dsp.DigitalDownConverter

Translate digital signal from intermediate frequency (IF) band to baseband and decimate it

Description

The dsp.DigitalDownConverter object translates digital signal from intermediate frequency (IF) band to baseband and decimates it.

To digitally downconvert the input signal:

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

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

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

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

Creation

Syntax

dwnConv = dsp.DigitalDownConverter

dwnConv = dsp.DigitalDownConverter(Name=Value)

Description

dwnConv = dsp.DigitalDownConverter returns a digital downconverter (DDC) System object™, dwnConv.

dwnConv = dsp.DigitalDownConverter(Name=Value) returns a DDC object, dwnConv, with the specified property Name set to the specified Value. You can specify additional 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.

DecimationFactor — Decimation factor

100 (default) | positive integer scalar | vector of positive integers

Set this property to a positive integer scalar, or to a 1-by-2 or 1-by-3 vector of positive integers.

When you set this property to a scalar, the object automatically chooses the decimation factors for each of the three filtering stages.

When you set this property to a 1-by-2 vector, the object bypasses the third filter stage and sets the decimation factor of the first and second filtering stages to the values in the first and second vector elements respectively. Both elements of the DecimationFactor vector must be greater than one.

When you set this property to a 1-by-3 vector, the i th element of the vector specifies the decimation factor for the ith filtering stage. The first and second elements of the DecimationFactor vector must be greater than one, and the third element must be 1 or 2.

Data Types: double

MinimumOrderDesign — Minimum order filter design

true (default) | false

When you set this property to true, the object designs filters with the minimum order that meets the passband ripple, stopband attenuation, passband frequency, and stopband frequency specifications that you set using the PassbandRipple, StopbandAttenuation, Bandwidth, StopbandFrequencySource, and StopbandFrequency properties.

When you set this property to false, the object designs filters with orders that you specify in the NumCICSections, SecondFilterOrder, and ThirdFilterOrder properties. The filter designs meet the passband and stopband frequency specifications that you set using the Bandwidth, StopbandFrequencySource, and StopbandFrequency properties.

Data Types: logical

NumCICSections — Number of sections of CIC decimator

3 (default) | positive integer scalar

Number of sections of CIC decimator, specified as a positive integer scalar.

Dependencies

This property applies when you set the MinimumOrderDesign property to false.

Data Types: double

SecondFilterOrder — Order of CIC compensation filter stage

12 (default) | positive integer scalar

Order of CIC compensation filter stage, specified as a positive integer scalar.

Dependencies

This property applies when you set the MinimumOrderDesign property to false.

Data Types: double

ThirdFilterOrder — Order of third filter stage

10 (default) | even positive integer

Order of third filter stage, specified as an even positive integer scalar. When you set the DecimationFactor property to a 1-by-2 vector, the object ignores the ThirdFilterOrder property because the third filter stage is bypassed.

Dependencies

This property applies when you set the MinimumOrderDesign property to false.

Data Types: double

Bandwidth — Two-sided bandwidth of input signal

200000 (default) | positive integer

Two-sided bandwidth BW of the input signal, specified as a positive integer in Hz or in normalized frequency units (since R2024b). The object sets the passband frequency of the cascade of filters to one-half of the value that you specify in the Bandwidth property. Set the value of this property to less than SampleRate/DecimationFactor. If you set NormalizedFrequency to true, set the value of this property to less than 2/DecimationFactor. (since R2024b)

Data Types: double

StopbandFrequencySource — Source of stopband frequency

Auto (default) | Property

Specify the source of the stopband frequency as Auto or Property.

When you set this property to Auto and set:

• NormalizedFrequency to false –– The object places the cutoff frequency of the cascade filter response at approximately F_c = Fs/(2M) Hz, where M is the total decimation factor that you specify in the DecimationFactor property. The object computes the stopband frequency as F_stop = F_c + (TW/2). TW is the transition bandwidth of the cascade response computed as 2×(F_c–F_p), and the passband frequency F_p equals BW/2, where BW is the two-sided bandwidth of the input signal.

