Digital Frequency Conversion Simulation Design

💡 My graduation project topic is a multi-frequency digital upconverter, so I first simulated the DUC, aiming to upsample an audio signal with a 48k sampling rate to a 6.144M sampling rate with 28 interpolation, and then modulate it with AM for transmission.

Matlab Simulation#

Basic Parameter Generation#

%% base data gen
fs_base=48e3;               % Sampling rate at input DUC
upsample_L=128;
fs_duc=fs_base*upsample_L;  % Sampling rate at output DUC
Fc=5e6;                     % Carrier Frequency
Fpass=20e3;                 % AM baseband width
Fstop=30e3;                 % Stopband
Ap=0.1;                     % Passband ripple
Ast=60;                     % Stopband attenuation
T = 1;                      % Duration
t = 0:1/fs_base:T-1/fs_base;% Time vector
outputframe=1;
N1_cycle = 128;
N2_cycle = 64;
N3_cycle = 32;
N4_cycle = 16;

The overall system rate is 48k×128=6.144M, achieved by enabling signal for sampling rate conversion. The signal output is stream output, with a frame size of 1.

Level 1 Lowpass FIR Interpolator#

%% First Lowpass Fir Interpolator

lowpassParams.FsIn=fs_base;
lowpassParams.InterpolationFactor = 2;
lowpassParams.FsOut=lowpassParams.FsIn*lowpassParams.InterpolationFactor;

lowpassSpec = fdesign.interpolator(lowpassParams.InterpolationFactor, ...
    'lowpass','Fp,Fst,Ap,Ast',Fpass,Fstop,Ap,Ast,lowpassParams.FsOut);
lowpassFilt = design(lowpassSpec,'SystemObject',true)

The input signal sampling rate is the baseband rate, and the output signal sampling rate is the baseband rate × interpolation factor. The filter coefficients are designed using fdesign.interpolator, and the filter's amplitude-frequency response is as follows:

Level 2 Lowpass Halfband Interpolator#

%%
% *Second Halfband Interpolator*
% 
% The halfband filter provides efficient interpolation by two. Halfband 
% filters are efficient for hardware because approximately half of their 
% coefficients are equal to zero, and those multipliers are excluded from
% the hardware implementation.   

 hbParams.FsIn = lowpassParams.FsOut;
 hbParams.InterpolationFactor = 2;
 hbParams.FsOut = lowpassParams.FsOut*hbParams.InterpolationFactor;
 hbParams.TransitionWidth = hbParams.FsIn - 2*Fstop; % Passband, since the interpolated spectrum will be periodically extended based on the input signal's sampling rate
                                                     % Subtracting 2 times Fstop ensures that the bandwidth of the retained signal after interpolation does not introduce aliasing, while ensuring sufficient attenuation
 hbParams.StopbandAttenuation = Ast;
 
 hbSpec = fdesign.interpolator(hbParams.InterpolationFactor,'halfband', ...
          'TW,Ast', ...
          hbParams.TransitionWidth, ...
          hbParams.StopbandAttenuation, ...
          hbParams.FsOut);

hbFilt = design(hbSpec,'SystemObject',true)

The passband of the halfband filter is the input signal sampling rate minus twice the cutoff frequency, ensuring that the frequency bands of the extended spectrum produced after interpolation can be filtered out without introducing aliasing, while ensuring sufficient attenuation.

The amplitude-frequency response of the halfband filter and the response of the two-stage filter cascade are as follows:

Level 3 CIC Compensation Filter#

Due to the non-flat passband of the CIC interpolation filter, a compensation filter needs to be added.

