# dsp.HighpassFilter

FIR or IIR highpass filter

## Description

The `dsp.HighpassFilter`

System object™ independently filters each channel of the input over time using the given design
specifications. You can set the `FilterType`

property of
`dsp.HighpassFilter`

to `'FIR'`

or `'IIR'`

to implement the object as an FIR or IIR highpass filter.

To filter each channel of your input:

Create the

`dsp.HighpassFilter`

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?

## Creation

### Description

returns a minimum
order FIR highpass filter, `HPF`

= dsp.HighpassFilter`HPF`

, with the default filter settings.
Calling the object with the default property settings filters the input data with a
stopband frequency of `8`

kHz, a passband frequency of
`12`

kHz, a stopband attenuation of `80`

dB, and a
passband ripple of `0.1`

dB.

returns a highpass filter, with additional properties specified by one or more
`HPF`

= dsp.HighpassFilter(`Name,Value`

)`Name,Value`

pair arguments. `Name`

is the
property name and `Value`

is the corresponding value.
`Name`

must appear inside single quotes (' '). You can specify
several name-value pair arguments in any order as
`Name1,Value1,...,NameN,ValueN`

.

## 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.

`SampleRate`

— Input sample rate

`44100`

(default) | positive real scalar

Input sample rate in Hz, specified as the comma-separated pair consisting of
`'SampleRate'`

and a positive real scalar.

**Data Types: **`single`

| `double`

`FilterType`

— Filter type

`'FIR'`

(default) | `'IIR'`

Filter type, specified as one of the following options:

`'FIR'`

— The object designs an FIR highpass filter.`'IIR'`

— The object designs an IIR highpass (biquad) filter.

`DesignForMinimumOrder`

— Minimum order filter design

`true`

(default) | `false`

Minimum order filter design, specified as the comma-separated pair consisting of
`'DesignForMinimumOrder'`

and a logical value. If this property is
`true`

, then `dsp.HighpassFilter`

designs filters with the minimum order that meets the passband frequency, stopband
frequency, passband ripple, and stopband attenuation specifications. Set these
specifications using the corresponding properties. If this property is
`false`

, then the object designs filters with the order that you
specify in the `FilterOrder`

property. This filter design meets the
passband frequency, passband ripple, and stopband attenuation specifications that you
set using the respective properties.

`FilterOrder`

— Order of the FIR or IIR filter

`50`

(default) | positive integer scalar

Order of the FIR or IIR filter, specified as the comma-separated pair consisting of
`'FilterOrder'`

and a positive integer scalar.

#### Dependencies

Specifying a filter order is only valid when the value of
`'DesignForMinimumOrder'`

is `false`

.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`StopbandFrequency`

— Filter stopband edge frequency

`8000`

(default) | real positive scalar

Filter stopband edge frequency in Hz, specified as the comma-separated pair
consisting of `'StopbandFrequency'`

and a real positive scalar. The
value of the stopband edge frequency in Hz must be less than the passband
frequency.

#### Dependencies

You can specify the stopband edge frequency only when
`'DesignForMinimumOrder'`

is `true`

.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`PassbandFrequency`

— Filter passband edge frequency

`12000`

(default) | real positive scalar

Filter passband edge frequency in Hz, specified as the comma-separated pair
consisting of `'PassbandFrequency'`

and a real positive scalar. The
value of the passband edge frequency in Hz must be less than half the
`SampleRate`

and greater than
`StopbandFrequency`

.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`StopbandAttenuation`

— Minimum attenuation in the stopband

`80`

(default) | real positive scalar

Minimum attenuation in the stopband in dB, specified as the comma-separated pair
consisting of `'StopbandAttenuation'`

and a real positive scalar.
Minimum attenuation in the stopband defaults to `80`

dB.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`PassbandRipple`

— Maximum ripple of filter response in the passband

`0.1`

(default) | real positive scalar

Maximum ripple of filter response in the passband, in dB, specified as the
comma-separated pair consisting of `'PassbandRipple'`

and a real
positive scalar. Maximum ripple of filter response defaults to `0.1`

dB.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

**Fixed-Point Properties**

`RoundingMethod`

— Rounding method for output fixed-point operations

`'Floor'`

(default) | `'Ceiling'`

| `'Convergent'`

| `'Nearest'`

| `'Round'`

| `'Simplest'`

| `'Zero'`

Rounding method for output fixed-point operations, specified as a character vector. For more information on the rounding modes, see Precision and Range.