• NormalizedFrequency to true –– The object places the cutoff frequency of the cascade filter response at approximately F_c = 1/M, where M is the total decimation factor that you specify in the DecimationFactor property. The object computes the stopband frequency as F_stop = F_c + (TW/2). TW is the transition bandwidth of the cascade response computed as 2×(F_c–F_p), and the passband frequency F_p equals BW/2, where BW is the two-sided bandwidth of the input signal.

When you set this property to Property, you can specify the stopband frequency value using the StopbandFrequency property.

StopbandFrequency — Stopband frequency

150000 (default) | positive scalar

Stopband frequency F_stop, specified as a positive scalar in Hz or in normalized frequency units (since R2024b).

Dependencies

To enable this property, set the StopbandFrequencySource property to Property.

Data Types: double

PassbandRipple — Passband ripple of cascade response in dB

0.1 (default) | positive scalar

Passband ripple of cascade response in dB, specified as a positive scalar. When you set the MinimumOrderDesign property to true, the object designs the filters so that the cascade response meets the passband ripple that you specify in the PassbandRipple property.

Dependencies

To enable this property, set the MinimumOrderDesign property to true.

Data Types: double

StopbandAttenuation — Stopband attenuation of cascade response in dB

60 (default) | positive scalar

Stopband attenuation of cascade response in dB, specified as a positive scalar. When you set the MinimumOrderDesign property to true, the object designs the filters so that the cascade response meets the stopband attenuation that you specify in the StopbandAttenuation property.

Dependencies

To enable this property, set the MinimumOrderDesign property to true.

Data Types: double

Oscillator — Type of oscillator

Sine wave (default) | NCO | Input port | None

Type of oscillator, specified as one of these options:

• Sine wave –– The object frequency down converts the input signal using a complex exponential obtained from samples of a sinusoidal trigonometric function.

• NCO –– The object performs frequency down conversion with a complex exponential obtained using a numerically controlled oscillator (NCO).

• Input port –– The object performs frequency down conversion using the complex oscillator signal, z, that you pass as an input to the object.

• None –– The mixer stage in the object is not present and the object acts as three stage cascaded decimator.

CenterFrequency — Center frequency of input signal

14000000 (default) | positive scalar

Center frequency of the input signal Fc, specified as a positive scalar in Hz or in normalized frequency units (since R2024b). The value of center frequency must be less than or equal to half the value of the SampleRate property. The object downconverts the input signal from the passband center frequency you specify in the CenterFrequency property to 0.

Dependencies

To enable this property, set the Oscillator property to Sine wave or NCO.

Data Types: double

NumAccumulatorBits — Number of NCO accumulator bits

16 (default) | positive integer

Number of NCO accumulator bits, specified as a positive integer in the range [1 128].

Dependencies

To enable this property, set the Oscillator property to NCO.

Data Types: double

NumQuantizedAccumulatorBits — Number of NCO quantized accumulator bits

12 (default) | positive integer

Number of NCO quantized accumulator bits, specified as an integer in the range [1 128]. The value you specify in this property must be less than the value you specify in the NumAccumulatorBits property.

Dependencies

To enable this property, set the Oscillator property to NCO.

Data Types: double

Dither — Dither control for NCO

true (default) | false

When you set this property to true, a number of dither bits specified in the NumDitherBits property will be used to apply dither to the NCO signal.

Dependencies

To enable this property, set the Oscillator property to NCO.

NumDitherBits — Number of NCO dither bits

4 (default) | positive integer

Number of NCO dither bits, specified as a positive integer smaller than the number of accumulator bits that you specify in the NumAccumulatorBits property.

Dependencies

To enable this property, set the Oscillator property to NCO and the Dither property to true.

Data Types: double

NormalizedFrequency — Option to set frequencies in normalized units

false (default) | true

Since R2024b

Option to set frequencies in normalized units, specified as one of these values:

• true –– The center frequency, stopband frequency, and bandwidth must be in the normalized frequency units (0 to 1).

