Digital Down-Converter

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

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Libraries:
DSP System Toolbox / Signal Operations

Description

The Digital Down-Converter (DDC) block converts a digitized real signal centered at an intermediate frequency (IF) to a baseband complex signal centered at zero frequency. The DDC block downsamples the frequency downconverted signal using a cascade of three decimation filters. This block designs the decimation filters according to the filter parameters you set in the block dialog box.

Examples

Digital Up and Down Conversion for Family Radio Service in Simulink

Implement Family Radio Service system using Digital Down-Converter and Digital Up-Converter blocks.

• Open Script

Ports

Input

Input 1 — Data input

column vector | matrix

Specify the data input as a column vector or a matrix. The number of rows in the input signal must be a multiple of the decimation factor that you specify in the Decimation factor parameter.

When the input data type is double or single precision, the output data type is the same as that of the input. When the input data type is a signed integer or fixed-point type, the output data type is defined by the Output parameter on the Data Types tab.

If the input is fixed point, it must be a signed integer or a signed fixed point value with a power-of-two slope and zero bias.

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

Osc — Oscillator signal

column vector | matrix

Specify the oscillator signal that the block uses to frequency down convert the input signal as a column vector or a matrix. The signal must be complex and its length must be equal to the length of the input.

When the oscillator input is fixed-point, it must be signed only.

Dependencies

To enable this port, set the Type of oscillator parameter to Input port.

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

Output

Output 1 — Downconverted and downsampled signal

column vector | matrix

The block outputs the downconverted and downsampled signal as a column vector or a matrix. The length of the output is equal to the length of the input divided by the value you specify in the Decimation factor parameter.

When the data type of the input is double or single precision, the data type of the output is the same as that of the input. When the input data type is fixed-point type or a signed integer, the output data type is defined by the Output parameter on the Data Types tab.

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

Parameters

Main Tab

Decimation factor — Decimation factor

100 (default) | positive integer ≥ 2 | vector of positive integers

Specify the decimation factor as a positive integer ≥ 2, or as a 1-by-2 or 1-by-3 vector of positive integers.

When you set this parameter to a scalar value, the block applies the same decimation factor to the three decimation filtering stages.

When you set this parameter to a 1-by-2 vector, the block applies the first and second values in the vector to the first and second filtering stages, respectively, and bypasses the third stage. Both elements of Decimation factor must be greater than 1.

When you set this parameter to a 1-by-3 vector, the block applies the values in the vector to the corresponding filtering stages. The first and second elements of Decimation factor must be greater than 1, and the third element must be 1 or 2.

Minimum order filter design — Design minimum-order filter

on (default) | off

When you select this check box, the block designs filters with the minimum possible order that meets the requirements specified in these parameters:

• Passband ripple of cascade response (dB)

• Stopband attenuation of cascade response (dB)

• Two-sided bandwidth of input signal

• Source of stopband frequency

• Stopband frequency

When you clear this check box, the block designs filters with orders that you specify in Number of sections of CIC decimator, Order of CIC compensation filter stage, and Order of third filter stage. The filter designs meet the passband and stopband frequency specifications that you set in Two-sided bandwidth of input signal, Source of stopband frequency, and Stopband frequency. By default, this check box is selected.

Number of sections of CIC decimator — Number of sections in CIC decimator

3 (default) | positive integer

Specify the number of sections in the CIC decimator as a positive integer.

Dependencies

To enable this parameter, clear the Minimum order filter design parameter.

Order of third filter stage — Order of third filter stage

10 (default) | even positive integer

Specify the order of the third filter stage as an even positive integer. When you specify Decimation factor as a 1-by-2 vector, the block ignores the value in this parameter because the block bypasses the third filter stage.

Dependencies

To enable this parameter, clear the Minimum order filter design parameter.

Source of stopband frequency — Source of stopband frequency

Auto (default) | Property

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

When you set this parameter to Auto and set:

• Sample rate mode to Specify on dialog –– The block places the cutoff frequency of the cascade filter response at approximately F_c = SampleRate/(2M) Hz, where M is the total decimation factor specified in Decimation factor. SampleRate is the input sample rate that you specify in the Input sample rate (Hz) parameter. The block 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), where the passband frequency F_p equals Bandwidth/2.

• Sample rate mode to Inherit from input port –– The block places the cutoff frequency of the cascade filter response at approximately F_c = SampleRate/(2M) Hz, where M is the total decimation factor specified in Decimation factor. SampleRate is computed as 1/ Ts, where Ts is the sample time of the input signal. The block 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), where the passband frequency F_p equals Bandwidth/2.

