Interpolation

Interpolate values of real input samples

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Libraries:
DSP System Toolbox / Signal Operations

Description

The Interpolation block interpolates discrete, real inputs by using linear or FIR interpolation. The block accepts a vector, a matrix, or an N-D array. The block outputs a scalar, a vector, a matrix, or an N-D array of the interpolated values.

You must specify the interpolation points, the times at which to interpolate values in a one-based interpolation array I_Pts. An entry of 1 in I_Pts refers to the first sample of the input data, an entry of 2.5 refers to the sample halfway between the second and third input sample, and so on. Depending on the dimensions of the input data, I_Pts can be a scalar, a length-P row, or a column vector, a P-by-N matrix, or an N-D array where P is the size of the first dimension of the N-D array. In most cases, P can be any positive integer. For more information about valid interpolation arrays, refer to the tables in Pts and Interpolation points.

In most cases, the block applies I_Pts across the first dimension of an N-D input array or to each input vector. You can set the block to apply the same interpolation array for all input data, static interpolation points entered on the block mask, or to use a different interpolation array for each N-D array, matrix, or vector input, time-varying interpolation points received through the Pts input port.

Ports

Input

In — Input signal

scalar | vector | matrix | N-D array

Input signal, specified as a scalar, vector, matrix, or N-D array.

This port is unnamed until Source of interpolation points is set to Input port.

Data Types: single | double

Pts — Interpolation points

scalar | vector | matrix | N-D array

Interpolation points, specified as a scalar, vector, matrix, or N-D array.

For more details on the block's behavior when the Source of interpolation points parameter is set to Input port, see How the Block Applies Interpolation Arrays to Inputs.

Dependencies

This port is unavailable until Source of interpolation points is set to Input port.

Data Types: single | double

Output

Out — Output signal

scalar | vector | matrix | N-D array

Output signal, specified as a vector, matrix, or N-D array.

This port is unnamed until Source of interpolation points is set to Input port.

Data Types: single | double

Parameters

Source of interpolation points — Interpolation point input method

Specify via dialog (default) | Input port

Choose how you want to specify the interpolation points:

• Specify via dialog –– The Interpolation points parameter becomes available. Use this option for static interpolation points.

• Input port –– The Pts port appears on the block. The block uses the input to this port as the interpolation points. Use this option for time-varying interpolation points.

For more information, see Specifying Static Interpolation Points and Specifying Time-Varying Interpolation Points.

Interpolation points — Interpolation points

[1.1 4.8 2.67 1.6 3.2]' (default) | scalar | vector | matrix | N-D array

The array of points in time at which to interpolate the input signal (I_Pts). An entry of 1 in I_Pts refers to the first sample of the input, an entry of 2.5 refers to the sample halfway between the second and third input sample, and so on. See How the Block Applies Interpolation Arrays to Inputs.

Tunable: Yes

Dependencies

This parameter becomes available only when the Source of interpolation points is set to Specify via dialog. For more information, see Specifying Static Interpolation Points.

Interpolation mode — Interpolation mode

Linear (default) | FIR

Sets the block to interpolate by either Linear or FIR interpolation. For more information, see Linear Interpolation Mode and FIR Interpolation Mode.

Interpolation filter half-length — Half length of FIR interpolation filter

3 (default) | positive integer

Specify the half-length of the FIR interpolation filter (P). To perform the interpolation in FIR mode, the block uses the nearest 2×P low-rate samples. In most cases, P low-rate samples must appear below and above each interpolation point. If you interpolate at a low-rate sample point, the block includes that low-rate sample in the required 2*P samples and requires only 2*P–1 neighboring low-rate samples. If an interpolation point does not have the required number of neighboring low-rate samples, the block interpolates that point using linear interpolation.

Dependencies

This parameter becomes available only when the Interpolation mode is set to FIR. For more information, see FIR Interpolation Mode.