% *CIC Compensation Interpolator*
% 
% Because the magnitude response of the last CIC filter has a significant 
% _droop_ within the passband region, the example uses an FIR-based droop 
% compensation filter to flatten the passband response. The droop 
% compensator has the same properties as the CIC interpolator. This filter
% implements interpolation by a factor of two, 
% so you must also specify bandlimiting characteristics for the filter.
% Also, specify the CIC interpolator properties that are used for this
% compensation filter as well as the later CIC interpolator. 
% 
% Use the |design| function to return a filter System object with the 
% specified characteristics. 

compParams.FsIn = hbParams.FsOut;
compParams.InterpolationFactor = 2;                                 % CIC compensation interpolation factor
compParams.FsOut = compParams.FsIn*compParams.InterpolationFactor;  % New sampling rate
compParams.Fpass = 1/2*compParams.FsIn + Fpass;                     % CIC compensation passband frequency
compParams.Fstop = 1/2*compParams.FsIn + 1/4*compParams.FsIn;       % CIC compensation stopband frequency
compParams.Ap = Ap;                                                 % Same passband ripple as overall filter
compParams.Ast = Ast;                                               % Same stopband attenuation as overall filter
N = 31;                                                             % 32 tap filter to take advantage of 16 cycles between input 

cicParams.InterpolationFactor = 16;  % CIC interpolation factor
cicParams.DifferentialDelay = 1;    % CIC interpolator differential delayb   
cicParams.NumSections = 4;          % CIC interpolator number of integrator and comb sections

compSpec = fdesign.interpolator(compParams.InterpolationFactor,'ciccomp', ...
           cicParams.DifferentialDelay, ...
           cicParams.NumSections, ...
           cicParams.InterpolationFactor, ...
           'N,Fp,Ap,Ast', ...
           N,compParams.Fpass,compParams.Ap,compParams.Ast, ...
           compParams.FsOut);
compFilt = design(compSpec,'SystemObject',true)

The reasons for setting the passband and stopband frequencies of the compensation filter are as follows:

compParams.Fpass = 1/2 * compParams.FsIn + Fpass:
The setting of the passband frequency Fpass here is based on the input sampling rate compParams.FsIn. The attenuation of the frequency response of the CIC filter typically becomes significant starting from FsIn/2, so the passband of the compensation filter is set to FsIn/2 + Fpass, ensuring that the compensation filter corrects the gain of the CIC filter within the passband, especially in the high-frequency part.
compParams.Fstop = 1/2 * compParams.FsIn + 1/4 * compParams.FsIn:
The stopband frequency is set to FsIn/2 + 1/4 * FsIn, which aims to further ensure that after interpolation, the out-of-band portion of the signal spectrum can be sufficiently attenuated to prevent aliasing. Since the interpolation process will periodically extend the input signal's spectrum, the stopband of the filter needs to cover these extended portions to ensure that unwanted signals are filtered out.

The amplitude-frequency response of the compensation filter is as follows:

Level 4 CIC Interpolator#

%%
% *CIC Interpolator*
% 
% The last filter stage is implemented as a CIC interpolator because of this
% type of filter's ability to efficiently implement a large decimation factor.
% The response of a CIC filter is similar to a cascade of moving average 
% filters, but a CIC filter uses no multiplication or division. As a result,
% the CIC filter has a large DC gain.
cicParams.InterpolationFactor = 16;  % CIC interpolation factor
cicParams.DifferentialDelay = 1;    % CIC interpolator differential delayb   
cicParams.NumSections = 4;          % CIC interpolator number of integrator and comb sections

cicParams.FsIn = compParams.FsOut;
cicParams.FsOut = cicParams.FsIn*cicParams.InterpolationFactor;

cicFilt = dsp.CICInterpolator(cicParams.InterpolationFactor, ...
          cicParams.DifferentialDelay,cicParams.NumSections)

After passing through three levels of two-fold interpolation filters, the final 16-fold interpolation through the CIC filter completes the 128-fold interpolation. The amplitude-frequency response is as follows:

Simulink Simulation#

duc-structure-pdf.pdf

📌 Use counters to generate different enable signals to control the filter for sampling rate changes

DUC_Module#

NCO_system#

This module is used to generate the baseband signal

The spectrum diagram is as follows

The time domain waveform is as follows

LP_system#

The first two-fold interpolation is performed on the signal, and the processed spectrum diagram is

The time domain waveform is

It can be seen that the high-frequency part in the spectrum has been partially filtered out, and a new value has been inserted between every two sample points in the time domain.