• Sample rate mode to Use normalized frequency (0 to 1) –– The block 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 Decimation factor. The block 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 Bandwidth/2.

When you set this parameter to Property, specify the stopband frequency in Stopband frequency.

Type of oscillator — Type of oscillator

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

Specify the oscillator type as one of the following:

• Sine wave — The block performs frequency down conversion on the input signal using a complex exponential obtained from samples of a sinusoidal trigonometric function.

• NCO — The block performs frequency down conversion on the input signal with a complex exponential obtained using a numerically controlled oscillator (NCO).

• Input port — The block performs frequency down conversion on the input signal using the complex signal that you provide through the Osc input port.

• None — The block does not require the mixer stage and acts as a three-stage cascaded decimator.

Center frequency of output signal — Center frequency of output signal

0.9333 (default) | positive scalar

Specify the center frequency of the output signal as a positive scalar in Hz or in normalized frequency units (since R2024b).

If you set the Sample rate mode parameter to:

• Specify on dialog or Inherit from input port –– The value of the center frequency is in Hz and must be less than half the sample rate of the input signal. The block downconverts the input signal from the passband center frequency, which you specify in Center frequency of output signal, to 0 Hz.

• Use normalized frequency (0 to 1) –– The value of the center frequency is in normalized frequency units. The value must be a positive scalar less than or equal to 1.0.

(since R2024b)

Dependency

To enable this parameter, set Type of oscillator to Sine wave or NCO.

Order of CIC compensation filter stage — Order of CIC compensation filter stage

12 (default) | positive integer

Specify the order of the CIC compensation filter stage as a positive integer.

Dependencies

To enable this parameter, clear the Minimum order filter design parameter.

Two-sided bandwidth of input signal — Two-sided bandwidth of input signal

0.0133 (default) | positive scalar

Specify the two-sided bandwidth of the input signal as a positive scalar in Hz or in normalized frequency units (since R2024b). The block sets the passband frequency of the cascade of filters to half of the value you specify in this parameter. Set the value of this parameter to less than Input sample rate (Hz)/Decimation factor. When you set Sample rate mode to Inherit from input port, set this value to less than ((1/Ts)/Decimation factor), where Ts is the sample time of the input signal. If you set Sample rate mode to Use normalized frequency (0 to 1), set this value to less than 1/Decimation factor.

Stopband frequency — Stopband frequency

0.01 (default) | positive scalar

Specify the stopband frequency as a positive scalar in Hz or in normalized frequency units (since R2024b).

Dependencies

To enable this parameter, set Source of stopband frequency to Property.

Passband ripple of cascade response (dB) — Passband ripple of cascade response

0.1 (default) | positive scalar

Specify the passband ripple of the cascade response in dB as a double-precision positive scalar. When you select the Minimum order filter design, the block designs the filters so that the cascade response meets the passband ripple that you specify in Passband ripple of cascade response (dB).

Dependencies

To enable this parameter, select the Minimum order filter design parameter.

Stopband attenuation of cascade response (dB) — Stopband attenuation of cascade response

60 (default) | positive scalar

Specify the stopband attenuation of the cascade response in dB as a double-precision positive scalar. When you select the Minimum order filter design parameter, the block designs the filters such that the cascade response meets the stopband attenuation that you specify in this parameter.

Dependencies

To enable this parameter, select the Minimum order filter design parameter.

Number of NCO accumulator bits — Number of NCO accumulator bits

16 (default) | positive integer

Specify the number of NCO accumulator bits as an integer scalar in the range [1 128].

Dependencies

To enable this parameter, set Type of oscillator to NCO.

Number of NCO quantized accumulator bits — Number of NCO quantized accumulator bits

12 (default) | positive integer in the range [1 128]

Specify the number of NCO quantized accumulator bits as an integer scalar in the range [1 128]. This value must be less than the value you specify in Number of NCO accumulator bits.

Dependencies

To enable this parameter, set Type of oscillator to NCO.

Dither control for NCO — Dither control for NCO

on (default) | off

When you select this check box, the block applies dither to the NCO signal according to the number of dither bits you specify in Number of NCO dither bits. By default, this check box is selected.

Dependencies

To enable this parameter, set Type of oscillator to NCO.

Number of NCO dither bits — Number of NCO dither bits

4 (default) | positive integer

Specify the number of NCO dither bits as an integer scalar smaller than the number of accumulator bits in Number of NCO accumulator bits.

Dependencies

To enable this parameter, set Type of oscillator to NCO and select the Dither control for NCO parameter.

