数字上变频仿真设计

💡 我的毕设题目为多频点数字上变频器，因此先做了 DUC 的仿真，目标是将 48k 采样率的音频信号进 28 插值到 6.144M 的采样率，并将其做 AM 调制后发射出去。

Matlab 仿真#

基本参数生成#

%% 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;                      % 持续时间
t = 0:1/fs_base:T-1/fs_base;% 时间向量
outputframe=1;
N1_cycle = 128;
N2_cycle = 64;
N3_cycle = 32;
N4_cycle = 16;

系统的整体速率为 48k×128=6.144M，通过使能信号进行采样率的变换。信号输出为流式输出，帧大小为 1 。

第一级低通 FIR 插值滤波器#

%% 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)

输入信号采样率为基带速率，输出信号采样率为基带速率 × 插值因子，通过 fdesign.interpolator 设计滤波器系数，滤波器的幅频响应如下：

第二级低通半带插值滤波器#

%%
% *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; % 通带，由于插值后频谱会根据输入信号的采样率做周期延拓
                                                     % 减去 2 倍的 Fstop 是为了确保插值后保留的信号带宽不会引入混叠，同时保证足够的衰减
 hbParams.StopbandAttenuation = Ast;
 
 hbSpec = fdesign.interpolator(hbParams.InterpolationFactor,'halfband', ...
          'TW,Ast', ...
          hbParams.TransitionWidth, ...
          hbParams.StopbandAttenuation, ...
          hbParams.FsOut);

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

半带滤波器的通带为输入信号采样率减去两倍的截止频率，确保插值后产生的频谱延拓的频带都能被滤除，不会引入混叠，同时保证了足够的衰减。

半带滤波器的幅频响应及两级滤波器级联的响应如下：

第三级 CIC 补偿滤波器#

由于 CIC 插值滤波器通带内不平坦，因此要加入补偿滤波器。

% *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)

补偿滤波器的通带和阻带频率的设置原因如下：

compParams.Fpass = 1/2 * compParams.FsIn + Fpass:
这里的通带频率 Fpass 的设置是基于输入采样率 compParams.FsIn。CIC 滤波器通常对频率响应的衰减从 FsIn/2 开始变得明显，所以补偿滤波器的通带设置为 FsIn/2 + Fpass，这样可以确保补偿滤波器修正 CIC 滤波器在通带内的增益，特别是在高频部分。
compParams.Fstop = 1/2 * compParams.FsIn + 1/4 * compParams.FsIn:
阻带频率的设置为 FsIn/2 + 1/4 * FsIn，其目的是进一步保证在插值之后，信号频谱的带外部分能够被足够衰减，防止混叠现象的发生。由于插值过程会把输入信号的频谱周期性延拓，滤波器的阻带需要覆盖到这些延拓部分，以保证无用信号被滤除。

补偿滤波器的幅频响应图如下：

第四级 CIC 插值滤波器#

%%
% *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)