Filter Design Toolbox

mfilt.cicinterp

Construct a cascaded integrator-comb interpolation filter object

Syntax

• hm = mfilt.cicinterp(r,m,n,ibits,obits)
  

Description

hm = mfilt.cicinterp(r,m,n,ibits,obits) constructs a cascaded integrator-comb (CIC) interpolation filter object.

The following table describes the input arguments for creating hm.

Input Arguments	Description
r	Interpolation factor applied. Sharpens the response curve to let you change the shape of the response.
m	Differential delay. Changes both the shape and number of nulls in the filter response. Also affects the null locations. Increasing m increases the number and sharpness of the nulls and response between nulls. Generally, one or two work as values for m.
n	Number of stages. Deepens the nulls in the response curve.
ibits	Word length of the input signal. It can be either 8, 16, or 32 bits (default is 16).
obits	Word length of the output signal. It can be any positive integer in the range of 1 to 32 (default is 16).

Objects have properties that control the way the object behaves. This table lists all the properties for the filter, with a description of each.

Name	Values	Default	Description
InterpolationFactor	Any positive integer	None	Amount to increase the sampling rate.
DifferentialDelay	Any integer	1	Sets the differential delay for the filter. Usually a value of one or two is appropriate.
FilterStructure	Any mfilt structure string	None	Reports the type of filter object, such as a decimator or fractional integrator. You cannot set this property--it is always read only and results from your choice of mfilt object.
InputBitWidth	8, 16, 32	16	Word length of the input samples.
NumOfSamplesProcessed	Any integer	0	Returns the number of samples processed during filtering. As a check, the number of samples reported processed plus the number of nonprocessed samples should be the total number of input samples.
NumberOfStages	Any positive integer	2	Number of stages used in the decimator.
OutputBitWidth	1 to 32	16	Word length of the output samples.
ResetBeforeFiltering	'off' or 'on'	on	Determine whether the filter states get restored to their starting values for each filtering operation. The starting values are the values in place when you create the filter if you have not changed the filter since you constructed it. ResetBeforeFiltering returns to zero any state that the filter changes during processing. States that the filter does not change are not affected.
States	Any int32 matrix having size (m+1,n)	2-by-2 matrix, int32	Stored conditions for the filter, including values for the interpolator and comb states. The matrix dimension entries m and n are the differential delay and number of filter stages.

About the States of the Filter

In the states property you find the states for both the integrator and comb portions of the filter. states is a matrix of dimensions m+1-by-n, with the states apportioned as follows:

• States for the integrator portion of the filter are stored in the first row of the state matrix.
• States for the comb portion fill the remaining rows in the state matrix.

In the state matrix, state values are specified and stored in int32 format.

Design Considerations

When you design your CIC interpolation filter, remember the following general points:

• The filter output spectrum has nulls at  = k * 2/rm radians, k = 1,2,3....
• Aliasing and imaging occur in the vicinity of the nulls.
• n, the number of stages in the filter, determines the passband attenuation. Increasing n improves the filter ability to reject aliasing and imaging, but it also increases the droop or rolloff in the filter passband. Using an appropriate FIR filter in series after the CIC interpolation filter can help you compensate for the induced droop.
• The DC gain for the filter is a function of the interpolation factor. Raising the interpolation factor increases the DC gain.

Examples

Demonstrate interpolation by a factor of two, in this case from 22.05 KHz to 44.1 KHz. Note the scaling required to see the results in the stem plot and to use the full range of the int16 data type.

• R = 2;                      % Interpolation factor
  hm = mfilt.cicinterp(R);    % Use default NumberofStages and 
                              % DifferentialDelay
  fs = 22.05e3;               % Original sampling frequency--22.05 KHz
  n = 0:5119;                 % 5120 samples, 0.232 second long signal
  x  = sin(2*pi*1e3/fs*n);    % Original signal, sinusoid at 1 KHz
    
  % Scale input to use the full dynamic range of the INT16 data type
  x = int16((2^15-1)*x/gain(hm));
    
  y_int = filter(hm,x); % 5120 samples, still 0.232 seconds
    
  % Scale the input and output to overlay plots
  x = double(x); x = x/max(abs(x)); 
  y = double(y_int); y = y/max(abs(y));
  stem(n(1:22)/fs,x(1:22),'filled'); % Plot original signal sampled 
                                     % at 22.05 KHz 
  hold on;
  stem(n(1:44)/(fs*R),y(4:47),'r');  % Plot interpolated signal 
                                     % (44.1 KHz) in red
  xlabel('Time (sec)');ylabel('Signal Value');
  

As you expect, the plot shows that the interpolated signal matches the input sine shape, with additional samples between each original sample.

Use the filter visualization tool (FVTool) to plot the response of the interpolator object. For example, to plot the response of an interpolator with an interpolation factor of 7, 4 stages, and 1 differential delay, do something like the following:

• hm = mfilt.cicinterp(7,1,4)
  fvtool(hm)
  

Algorithm

To show how the CIC interpolation filter is constructed, the following figure presents a block diagram of the filter structure for a two-stage CIC decimation filter (n = 2). fs is the high sampling rate, the input to the decimation process.

For details about the bits that are removed in the integrator section, refer to [1] in References.

See Also

cicdecimate, cicinterpolate, mfilt, mfilt.cicdecim, mfilt.cicdecimzerolat, mfilt.cicinterpzerolat

References

[1]  Hogenauer, E. B., "An Economical Class of Digital Filters for Decimation and Interpolation," IEEE Transactions on Acoustics, Speech, and Signal Processing, ASSP-29(2): pp. 155-162, 1981

[2]  Meyer-Baese, Uwe, "Hogenauer CIC Filters," in Digital Signal Processing with Field Programmable Gate Arrays, Springer, 2001, pp. 155-172

mfilt.cicdecimzerolat

mfilt.cicinterpzerolat