Sample rate mode — Mode to specify the input sample rate

Use normalized frequency (0 to 1) (default) | Specify on dialog | Inherit from input port

Since R2024b

Specify the input sample rate using one of these options:

• Use normalized frequency (0 to 1) –– Specify the center frequency, two-sided bandwidth, and stopband frequency in normalized frequency units (0 to 1).

• Specify on dialog –– Specify the input sample rate in the block dialog box using the Input sample rate (Hz) parameter.

• Inherit from input port –– The block inherits the sample rate from the input signal. The block computes the sample rate as N/Ts, where N is the frame size of the input signal, and Ts is the sample time of the input signal.

Input sample rate (Hz) — Sample rate of input signal

30e6 (default) | positive scalar

Specify the sample rate of the input signal in Hz as a positive scalar greater than or equal to twice the value in Center frequency of output signal.

Dependencies

To enable this parameter, set the Sample rate mode parameter to Specify on dialog. (since R2024b)

View Filter Response — View Filter Response

button

Click this button to open the Filter Visualization Tool (FVTool) and display the magnitude and phase response of each stage as well as the cascade of stages in the Digital Down-Converter. The response is based on the values you specify in the block parameters dialog box. Changes made to these parameters update FVTool.

To update the magnitude response while FVTool is running, modify the parameters in the dialog box and click Apply.

Simulate using — Type of simulation to run

Interpreted execution (default) | Code generation

Specify the type of simulation to run. You can set this parameter to:

• Interpreted execution –– Simulate model using the MATLAB^® interpreter. This option shortens startup time.

• Code generation –– Simulate model using generated C code. The first time you run a simulation, Simulink^® generates C code for the block. The C code is reused for subsequent simulations as long as the model does not change. This option requires additional startup time but provides faster subsequent simulations.

Data Types Tab

Stage input — Stage input

Inherit: Same as input (default) | fixdt([],16,0)

Specify the data type of the input in the first, second, and third filter stages. You can set this parameter to one of the following:

• Inherit: Same as input (default) — The block inherits the Stage input data type from the input signal.

• fixdt([],16,0) — The block uses the fixed-point data type with binary-point scaling. Specify the sign mode of this data type as [] or true.

• An expression that evaluates to a data type, for example, numerictype([],16,15). Specify the sign mode of this data type as [] or true.

For help with setting the stage input parameter, you can click the Show data type assistant button to display the data type assistant.

See Specify Data Types Using Data Type Assistant (Simulink) for more information.

Output — Output

Inherit: Same as input (default) | fixdt([],16,0)

Specify the data type of the block output. You can set this parameter to:

• Inherit: Same as input (default) — The block Inherits the output datatype from the input.

• fixdt([],16,0) — The block uses the fixed-point data type with binary point scaling. Specify the sign mode of this data type as [] or true.

• An expression that evaluates to a data type, for example, numerictype([],16,15). Specify the sign mode of this data type as [] or true.

For help with setting the Output parameter, you can click the Show data type assistant button to display the data type assistant.

See Specify Data Types Using Data Type Assistant (Simulink) for more information.

Minimum — Minimum

[] (default) | scalar

Specify the minimum value of the block output. The default value is [] (unspecified). Simulink software uses this value to perform:

• Simulation range checking (see Specify Signal Ranges (Simulink))

• Automatic scaling of fixed-point data types

Maximum — Maximum

[] (default) | scalar

Maximum value of the block output. The default value is [] (unspecified). Simulink software uses this value to perform:

• Simulation range checking (see Specify Signal Ranges (Simulink))

• Automatic scaling of fixed-point data types

Lock data type settings against changes by the fixed-point tools — Prevent fixed-point tools from overriding data types

off (default) | on

Select this parameter to prevent the fixed-point tools from overriding the data types you specify in the block dialog box.

Block Characteristics

Data Types	double | fixed point | integer | single
Direct Feedthrough	no
Multidimensional Signals	no
Variable-Size Signals	no
Zero-Crossing Detection	no

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 Simulink® Coder™.

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.

Version History

Introduced in R2015a

R2024b: Support for normalized frequencies

When you set the Sample rate mode parameter to Use normalized frequency (0 to 1), you can specify the two-sided bandwidth of the input signal, center frequency of the output signal, and the stopband frequency in normalized frequency units (0 to 1).

R2024a: Change in the default value of Simulate using parameter

The default value of the Simulate using parameter is now Interpreted execution. With this change, the block uses the MATLAB interpreter for simulation by default.