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# dsp.HDLNCO System object

Generate real or complex sinusoidal signals—optimized for HDL code generation

## Description

The HDL NCO System object™ generates real or complex sinusoidal signals. In addition, the HDL NCO System object provides hardware-friendly control signals, optional reset signal, optional valid input signal, optional phase output signal, and an optional external dither input signal. It uses the same phase accumulation and lookup table technology as implemented in the NCO System object. You can use the lookup table compression option to significantly reduce the lookup table size with less than one LSB loss in precision. The System object does not support the property that allows the block to synthesize the LUT to a ROM on an FPGA.

Given a desired output frequency F0, calculate the phase_increment input value using

`$phaseincrement=\left(\frac{{F}_{0}\cdot {2}^{N}}{{F}_{s}}\right)$`
where N is the accumulator word length and
`${F}_{s}=\frac{1}{{T}_{s}}=\frac{1}{sampletime}$`
You can specify the phase increment using a property or an input argument.

The frequency resolution of an NCO is defined by

`$\Delta f=\frac{1}{{T}_{s}\cdot {2}^{N}}\text{Hz}$`

Given a desired phase offset (in radians), calculate the phase_offset input value using

`$phaseoffset=\frac{{2}^{N}\cdot desiredphaseoffset}{2\pi }$`
You can specify the phase offset using a property or an input argument.

To generate real or complex sinusoidal signals:

1. Create the dsp.HDLNCO object and set its properties.

2. Call the object with arguments, as if it were a function.

## Creation

### Syntax

``HDLNCO = dsp.HDLNCO``
``HDLNCO = dsp.HDLNCO(Name,Value)``
``HDLNCO = dsp.HDLNCO(Inc,'PhaseIncrementSource','Property')``

### Description

````HDLNCO = dsp.HDLNCO` returns a numerically controlled oscillator (NCO) System object, `HDLNCO`, that generates a real or complex sinusoidal signal. The amplitude of the generated signal is always 1.```

example

````HDLNCO = dsp.HDLNCO(Name,Value)` returns an HDL NCO System object, `HDLNCO`, with properties set using one or more name-value pairs. Enclose each property name in single quotes.```
````HDLNCO = dsp.HDLNCO(Inc,'PhaseIncrementSource','Property')` returns an HDL NCO System object, `HDLNCO`, with the `PhaseIncrement` property set to `Inc`. `Inc` is an integer scalar. To use the PhaseIncrement property, set the PhaseIncrementSource property to `Property`. You can add other `Name,Value` pairs before or after `PhaseIncrementSource`.```

## Properties

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### Note

This object supports floating point types for simulation but not for HDL code generation. When a data input is fixed point, or when no data input ports are enabled, the object computes the output waveform based on the fixed-point property settings. When a data input is floating-point, the object ignores NumDitherBits, PhaseQuantization, NumQuantizerAccumulatorBits, LUTCompress, and the fixed-point data type properties, and computes a double-precision output waveform.

When you switch to using a floating-point phase increment, you must adjust the value of the increment to account for the lack of phase quantization.

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.

### Waveform Generation

Source of phase increment, specified as `'Input port'`, or `'Property'`. You can set the phase increment from an input argument or from a property.

Phase increment for generating the waveform, specified as a scalar integer. `double` and `single` are allowed for simulation but not for HDL code generation.

#### Dependencies

This property applies when you set the `PhaseIncrementSource` property to `'Property'`.

Data Types: `single` | `double` | `int8` | `int16` | `int32` | `uint8` | `uint16` | `uint32` | `fixdt([],N,0)`

Source of phase offset, specified as `'Input port'`, or `'Property'`. You can set the phase offset from an input argument or from a property.

Phase offset, specified as a scalar integer. `double` and `single` are allowed for simulation but not for HDL code generation.

#### Dependencies

This property applies when you set the `PhaseOffsetSource` property to `'Property'`.

Data Types: `single` | `double` | `int8` | `int16` | `int32` | `uint8` | `uint16` | `uint32` | `fixdt([],N,0)`

Source of number of dither bits, specified as `'Input port'`, `'Property'`, or `'None'`. You can set the dither from an input port or from a parameter, or you can disable dither. When you select `'Property'`, configure the dither in `NumDitherBits` property.

Number of dither bits, specified as a positive integer.

#### Dependencies

This property applies when you set the `DitherSource` property to `'Property'`.

Whether to quantize accumulated phase, specified as `true` or `false`. When this option is enabled, the NCO output is calculated by quantizing the result of the phase accumulator to a fixed bit- width. This quantized value is used to select a waveform value from the lookup table. Select the resolution of the lookup table using the `NumQuantizerAccumulatorBits` property.

The frequency resolution of an NCO is defined by

`$\Delta f=\frac{1}{{T}_{s}\cdot {2}^{N}}\text{Hz}$`

When you disable this option,

Number of quantizer accumulator bits, specified as an integer scalar greater than 1 and less than the accumulator word length. The lookup table of sine values has 2`NumQuantizerAccumulatorBits` entries.

#### Dependencies

This property applies when you set `PhaseQuantization` to `true`.

Whether to enable lookup table compression, specified as `true` or `false`. By default, the object implements a compressed lookup table. The Sunderland compression method reduces the size of the lookup table with less than one LSB loss in precision. The spurious free dynamic range (SFDR) is empirically 1-3dB lower than the non-compressed case. With a compressed lookup table, you can increase the word length of the accumulator, and the number of quantize bits, to improve the performance. For detail of the compression method, see Algorithms.

When this option is disabled, the output matches the output of the `dsp.NCO` System object.

Type of output waveform. If you select `'Complex exponential'`, the output is of the form `sine + j*cosine`. If you select `'Sine and cosine'`, the object returns an additional output.

Whether to return current phase, specified as `true` or `false`. Set this property to `true` to return the current phase along with the output waveform.

### Control Signals

Whether to enable reset argument, specified as `true` or `false`. Set this property to `true` to enable a reset argument to the object.

Whether to enable valid input signal, specified as `true` or `false`. Set this property to `false` to disable the `ValidIn` input argument to the object.

### Data Types

Overflow mode for fixed-point operations. `OverflowAction` is a read-only property with value `'Wrap'`.

Rounding mode for fixed-point operations. `RoundingMethod` is a read-only property with value `'Floor'`.

Accumulator data type. This property is read-only, with value ```'Binary point scaling'```. The accumulator sign, word length, and fraction length are taken from the following three properties.

Signed or unsigned accumulator data format. This property is read-only. All output is signed format.

Accumulator word length, in bits, specified as a scalar integer.

Accumulator fraction length, in bits, specified as a scalar integer.

Output data type. If this property is set to ```'Binary point scaling'```, the output sign, word length, and fraction length are taken from the following three properties.

Signed or unsigned output data format. This property is read-only. All output is signed format.

Output word length, in bits, specified as a scalar integer.

Output fraction length, in bits, specified as a scalar integer.

## Usage

For versions earlier than R2016b, use the `step` function to run the System object™ algorithm. The arguments to `step` are the object you created, followed by the arguments shown in this section.

For example, `y = step(obj,x)` and `y = obj(x)` perform equivalent operations.

### Syntax