Interpolation points per input sample — Interpolation points per sample

3 (default)

Number of points per input sample, upsampling factor (L), at which the block computes a unique FIR interpolation filter. To perform the FIR interpolation, the block uses a polyphase structure that has L filter arms of length 2*P.

For example, if L=4, the block constructs a polyphase filter with four arms. The block then interpolates at points corresponding to 1 +i/L, 2 +i/L, 3 +i/L..., where the integers 1, 2, and 3 represent the low-rate samples, and i=0,1,2,3. To interpolate at a point that does not directly correspond to an arm of the polyphase filter requires an extra computation. The block first rounds that point down to the nearest value that does correspond to an arm of the polyphase filter. To interpolate at the point 2.2, the block rounds 2.2 down to 2, and computes the FIR interpolation by using the first arm of the polyphase filter structure. Similarly, to interpolate the point 2.65, the block rounds the value down to 2.5 and uses the third arm of the polyphase filter structure.

Dependencies

This parameter becomes available only when the Interpolation mode is set to FIR. For more information, see FIR Interpolation Mode.

Normalized input bandwidth — Normalized input bandwidth

0.5 (default) | scalar in (0 1]

The bandwidth of the input divided by Fs/2 (half the input sample frequency), specified as a scalar in the range (0 1].

Dependencies

This parameter becomes available only when the Interpolation mode is set to FIR. For more information, see FIR Interpolation Mode.

Out of range interpolation points — Error handling for out-of-range points

Clip (default) | Clip and warn | Error

Valid values in the interpolation array I_Pts range from 1 to the number of samples in each channel of the input. For instance, given a length-5 input vector D, all entries of I_Pts must range from 1 to 5. I_Pts cannot contain entries such as 7 or -9 because there is no 7th or -9th entry in D.

The Out of range interpolation points parameter sets how the block handles interpolation points that are fall outside the valid range. The parameter has these settings:

• Clip — The block replaces any out-of-range values in I_Pts with the closest value in the valid range (from 1 to the number of input samples), and then proceeds with computations by using the clipped version of I_Pts.

• Clip and warn — In addition to Clip, the block issues a warning at the MATLAB^® command line every time clipping occurs.

• Error — When the block encounters an out-of-range value in I_Pts, the simulation stops, and the block issues an error at the MATLAB command line.

As an example of clipping, suppose the block is set to clip out-of-range interpolation points and gets these input vector and interpolation points:

• D = [11 22 33 44]'

• IPts = [10 2.6 -3]'

Because D has four samples, valid interpolation points range from 1 to 4. The block clips the interpolation point 10 to 4 and the point -3 to 1, resulting in the clipped interpolation vector IPtsClipped = [4 2.6 1]'.

Block Characteristics

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

More About

Specifying Static Interpolation Points

To supply the block with a static interpolation array, that is an interpolation array applied to every vector or N-D array of input data), perform the following steps:

1. Set the Source of interpolation points parameter to Specify via dialog.

2. Enter the interpolation array in the Interpolation points parameter. To learn about interpolation arrays, see How the Block Applies Interpolation Arrays to Inputs.

Specifying Time-Varying Interpolation Points

To supply the block with time-varying interpolation arrays, where the block uses a different interpolation array for each vector or N-D array input, perform the following steps:

1. Set the Source of interpolation points parameter to Input port. The Pts port appears on the block.

2. Generate a signal of interpolation arrays and supply it to the Pts port. The block uses the input to this port as the interpolation points. To learn about interpolation arrays, see How the Block Applies Interpolation Arrays to Inputs.

How the Block Applies Interpolation Arrays to Inputs

The interpolation array I_Pts represents the points in time at which to interpolate values of the input signal. An entry of 1 in I_Pts refers to the first sample of the input, an entry of 2.5 refers to the sample halfway between the second and third input sample, and so on. In most cases, when I_Pts is a vector, it can be of any length.

