supports Coefficient source options Dialog parameters, Filter object, or Auto.

Block Optimizations

To reduce area or increase speed, the FIR Decimator block supports block-level optimizations.

Right-click on the block or the subsystem to open the corresponding HDL Properties dialog box and set optimization properties.

Serial Architectures	When you select Fully Serial architecture, the SerialPartition property is set on the FIR Interpolation Block.
Distributed Arithmetic	Distributed Arithmetic properties DALUTPartition and DARadix are supported for the Distributed Arithmetic (DA) architecture with a default FIR filter structure. structures.
Pipelining	When you use AddPipelineRegisters, registers are placed based on the filter structure. The pipeline register placement determines the latency. A pipeline register is added between levels of a tree-based adder, for a latency of ceil(log2(PL))-1, where PL is polyphase filter length.

HDL Filter Properties

AddPipelineRegisters	Insert a pipeline register between stages of computation in a filter. See also AddPipelineRegisters (HDL Coder).
CoeffMultipliers	Specify the use of canonical signed digit (CSD) optimization to decrease filter area by replacing coefficient multipliers with shift-and-add logic. When you choose a fully parallel filter implementation, you can set CoeffMultipliers to csd or factored-csd. The default is multipliers, which retains multipliers in the HDL. See also CoeffMultipliers (HDL Coder).
DALUTPartition	Specify distributed arithmetic partial-product LUT partitions as a vector of the sizes of each partition. The sum of all vector elements must be equal to the filter length. The maximum size for a partition is 12 taps. Set DALUTPartition to a scalar value equal to the filter length to generate DA code without LUT partitions. See also DALUTPartition (HDL Coder).
DARadix	Specify how many distributed arithmetic bit sums are computed in parallel. A DA radix of 8 (2^3) generates a DA implementation that computes three sums at a time. The default value is 2^1, which generates a fully serial DA implementation. See also DARadix (HDL Coder).
MultiplierInputPipeline	Specify the number of pipeline stages to add at filter multiplier inputs. See also MultiplierInputPipeline (HDL Coder).
MultiplierOutputPipeline	Specify the number of pipeline stages to add at filter multiplier outputs. See also MultiplierOutputPipeline (HDL Coder).
SerialPartition	Specify partitions for partly serial or cascade-serial filter implementations as a vector of the lengths of each partition. For a fully serial implementation, set this parameter to the length of the filter. See also SerialPartition (HDL Coder).

HDL Block Properties

ConstrainedOutputPipeline	Number of registers to place at the outputs by moving existing delays within your design. Distributed pipelining does not redistribute these registers. The default is 0. For more details, see ConstrainedOutputPipeline (HDL Coder).
InputPipeline	Number of input pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is 0. For more details, see InputPipeline (HDL Coder).
OutputPipeline	Number of output pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is 0. For more details, see OutputPipeline (HDL Coder).

Restrictions

• You must set Initial conditions to zero. HDL code generation is not supported for nonzero initial states.

• Vector and frame inputs are not supported for HDL code generation.

• When you select Dialog parameters, the following fixed-point options are not supported for HDL code generation:

  • Coefficients: Slope and Bias scaling

• CoeffMultipliers options are supported only when using a fully parallel architecture. When you select a serial architecture, CoeffMultipliers is hidden from the HDL Block Properties dialog box.

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.