FM调制是是恒包络调制，基本没有峰均比，PA利用率高，相对于幅度调制有更好的抗干扰性能，缺点是带宽利用率低。
FM调制
FM调制信号表示如下，其实质是差分频率调制，即该sample的频率是前一个sample的频率加上调制信号变化量，具体表现为每个sample相位的变化。
假设|x(t)| ≤ 1，则fd是相对于中心频点的最大频偏。当x(t)恒等于1时，等效为上变频fd。
FM调制通常会拓展频谱，这是因为频率调制的本质是搬频，占用带宽为最大的搬频距离加上基带带宽，即R+2*fd，其中R为基带信号带宽（符号速率），调制因子dm=fd/fmax，fmax=R/2，|x(t)| ≤ 1
FM解调
FM解调使用差分解调，提取相位变化量。
调制信号大小
根据FM调制原理，t时刻调制的相位为
2*pi*fd*x(t-1)/fs+2*pi*fd*x(t)/fs
其中dt = 1/fs，相位增量为2*pi*fd*x(t)/fs，需要满足在[-pi pi]的范围内，即x(t)*fd/fs的绝对值应小于0.5，否则会造成相位溢出失真。
在保证相位无失真的情况下调整x(t)的增益可直接调整调制信号带宽。
FM实现
FM实现需要框图如下，解调时的fs可以不等于调制时的fs，具体通过延时N来调整，不能让相位溢出
Matlab仿真
频谱仿真
%% Plot Spectrum of FM Modulated Baseband Signal
% Apply FM baseband modulation to BPSK source and plot its
% spectrum.
clear;close all;
% Set the example parameters.
fs = 20e3; % Sample rate (Hz)
ts = 1/fs; % Sample period (s)
Rs = 1e3; % Baseband symbol rate
dm = 1; % FM modulation factor
fd = Rs/2*dm; % Frequency deviation (Hz)
Nup = fs/Rs; % Up-sampling times
%%
% Create a BPSK symbol source having a duration of 1s.
%%
Nsymb = 1*Rs;
symbBpsk = (randi([0 1],Nsymb, 1)-0.5)*2;
%%
% Upsampleing BPSK symbol to fs and shape it by Raised cosine FIR pulse-shaping filter
%%
rrcFilter = rcosdesign(0.25,20,Nup,'norm');
dataRrcIn = upsample(symbBpsk,Nup);
dataRrcTemp = conv(dataRrcIn,rrcFilter);
NtailRrc = floor(length(rrcFilter)/2);
dataRrcOut = dataRrcTemp(NtailRrc+1:end-NtailRrc);
% Scale power, normalise the power of optimum sampling point, the scale
% of FM input signal will directly determine FM bandwidth
xOptSamp = dataRrcOut(1:Nup:end);
plot(xOptSamp,'*');
x = dataRrcOut/mean(abs(xOptSamp));
plot(x,'*');
%%
% Create an FM modulator System object and modulate the input signal.
%%
MOD1 = comm.FMModulator('SampleRate',fs,'FrequencyDeviation',fd);
y = step(MOD1,x);
%%
% Create another modulator object, |MOD2|, whose frequency deviation is
% two times larger and apply FM modulation.
%%
MOD2 = comm.FMModulator('SampleRate',fs,'FrequencyDeviation',2*fd);
z = step(MOD2,x);
%%
% Plot the spectra of the two modulated signals. The larger frequency deviation
% associated with channel 2 results in a noise level that is 10 dB higher.
%%
SA = dsp.SpectrumAnalyzer('SampleRate',fs,'ShowLegend',true);
step(SA,[x y z])
%%
调整信号大小仿真
% FM link
clear;close all;
fb = 1e3;
dm = 1;
fd = Rs/2*dm; % Frequency deviation (Hz)
fs = 8e3;
Nup = fs/fb;
data = (randi([0 1],1000, 1)-0.5)*2; % BPSK
figure;plot(data,'-*');
% 成型滤波器
rrcFilter = rcosdesign(0.25,20,Nup,'norm');
dataRrcIn = upsample(data,Nup);
dataRrcTemp = conv(dataRrcIn,rrcFilter);
NtailRrc = floor(length(rrcFilter)/2);
dataRrcOut = dataRrcTemp(NtailRrc+1:end-NtailRrc);
dataIn = dataRrcOut/mean(abs(dataRrcOut)); % Scale power
% 调制相位需要控制在[-pi pi],否则会造成相位失真，即 dataIn*fd/fs的绝对值不能超过0.5
dataIn = dataIn*fs/fd*0.5;
maxDelta = max(abs(dataIn*fd/fs))
FMMethod = comm.FMModulator('SampleRate',fs,'FrequencyDeviation',fd);
modSymb = step(FMMethod,dataIn);
FMDeMethod = comm.FMDemodulator('SampleRate',fs,'FrequencyDeviation',fd);
demodSymb = step(FMDeMethod,modSymb);
isequal(fi(dataIn,1,13,10),fi(demodSymb,1,13,10))
return
% my function
addTemp = 0;
for i = 1:length(dataIn)
addTemp = dataIn(i)+addTemp;
modPhase(i,1) = 2*pi*fd*addTemp*(1/fs);
end
modSymbOut = exp(1j*modPhase);
dataDemodIn = modSymbOut;
% demod
dataDemodOut(1,1) = angle(dataDemodIn(1))/(2*pi*fd/fs);
Ndelay = 1;
for i = 1:length(dataDemodIn)-Ndelay
deltaPhase = dataDemodIn(i+Ndelay)*conj(dataDemodIn(i));
dataDemodOut(i+1,1) = angle(deltaPhase)/(2*pi*fd/fs);
end
isequal(fi(dataIn,1,13,10),fi(dataDemodOut,1,13,10))
