# dsp.DCBlocker

Block DC component (offset) from input signal

## Description

The `dsp.DCBlocker`

System object™ removes the DC offset from each channel (column) of the input signal. The
operation runs over time to continually estimate and remove the DC offset.

To block the DC component of the input signal:

Create the

`dsp.DCBlocker`

object and set its properties.Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

The object supports C/C++ code generation and SIMD code generation under certain conditions. For more information, see Code Generation.

## Creation

### Description

creates a DC blocker
System object, `dcblker`

= dsp.DCBlocker`dcblker`

, to block the DC component from each channel
(column) of the input signal.

creates a DC blocker System object, `dcblker`

= dsp.DCBlocker(`Name=Value`

)`dcblker`

, with each specified property set to the
specified value.

**Example: **`dcblker = dsp.DCBlocker(Algorithm='FIR')`

## Properties

Unless otherwise indicated, properties are *nontunable*, which means you cannot change their
values after calling the object. Objects lock when you call them, and the
`release`

function unlocks them.

If a property is *tunable*, you can change its value at
any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

`Algorithm`

— Algorithm for estimating DC offset

`'IIR'`

(default) | `'FIR'`

| `'CIC'`

| `'Subtract mean'`

Algorithm for estimating DC offset, specified as one of the following:

`'IIR'`

–– The object uses a recursive estimate based on a narrow, lowpass elliptic filter. The Order property sets the order of the filter, and the NormalizedBandwidth property sets its bandwidth. This algorithm typically uses less memory than the FIR algorithm and is more efficient.`'FIR'`

–– The object uses a nonrecursive, moving average estimate based on a finite number of past input samples. The Length property sets the number of samples. The FIR filter has a linear phase response and does not cause any phase distortion to the signal. The IIR filter requires less memory and is more efficient to implement.`'CIC'`

–– The object uses a CIC decimator, with a decimation factor of 1, whose differential delay is calculated using the`NormalizedBandwidth`

property. It uses two sections to ensure that the first sidelobe attenuation is at least 25 dB below the main lobe of the filter. This algorithm requires fixed-point inputs and can be used for HDL code generation.`'Subtract mean'`

–– The object computes the means of the columns of the input matrix, and subtracts the means from the input. This method does not retain state between inputs.

You can visualize the IIR, FIR, and CIC responses by using the `fvtool`

function.

`NormalizedBandwidth`

— Normalized bandwidth of lowpass IIR or CIC filter

`0.001`

(default) | real scalar greater than 0 and less than 1

Normalized bandwidth of the IIR or CIC filter, specified as a real scalar greater than 0 or less than 1. The normalized bandwidth is used to estimate the DC component of the input signal.

#### Dependencies

This property applies only when you set the Algorithm property to `'IIR'`

or
`'CIC'`

.

`Order`

— Order of lowpass IIR elliptic filter

`6`

(default) | integer greater than 3

Order of the lowpass IIR elliptic filter that is used to estimate the DC level, specified as an integer greater than 3.

#### Dependencies

This property applies only when you set the Algorithm property to
`'IIR'`

.

`Length`

— Number of past input samples used in FIR algorithm

`50`

(default) | positive integer

Number of past input samples used in the FIR algorithm to estimate the running mean, specified as a positive integer.

#### Dependencies

This property applies only when you set the Algorithm property to
`'FIR'`

.

## Usage

### Description

removes the DC component from each channel (column) of the input and returns the
output.`dcblkerOut`

= dcblker(`input`

)

### Input Arguments

`input`

— Input signal

vector | matrix | *N*-D array

Data input to the DC blocker object, specified as a vector, matrix, or
*N*-D array.