  When you set the NormalizedFrequency property to true while creating the object and you do not set the frequency specifications, the object automatically sets the default values to normalized frequency units using the default sample rate of 30 MHz.

  ddc = dsp.DigitalDownConverter(NormalizedFrequency=true)
  

  ddc = 
    dsp.DigitalDownConverter with properties:
  
             DecimationFactor: 100
           MinimumOrderDesign: true
                    Bandwidth: 0.0133
      StopbandFrequencySource: 'Auto'
               PassbandRipple: 0.1000
          StopbandAttenuation: 60
                   Oscillator: 'Sine wave'
              CenterFrequency: 0.9333
          NormalizedFrequency: true
  

  When you set the NormalizedFrequency property to true after you create the object, you must specify the center frequency, stopband frequency, and bandwidth in normalized units before you run the object algorithm.

  ddc = dsp.DigitalDownConverter

  ddc = 
    dsp.DigitalDownConverter with properties:
  
             DecimationFactor: 100
           MinimumOrderDesign: true
                    Bandwidth: 200000
      StopbandFrequencySource: 'Auto'
               PassbandRipple: 0.1000
          StopbandAttenuation: 60
                   Oscillator: 'Sine wave'
              CenterFrequency: 14000000
          NormalizedFrequency: false
                   SampleRate: 30000000
  

  To specify the normalized frequency values, set NormalizedFrequency to true and manually convert the frequency values in Hz to the normalized values using the input sample rate in Hz. For example, if the input sample rate Fs is 30 MHz, the corresponding bandwidth value in normalized units is BW_Hz/(Fs/2), the corresponding center frequency in normalized units is F_cHz/(Fs/2), and the corresponding stopband frequency in normalized units is F_stopHz/(Fs/2).

  ddc = dsp.DigitalDownConverter;
  ddc.NormalizedFrequency = true;
  ddc.Bandwidth = 200000/(30e6/2);
  ddc.CenterFrequency = 14e6/(30e6/2)
  

  ddc = 
    dsp.DigitalDownConverter with properties:
  
             DecimationFactor: 100
           MinimumOrderDesign: true
                    Bandwidth: 0.0133
      StopbandFrequencySource: 'Auto'
               PassbandRipple: 0.1000
          StopbandAttenuation: 60
                   Oscillator: 'Sine wave'
              CenterFrequency: 0.9333
          NormalizedFrequency: true
  

• false –– The bandwidth, stopband frequency, and center frequency values are in Hz. You can specify the input sample rate through the SampleRate property.

Data Types: logical

SampleRate — Sample rate of input signal

30000000 (default) | positive scalar

Sample rate of the input signal Fs, specified as a positive scalar value greater than or equal to twice the value of the CenterFrequency property.

Dependencies

To enable this property, set NormalizedFrequency to false. (since R2024b)

Data Types: single | double

Fixed-Point Properties

FiltersInputDataType — Data type of input of each filter stage

Same as input (default) | Custom

Specify the data type at the input of the first, second, and third (if it has not been bypassed) filter stages as one of Same as input | Custom. The object casts the data at the input of each filter stage according to the value you set in this property.

CustomFiltersInputDataType — Fixed-point data type of input of each filter stage

numerictype([],16,15) (default) | numeric type

Specify the filters input fixed-point type as a scaled numerictype (Fixed-Point Designer) object with a Signedness of Auto.

Dependencies

This property applies when you set the FiltersInputDataType property to Custom.

OutputDataType — Data type of output

Same as input (default) | Custom

Specify the data type of output as Same as input | Custom.

CustomOutputDataType — Fixed-point data type of output

numerictype([],16,15) (default) | numeric type

Specify the output fixed-point type as a scaled numerictype (Fixed-Point Designer) object with a Signedness of Auto.

Dependencies

This property applies when you set the OutputDataType property to Custom.

Usage

Syntax

y = dwnConv(x)

y = dwnConv(x,z)

Description

y = dwnConv(x) takes an input x and outputs a signal, y that is frequency downconverted and downsampled.

y = dwnConv(x,z) uses the complex input, z, as the oscillator signal used to frequency down convert input x when you set the Oscillator property to Input port.

Input Arguments

x — Data input

column vector | matrix

Data input, specified as a column vector or a matrix. The length of input x must be a multiple of the decimation factor. When the data type of x is double or single precision, the data type of y is the same as that of x. When the data type of x is of a fixed-point type, the data type of y is defined by the OutputDataType property.

The input can have multiple channels only if its data type is double or single. The input can be of data type double, single, signed integer, or signed fixed-point (fi objects).