Valid values in the interpolation array, I_Pts, range from 1 to the number of samples in each channel of the input. To learn how the block handles out-of-range interpolation values, see Out of range interpolation points.

Depending on the dimension of the input and the dimension of I_Pts, the block usually applies I_Pts to the input in one of the following ways:

• Applies the I_Pts array across the first dimension of an N-D array, resulting in an N-D array output.

• Applies the vector I_Pts to each input vector (as if the input vector were a single channel), resulting in a vector output with the same orientation as the input (row or column).

These tables summarize how the block applies the interpolation array I_Pts to all the possible types of inputs and shows the resulting output dimensions.

The first table describes the block's behavior when the Source of interpolation points is Specify via dialog.

Specify Interpolation Points Through Dialog Box

Input Dimensions	Valid Dimensions of Interpolation Array I Pts	How Block Applies I Pts to Input	Output Dimensions (Frame-Based)
M-by-N-by-K matrix	P-by-1 column	Applies IPts to the first dimension of the input	P-by-N-by-K array
	P-by-N-by-K matrix	Applies each column of IPts (each element of IPts) to the corresponding column of the input matrix	P-by-N-by-K array
M-by-N matrix	1-by-N row	Applies each column of IPts (each element of IPts) to the corresponding column of the input matrix	1-by-N row
	P-by-1 column	Applies IPts to each input column	P-by-N matrix
	P-by-N matrix	Applies the columns of IPts to the corresponding columns of the input matrix
M-by-1 column	P-by-1 column	Applies IPts to the input column	P-by-1 column
1-by-N row (not recommended)	1-by-N row	Not Applicable. Block copies input vector	1-by-N row, a copy of the input vector
	P-by-1 column		P-by-N matrix where each row is a copy of the input vector
	P-by-N matrix

The next table describes the block's behavior when the Source of interpolation points is Input port.

Specify Interpolation Points Through Input Port

Input Dimensions	Valid Dimensions of Interpolation Array I Pts	How Block Applies I Pts to Input	Output Dimensions (Frame-Based)
M-by-N-by-K matrix	Unoriented vector or column vector of length P	Applies IPts to the first dimension of the input	P-by-N-by-K array
	P-by-N-by-K matrix	Applies each column of IPts (each element of IPts) to the corresponding column of the input matrix	P-by-N-by-K array
M-by-N matrix	1-by-N row	Applies each column of IPts (each element of IPts) to the corresponding column of the input matrix	1-by-N row
	P-by-1 column	Applies IPts to each input column	P-by-N matrix
	P-by-N matrix	Applies the columns of IPts to the corresponding columns of the input matrix
M-by-1 column	P-by-1 column	Applies IPts to the input column	P-by-1 column
1-by-N row (not recommended)	1-by-N row	Not Applicable. Block copies input vector	1-by-N row, a copy of the input vector
	P-by-1 column		P-by-N matrix where each row is a copy of the input vector
	P-by-N matrix

Algorithms

Linear Interpolation Mode

When Interpolation mode is set to Linear, the block interpolates data values by assuming that the data varies linearly between samples taken at adjacent sample times.

For instance, if the input signal D = [1 2 1.5 3 0.25]', the plot on the left shows the samples in D and the plot on the right shows the linearly interpolated values between the samples in D.

The following figure illustrates the case of a block in linear interpolation mode that is set to clip out-of-range interpolation points. The vector D supplies the input data and the vector I_Pts supplies the interpolation points:

• D = [1 2 1.5 3 0.25]'

• IPts = [-4 2.7 4.3 10]'

The block clips the invalid interpolation points and outputs the linearly interpolated values in a vector, [1 1.65 2.175 0.25]'.

FIR Interpolation Mode

When Interpolation mode is set to FIR, the block interpolates data values by using an FIR interpolation filter, specified by various block parameters. For more information, see FIR Interpolation Mode in the Variable Fractional Delay block reference.

Extended Capabilities

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

Version History

Introduced before R2006a