``````[Y,ValidOut] = HDLNCO(Inc,ValidIn)``````
``````[Y,ValidOut] = HDLNCO``````
``````[Y,ValidOut] = HDLNCO(Inc,Offset,Dither,ValidIn)``````
``[Y,Phase,ValidOut] = HDLNCO(___)``

### Description

The object returns the waveform value, `Y`, as a sine value, a cosine value, a complex exponential value, or a [`Sine,Cosine`] pair of values, depending on the Waveform property.

``````[Y,ValidOut] = HDLNCO(Inc,ValidIn)``` returns a sinusoidal signal, `Y`, generated by the HDLNCO System object, with the specified phase increment, `Inc`. When `ValidIn` is `true`, `Inc` is added to the accumulator.```

example

``````[Y,ValidOut] = HDLNCO``` returns a waveform, `Y`, using waveform parameters from properties rather than input arguments.To use this syntax, set the PhaseIncrementSource, PhaseOffsetSource, and DitherSource properties to `'Property'`, and ValidInputPort to `false`. These properties are independent of each other. You can mix and match the activation of these arguments. For example: hdlnco = dsp.HDLNCO('PhaseIncrementSource','Property', ... 'PhaseIncrement',phIncr,... 'PhaseOffset',phOffset,... 'ValidInputPort',false,... 'NumDitherBits',4)```

example

``````[Y,ValidOut] = HDLNCO(Inc,Offset,Dither,ValidIn)``` returns a waveform, `Y`, with phase increment, `Inc`, phase offset, `Offset`, and dither, `Dither`. This syntax applies when you set the PhaseIncrementSource, PhaseOffsetSource, and DitherSource properties to `'Input port'`. These properties are independent of each other. You can mix and match the activation of these arguments. `PhaseIncrementSource` is `'Input port'` by default. For example: hdlnco = dsp.HDLNCO('PhaseOffsetSource','Input port',... 'DitherSource','Input port') for k = 1:1/Ts y(k) = hdlnco(phIncr,phOffset,ditherBits,true); end```
````[Y,Phase,ValidOut] = HDLNCO(___)` returns a waveform, `Y`, and output `Phase`. To use this syntax, set the PhasePort property to `true`. This syntax can include any of the arguments from other syntaxes. For example: hdlnco = dsp.HDLNCO('PhaseOffsetSource','Input port',... 'DitherSource','Input port',... 'PhasePort',true) for k = 1:1/Ts [phase(k),y(k)] = hdlnco(phIncr,phOffset,ditherBits,true); end```

### Input Arguments

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Phase increment, specified as a scalar integer. `double` and `single` are allowed for simulation but not for HDL code generation.