Data Types: single | double | int8 | int16 | int32 | int64 | fi
Complex Number Support: Yes

z — Oscillator signal

column vector | matrix

Oscillator signal used to frequency down convert the input signal, specified as a column vector or a matrix. This input must be complex. The length of z must be equal to the length of x. z can be double, single, signed integer, or signed fixed-point (fi objects).

Dependencies

This input applies when you set the Oscillator property to Input port.

Data Types: single | double | int8 | int16 | int32 | int64 | fi
Complex Number Support: Yes

Output Arguments

y — Down converted and down sampled signal

column vector | matrix

Down converted and down sampled signal, returned as a column vector or a matrix. The length of y is equal to the length of x divided by the DecimationFactor. When the data type of x is double or single precision, the data type of y is the same as that of x. When the data type of x is of a fixed point type, the data type of y is defined by the OutputDataType property.

Data Types: single | double | int8 | int16 | int32 | int64 | 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.DigitalDownConverter

getDecimationFactors	Get decimation factors of each filter stage of a digital down converter
getFilterOrders	Get orders of digital down converter or digital up converter filter cascade
getFilters	Get handles to digital down converter or digital up converter filter cascade objects
groupDelay	Group delay of digital down converter or digital up converter filter cascade
visualize	Display response of digital down converter or digital up converter filter cascade
generatehdl	Generate HDL code for quantized DSP filter (requires Filter Design HDL Coder)

Common to All System Objects

step	Run System object algorithm
release	Release resources and allow changes to System object property values and input characteristics
reset	Reset internal states of System object

Examples

Upconvert and Downconvert a Sine Wave Signal

Create a digital up converter object that up samples a 1 KHz sinusoidal signal by a factor of 20 and up converts it to 50 KHz. Create a digital down converter object that down converts the signal to 0 Hz and down samples it by a factor of 20.

Create a sine wave generator to obtain the 1 KHz sinusoidal signal with a sample rate of 6 KHz.

Fs = 6e3; % Sample rate
sine = dsp.SineWave(Frequency=1000,...
    SampleRate=Fs,...
    SamplesPerFrame=1024);
x = sine(); % generate signal

Create a DigitalUpConverter object. Use minimum order filter designs and set passband ripple to 0.2 dB and the stopband attenuation to 55 dB. Set the double sided signal bandwidth to 2 KHz.

upConv = dsp.DigitalUpConverter(... 
 InterpolationFactor=20,...
 SampleRate=Fs,...
 Bandwidth=2e3,...
 StopbandAttenuation=55,...
 PassbandRipple=0.2,...
 CenterFrequency=50e3);

Create a DigitalDownConverter object. Use minimum order filter designs and set the passband ripple to 0.2 dB and the stopband attenuation to 55 dB.

dwnConv = dsp.DigitalDownConverter(...
  DecimationFactor=20,...
  SampleRate=Fs*20,...
  Bandwidth=3e3,...
  StopbandAttenuation=55,...
  PassbandRipple=0.2,...
  CenterFrequency=50e3);

Create a spectrum estimator to visualize the signal spectrum before up converting, after up converting, and after down converting.

window = hamming(floor(length(x)/10));
figure; pwelch(x,window,[],[],Fs,'centered')
title('Spectrum of baseband signal x')

Up convert the signal and visualize the spectrum

xUp = upConv(x); % up convert
window = hamming(floor(length(xUp)/10));
figure; pwelch(xUp,window,[],[],20*Fs,'centered');
title('Spectrum of up converted signal xUp')

Down convert the signal and visualize the spectrum

xDown = dwnConv(xUp); % down convert
window = hamming(floor(length(xDown)/10));
figure; pwelch(xDown,window,[],[],Fs,'centered')
title('Spectrum of down converted signal xDown')

Visualize the response of the decimation filters

visualize(dwnConv)

Get Decimation Factors

Get decimation factors of each filter stage of the dsp.DigitalDownConverter System object™.