`CoefficientsDataType`

— Word and fraction lengths of coefficients

`numerictype([],16)`

(default) | `numerictype`

object

Word and fraction lengths of coefficients, specified as a
`numerictype`

object. The default,
`numerictype(1,16)`

corresponds to a signed numeric type object with
16-bit coefficients and a fraction length determined based on the coefficient values, to
give the best possible precision.

This property is not tunable.

Word length of the output is same as the word length of the input. Fraction length of the output is computed such that the entire dynamic range of the output can be represented without overflow. For details on how the fraction length of the output is computed, see Fixed-Point Precision Rules for Avoiding Overflow in FIR Filters.

## Usage

### Syntax

### Description

### Input Arguments

`x`

— Noisy data input

vector | matrix

Noisy data input, specified as a vector or a matrix. If the input signal is a matrix, each column of the matrix is treated as an independent channel. The number of rows in the input signal denote the channel length. This object accepts variable-size inputs. After the object is locked, you can change the size of each input channel, but you cannot change the number of channels.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

| `fi`

**Complex Number Support: **Yes

### Output Arguments

`y`

— Filtered output

vector | matrix

Filtered output, returned as a vector or a matrix. The output has the same size, data type, and complexity characteristics as the input.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

| `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.HighpassFilter`

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

`fvtool` | Visualize frequency response of DSP filters |

`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 |

`generatehdl` | Generate HDL code for quantized DSP filter (requires Filter Design HDL Coder) |

`measure` | Measure frequency response characteristics of filter System object |

## Examples

### Impulse and Frequency Response of FIR and IIR Highpass Filters

Create a minimum order FIR highpass filter for data sampled at 44.1 kHz. Specify a passband frequency of 12 kHz, a stopband frequency of 8 kHz, a passband ripple of 0.1 dB, and a stopband attenuation of 80 dB.

Fs = 44.1e3; filtertype = 'FIR'; Fpass = 12e3; Fstop = 8e3; Rp = 0.1; Astop = 80; FIRHPF = dsp.HighpassFilter('SampleRate',Fs,... 'FilterType',filtertype,... 'PassbandFrequency',Fpass,... 'StopbandFrequency',Fstop,... 'PassbandRipple',Rp,... 'StopbandAttenuation',Astop);

Design a minimum order IIR highpass filter with the same properties as the FIR highpass filter. Use `clone`

to create a system object with the same properties as the FIR Highpass filter. Change the `FilterType`

property of the cloned filter to `IIR`

.

```
IIRHPF = clone(FIRHPF);
IIRHPF.FilterType = 'IIR';
```

Plot the impulse response of the FIR highpass filter. The zeroth order coefficient is delayed by 19 samples, which is equal to the group delay of the filter. The FIR highpass filter is a causal FIR filter

fvtool(FIRHPF,'Analysis','impulse')

Plot the impulse response of the IIR highpass filter.

fvtool(IIRHPF,'Analysis','impulse')

Plot the magnitude and phase response of the FIR highpass filter.

fvtool(FIRHPF,'Analysis','freq')

Plot the magnitude and phase response of the IIR highpass filter.

fvtool(IIRHPF,'Analysis','freq')

Calculate the cost of implementing the FIR highpass filter.

cost(FIRHPF)

`ans = `*struct with fields:*
NumCoefficients: 39
NumStates: 38
MultiplicationsPerInputSample: 39
AdditionsPerInputSample: 38

Calculate the cost of implementing the IIR highpass filter. The IIR filter is more efficient to implement than its FIR counterpart.

cost(IIRHPF)

`ans = `*struct with fields:*
NumCoefficients: 18
NumStates: 14
MultiplicationsPerInputSample: 18
AdditionsPerInputSample: 14

Calculate the group delay of the FIR highpass filter.

grpdelay(FIRHPF)

Calculate the group delay of the IIR highpass filter. The FIR filter has a constant group delay (linear phase) while its IIR counterpart does not.

grpdelay(IIRHPF)

### Filter White Gaussian Noise with an IIR Highpass filter

**Note**: If you are using R2016a or an earlier release, replace each call to the object with the equivalent step syntax. For example, `obj(x)`

becomes `step(obj,x)`

.