#### Dependencies

The object accepts this argument when you set the PhaseIncrementSource property to ```'Input port'```.

Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `fixdt([],N,0)`

Enable signal, specified as a `logical` scalar. The object increments the phase when `ValidIn` input is high. When `ValidIn` is low, the phase is held.

#### Dependencies

The object accepts this argument when you set the ValidInputPort property to `true`.

Data Types: `logical`

Phase offset, specified as a scalar integer. T `double` and `single` are allowed for simulation but not for HDL code generation.

#### Dependencies

The object accepts this argument when you set the PhaseOffsetSource property to `'Input port'`.

Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `fixdt([],N,0)`

Dither, specified as a scalar integer. `double` and `single` are allowed for simulation but not for HDL code generation.

#### Dependencies

The object accepts this argument when you set the DitherSource property to `'Input port'`.

Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `fixdt([],N,0)`

Request reset of the accumulator, specified as a `logical` scalar value. The object resets the accumulator to zero when `Reset` is high.

#### Dependencies

The object accepts this argument when you set the ResetAction property to `true`.

Data Types: `logical`

### Output Arguments

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Waveform, returned as a scalar fixed-point or floating-point value, or as a [`Sine,Cosine`] pair of values.

#### Dependencies

The type of the output waveform depends on the Waveform property.

• `'Sine'` (default) — returns a generated sine wave

• `'Cosine'` — returns a generated cosine wave

• `'Complex exponential'` — returns a wave in the form `sine + j*cosine`

• `'Sine and cosine'` — returns a pair of values representing corresponding sine and cosine waves

Validity of the `Y` output, returned as a `logical` scalar. When `ValidOut` is high, the data output is valid. When `ValidOut` is low, the data output is not valid.

Data Types: `logical`

Current phase of the NCO, returned as a scalar of type `fixdt(1,M,-Z)`, where M is the number of quantized accumulator bits, and Z is the accumulator word length. The object returns `Phase` as floating point if the input to the object is floating point. Floating point is allowed for simulation but not for HDL code generation.

#### Dependencies

The object returns this additional output when you set the PhasePort property to `true`.

Data Types: `single` | `double` | `fixdt(1,NumQuantizerAccumulatorBits,-AccumulatorWL)`

## 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)`
 `step` Run System object algorithm `clone` Create duplicate System object `getNumInputs` Number of inputs required to call the System object `getNumOutputs` Number of outputs from calling the System object `isLocked` Determine if System object is locked `release` Release resources and allow changes to System object property values and input characteristics `reset` Reset internal states of System object

## Examples

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This example shows how to design an HDL-compatible NCO source.

```F0 = 510; % Output frequency = 510 Hz df = 0.05; % Frequency resolution = 0.05 Hz minSFDR = 96; % Spurious free dynamic range >= 96 dB Ts = 1/4000; % Sample period = 1/4000 seconds dphi = pi/2; % Desired phase offset = pi/2; ```

Calculate the number of accumulator bits required for the frequency resolution, and the number of quantized accumulator bits to satisfy the SFDR requirement.

```Nacc = ceil(log2(1/(df*Ts))); actdf = 1/(Ts*2^Nacc); % Actual frequency resolution achieved Nqacc = ceil((minSFDR-12)/6); ```

Calculate the phase increment and offset.

```phIncr = round(F0*Ts*2^Nacc); phOffset = 2^Nacc*dphi/(2*pi); ```

Construct a NCO HDL System object™. Set the properties to the values calculated. Call the object to generate data points in a sine wave. The input to the object is a valid signal.

Note: This object syntax runs only in R2016b or later. If you are using an earlier release, replace each call of an object with the equivalent `step` syntax. For example, replace `myObject(x)` with `step(myObject,x)`.

```hdlnco = dsp.HDLNCO('PhaseIncrementSource','Property', ... 'PhaseIncrement',phIncr,... 'PhaseOffset',phOffset,... 'NumDitherBits',4, ... 'NumQuantizerAccumulatorBits',Nqacc,... 'AccumulatorWL',Nacc) for k = 1:1/Ts y(k) = hdlnco(true); end ```
```hdlnco = dsp.HDLNCO with properties: PhaseIncrementSource: 'Property' PhaseIncrement: 16712 PhaseOffsetSource: 'Property' PhaseOffset: 32768 DitherSource: 'Property' NumDitherBits: 4 PhaseQuantization: true NumQuantizerAccumulatorBits: 14 LUTCompress: false ResetAction: false ValidInputPort: true Waveform: 'Sine' PhasePort: false Use get to show all properties ```

Plot the mean-square spectrum of the 510 Hz sine wave generated by the NCO.

```sa = dsp.SpectrumAnalyzer('SampleRate',1/Ts); sa.SpectrumType = 'Power density'; sa.PlotAsTwoSidedSpectrum = false; sa(y'); ```

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