**Example: **```
t = (0:0.001:100)'; x = sin(30*pi*t) +
1;
```

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `fi`

**Complex Number Support: **Yes

### Output Arguments

`dcblkerOut`

— Signal with DC component removed

vector | matrix | *N*-D array

Signal with DC component removed, returned as a vector, matrix, or
*N*-D array. The output dimensions match the input
dimensions.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `fi`

**Complex Number Support: **Yes

## Object Functions

To use an object function, specify the
System object as the first input argument. For
example, to release system resources of a System object named `obj`

, use
this syntax:

release(obj)

### Specific to `dsp.DCBlocker`

`freqz` | Frequency response of discrete-time filter System object |

`filterAnalyzer` | Analyze filters with Filter Analyzer app |

`impz` | Impulse response of discrete-time filter System object |

`info` | Information about filter System object |

`coeffs` | Returns the filter System object coefficients in a structure |

`cost` | Estimate cost of implementing filter System object |

`grpdelay` | Group delay response of discrete-time filter System object |

`outputDelay` | Determine output delay of single-rate or multirate filter |

## Examples

### Remove DC Component and Display Results

Remove the DC component of an input signal using the IIR, FIR, and subtract mean estimation algorithms.

Create a signal composed of a 15 Hz tone, a 25 Hz tone, and a DC offset.

t = (0:0.001:100)'; x = sin(30*pi*t) + 0.33*cos(50*pi*t) + 1;

Create three DC blocker objects for the three estimation algorithms.

dc1 = dsp.DCBlocker('Algorithm','IIR','Order', 6); dc2 = dsp.DCBlocker('Algorithm','FIR','Length', 100); dc3 = dsp.DCBlocker('Algorithm','Subtract mean');

For each second of time, pass the input signal through the DC blockers. By implementing the DC blockers in 1-second increments, you can observe differences in the convergence times.

for idx = 1 : 100 range = (1:1000) + 1000*(idx-1); y1 = dc1(x(range)); % IIR estimate y2 = dc2(x(range)); % FIR estimate y3 = dc3(x(range)); % Subtract mean end

Plot the input and output data for the three DC blockers for the first second of time, and show the mean value for each signal. The mean values for the three algorithm types show that the `FIR`

and `Subtract mean`

algorithms converge more quickly.

plot(t(1:1000),x(1:1000), ... t(1:1000),y1, ... t(1:1000),y2, ... t(1:1000),y3); xlabel('Time (sec)') ylabel('Amplitude') legend(sprintf('Input DC:%.3f',mean(x)), ... sprintf('IIR DC:%.3f',mean(y1)), ... sprintf('FIR DC:%.3f',mean(y2)), ... sprintf('Subtract mean DC:%.3f',mean(y3)));

### Frequency Response Before and After DC Blocker

Compare the spectrum of an input signal with a DC offset to the spectrum of the same signal after applying a DC blocker. Enable the DC blocker to use the `FIR`

estimation algorithm.

Create an input signal composed of three tones and that has a DC offset of 1. Set the sampling frequency to 1 kHz and set the signal duration to 100 seconds.

fs = 1000; t = (0:1/fs:100)'; x = sin(30*pi*t) + 0.67*sin(40*pi*t) + 0.33*sin(50*pi*t) + 1;

Create a DC blocker object that uses the FIR algorithm to estimate the DC offset.

dcblker = dsp.DCBlocker('Algorithm','FIR','Length',100);

Create a spectrum analyzer with power units set to `dBW`

and a frequency range of `[-30 30]`

to display the frequency response of the input signal. Using the `clone`

function, create a second spectrum analyzer to display the response of the output. Then, use the `Title`

property of the spectrum analyzers to label them.

hsa = spectrumAnalyzer('SampleRate',fs, ... 'Method','welch',... 'AveragingMethod','exponential',... 'SpectrumUnits','dBW','FrequencySpan','start-and-stop-frequencies',... 'StartFrequency',-30,'StopFrequency',30,'YLimits',[-200 20],... 'Title','Signal Spectrum'); hsb = clone(hsa); hsb.Title = 'Signal Spectrum After DC Blocker';

Pass the input signal, `x`

, through the DC blocker to generate the output signal, `y`

.

y = dcblker(x);

Use the first spectrum analyzer to display the frequency characteristics of the input signal. The tones at 15, 20, and 25 Hz, and the DC component, are clearly visible.