Set up the IIR highpass filter. The sampling rate of the white Gaussian noise is 44,100 Hz. The passband frequency of the filter is 12 kHz, the stopband frequency is 8 kHz, the passband ripple is 0.1 dB, and the stopband attenuation is 80 dB.

Fs = 44.1e3; filtertype = 'IIR'; Fpass = 12e3; Fstop = 8e3; Rp = 0.1; Astop = 80; hpf = dsp.HighpassFilter('SampleRate',Fs,... 'FilterType',filtertype,... 'PassbandFrequency',Fpass,... 'StopbandFrequency',Fstop,... 'PassbandRipple',Rp,... 'StopbandAttenuation',Astop);

View the magnitude response of the highpass filter.

fvtool(hpf)

Create a spectrum analyzer object.

sa = spectrumAnalyzer('SampleRate',44.1e3,... 'PlotAsTwoSidedSpectrum',false,'ShowLegend',true,'YLimits',... [-150 30],... 'Title',... 'Input Signal and Output Signal of IIR Highpass Filter'); sa.ChannelNames = {'Input','Output'};

Filter the white Gaussian noisy input signal. View the input and output signals using the spectrum analyzer.

for k = 1:100 Input = randn(1024,1); Output = hpf(Input); sa([Input,Output]); end

### Measure Frequency Response Characteristics of Highpass Filter

Measure the frequency response characteristics of a highpass filter. Create a `dsp.HighpassFilter`

System object with default properties. Measure the frequency response characteristics of the filter.

HPF = dsp.HighpassFilter

HPF = dsp.HighpassFilter with properties: FilterType: 'FIR' DesignForMinimumOrder: true StopbandFrequency: 8000 PassbandFrequency: 12000 StopbandAttenuation: 80 PassbandRipple: 0.1000 SampleRate: 44100 Show all properties

HPFMeas = measure(HPF)

HPFMeas = Sample Rate : 44.1 kHz Stopband Edge : 8 kHz 6-dB Point : 10.418 kHz 3-dB Point : 10.8594 kHz Passband Edge : 12 kHz Stopband Atten. : 81.8558 dB Passband Ripple : 0.08066 dB Transition Width : 4 kHz

## Algorithms

### FIR Highpass Filter

When the `FilterType`

property is set to `'FIR'`

, the
`dsp.HighpassFilter`

object acts as a FIR highpass filter.
In this configuration, `dsp.HighpassFilter`

is an
alternative to using `firceqrip`

and `firgr`

with
`dsp.FIRFilter`

. This object condenses the two-step process into one. For
the minimum order design, the object uses generalized Remez FIR filter design algorithm. For
the specified order design, the object uses constrained equiripple FIR filter design
algorithm. The designed filter is then implemented as a linear phase Type-1 filter with a
`Direct form`

structure. You can use `measure`

to verify that the design meets the prescribed specifications.

### IIR Highpass Filter

When the `FilterType`

property is set to `'IIR'`

, the
`dsp.HighpassFilter`

object acts as an IIR highpass
filter. In this configuration, this object uses the elliptic design method to compute the
SOS and scale values required to meet the filter design specifications. The object uses the
SOS and scale values to set up a `Direct form I`

biquadratic IIR filter,
which forms the basis of the IIR version of the `dsp.HighpassFilter`

System object. You can use `measure`

to verify that the design meets the
prescribed specifications.

## References

[1] Shpak, D.J., and A. Antoniou. "A generalized Remez method for the design of FIR
digital filters." *IEEE ^{®} Transactions on Circuits and Systems*. Vol. 37, Issue 2, Feb. 1990,
pp. 161–174.

[2] Selesnick, I.W., and C. S. Burrus. "Exchange algorithms that complement the
Parks-McClellan algorithm for linear-phase FIR filter design." *IEEE Transactions on Circuits and Systems*. Vol. 44, Issue 2, Feb. 1997,
pp. 137–143.

## 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 supports code generation for ARM^{®}
Cortex^{®}-M and ARM
Cortex-A processors. To learn more about
ARM
Cortex code generation, see Code Generation for ARM Cortex-M and ARM Cortex-A Processors.

This object also supports SIMD code generation using Intel AVX2 technology under these conditions:

`FilterType`

is set to`'FIR'`

.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™.

This object supports HDL code generation with the Filter Design HDL Coder™ product. For workflows and limitations, see Generate HDL Code for Filter System Objects (Filter Design HDL Coder).

## Version History

**Introduced in R2015a**

## See Also

### Functions

### Objects

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