Create a dsp.DigitalDownConverter System object with the default settings. Using the getDecimationFactors function, obtain the decimation factors of each stage of the object.

dwnConv = dsp.DigitalDownConverter

dwnConv = 
  dsp.DigitalDownConverter with properties:

           DecimationFactor: 100
         MinimumOrderDesign: true
                  Bandwidth: 200000
    StopbandFrequencySource: 'Auto'
             PassbandRipple: 0.1000
        StopbandAttenuation: 60
                 Oscillator: 'Sine wave'
            CenterFrequency: 14000000
        NormalizedFrequency: false
                 SampleRate: 30000000

  Use get to show all properties

M = getDecimationFactors(dwnConv) %#ok

M = 1×3

    25     2     2

The DecimationFactor property of the object is set to 100. The output M is by default a 1-by-3 vector, where each element in the vector is a factor of the overall decimation factor.

When you set the DecimationFactor to a 1-by-2 vector, the object bypasses the third filter stage and sets the decimation factor of the first and second filtering stages to the values in the first and second vector elements respectively.

dwnConv.DecimationFactor = [10 10]

dwnConv = 
  dsp.DigitalDownConverter with properties:

           DecimationFactor: [10 10]
         MinimumOrderDesign: true
                  Bandwidth: 200000
    StopbandFrequencySource: 'Auto'
             PassbandRipple: 0.1000
        StopbandAttenuation: 60
                 Oscillator: 'Sine wave'
            CenterFrequency: 14000000
        NormalizedFrequency: false
                 SampleRate: 30000000

  Use get to show all properties

M = getDecimationFactors(dwnConv)

M = 1×2

    10    10

The output of the getDecimationFactors function is now a 1-by-2 vector.

More About

Fixed Point

The following block diagram represents the DDC arithmetic with signed fixed-point inputs.

• WL is the word length of the input, and FL is the fraction length of the input.

• The input of each filter is cast to the filter input data type. In the dsp.DigitalDownConverter object, you can specify the filter input data type through the FiltersInputDataType and CustomFiltersInputDataType properties. In the Digital Down-Converter block, you can specify the filter input data type through the Stage input parameter.

• The oscillator output is cast to a word length equal to the input word length plus one. The fraction length is equal to the input word length minus one.

• The scaling at the output of the CIC decimator consists of coarse- and fine-gain adjustments. The coarse gain is achieved using the reinterpretcast (Fixed-Point Designer) function on the CIC decimator output. The fine gain is achieved using full-precision multiplication.

The following figure depicts the coarse-gain and fine-gain operations.

If the normalization gain is G (where 0<G≦1), then:

• WLcic is the word length of the CIC decimator output and FLcic is the fraction length of the CIC decimator output.

• F1 = abs(nextpow2(G)), indicating the part of G achieved using bit shifts (coarse gain).

• F2 = fraction length specified by the filter input data type.

• fg = fi((2^F1)*G, true, 16), which indicates that the remaining gain cannot be achieved with a bit shift (fine gain).

Algorithms

The digital down converter downconverts the input signal by multiplying it with a complex exponential that has the specified center frequency. The algorithm downsamples the frequency downconverted signal using a cascade of three decimation filters. In this case, the filter cascade consists of a CIC decimator, a CIC compensator, and a third FIR decimation stage. The following block diagram shows the architecture of the digital down converter.

The scaling section normalizes the CIC gain and the oscillator power. It can also contain a correction factor to achieve the desired ripple specification. When you specify an oscillator signal through the input port, the normalization factor does not include the oscillator power factor. Depending on how you set the decimation factor, the block bypasses the third filter stage. When the input data type is double or single, the algorithm implements an N-section CIC decimation filter as an FIR filter with a response that corresponds to a cascade of N boxcar filters. The algorithm emulates a CIC filter with an FIR filter so that you can run simulations with floating-point data. When the input data type is fixed-point, the algorithm implements a true CIC filter with actual comb and integrator sections.

This block diagram represents the DDC arithmetic with single or double-precision, floating-point inputs.

For details about fixed-point operation, see Fixed Point.

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™.

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 R2012a

R2024b: visualizeFilterStages has been renamed to visualize

The visualizeFilterStages function has been renamed to visualize. Existing instances of this function continue to run. For new instances, use visualize.

R2024b: visualize launches MATLAB figure

The visualize function now launches a MATLAB^® figure to display the magnitude response of the digital down converter filter cascade.

R2024b: Support for normalized frequencies

When you set the NormalizedFrequency property to true, you must specify the bandwidth, stopband frequency, and the center frequency in normalized frequency units (0 to 1). For more information, see the NormalizedFrequency property description.