hsa(x)

Use the second spectrum analyzer to display the frequency characteristics of the output signal. The DC component has been removed.

hsb(y)

## Algorithms

The DC blocker subtracts the DC component from the input signal. You can estimate the DC component by using the IIR, FIR, CIC, or subtract mean algorithm.

### IIR

Pass the input signal through an IIR lowpass elliptical filter.

The elliptical IIR filter has a passband ripple of 0.1 dB and a stopband attenuation of 60 dB. You specify the normalized bandwidth and the filter order.

### FIR

Pass the input signal through an FIR filter that uses a nonrecursive moving average from a finite number of past input samples.

The FIR filter coefficients are given as `ones(1,Length)/Length`

, where `Length`

is the number of past input samples for FIR algorithm. The FIR filter structure is a direct form I transposed structure.

### CIC

Pass the input signal through a CIC filter. Because the CIC filter amplifies the signal, the filter gain is estimated and subtracted from the DC estimate.

The Cascaded Integrator-Comb (CIC) filter consists of two integrator-comb pairs. These pairs help to ensure that the peak of the first sidelobe of the filter response is attenuated by at least 25 dB relative to the peak of the main lobe. The normalized 3 dB bandwidth is used to calculate the differential delay. The delay is used to determine the gain of the CIC filter. The inverse of the filter gain is used as a multiplier, which is applied to the output of the CIC filter. This ensures that the aggregate gain of the DC estimate is 0 dB.

The following equation characterizes the aggregate magnitude response of the filter and the multiplier:

$$\left|H({e}^{j\omega})\right|={\left|\frac{\mathrm{sin}(M{\scriptscriptstyle \frac{\pi}{2}}{B}_{norm})}{M\mathrm{sin}({\scriptscriptstyle \frac{\pi}{2}}{B}_{norm})}\right|}^{N}$$

*B*is the normalized bandwidth such that 0 <_{norm}*B*< 1._{norm}*M*is the differential delay in samples.*N*is the number of sections, equal to 2.

Set the differential delay, *M*, to the smallest integer such that |*H(e ^{jω})*| < 1/√2. Once

*M*is known, the gain of the CIC filter is calculated as

*M*. Therefore, to precisely compensate for the filter gain, the multiplier is set to (

^{N}*1/M*)

*.*

^{N}### Subtract mean

Compute the mean value of each column of the input signal and subtract the mean from the input. For example, if the input is [1 2 3 4; 3 4 5 6], then a DC Blocker set to this mode outputs [-1 -1 -1 -1; 1 1 1 1].

## References

[1] Nezami, M. “Performance Assessment of Baseband Algorithms for Direct Conversion Tactical Software Defined Receivers: I/Q Imbalance Correction, Image Rejection, DC Removal, and Channelization.” MILCOM, 2002.

## Extended Capabilities

### C/C++ Code Generation

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

Usage notes and limitations:

See System Objects in MATLAB Code Generation (MATLAB Coder).

This object also supports SIMD code generation using Intel^{®} AVX2 code replacement library when the input signal has a data type of
`single`

or `double`

.

The SIMD technology significantly improves the performance of the generated code. For more information, see SIMD Code Generation. To generate SIMD code from this object, see Use Intel AVX2 Code Replacement Library to Generate SIMD Code from MATLAB Algorithms.

### HDL Code Generation

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

The software supports `double`

and
`single`

data types for simulation, but not for HDL code generation.

To generate HDL code from predefined System objects, see HDL Code Generation from Viterbi Decoder System Object (HDL Coder).

## Version History

**Introduced in R2014a**

### R2024b: Support for filter analysis functions

When you set `Algorithm`

to `'FIR'`

,
`'IIR'`

, or `'CIC'`

, the `dsp.DCBlocker`

object supports certain filter analysis functions listed in Analysis Functions for Filter System Objects. For
more information, see the Version History section in the individual analysis function
reference pages.

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