Основы цифровой обработки сигналов

ОтношениеЧастот = 0 # @param {type:"slider",min:0,max:2,step:0.1}
Фаза = 0 # @param {type:"slider",min:0,max:360,step:5}
Синусоида = false # @param {type:"boolean"}
            
n = 0:25;
freq = ОтношениеЧастот / 2;
phase = Фаза*pi/180;
timeSignalFreq = ones(length(n));
timeSignalFreq = cos.(0.5.*n .- phase);

if Синусоида
    probeSignal = cos.(freq.*n) + sin.(freq.*n)*im;
else
    probeSignal = cos.(freq.*n);
end

product = timeSignalFreq .* probeSignal;
productSum = sum(product);

p1 = plot(n,timeSignalFreq,lc=:black,la=0.35,m=:c,mc=:black,msc=:black,ma=0.35,ms=5);
    if Синусоида
        p1 = scatter!(n,real(probeSignal),mc=:red,msc=:red,ma=0.65,ms=3)
        p1 = scatter!(n,imag(probeSignal),mc=:blue,msc=:blue,ma=0.65,ms=3)
    else
        p1 = scatter!(n,probeSignal,mc=:red,ma=0.75,ms=3)
    end
p1 = hline!([0], lc=:black, la=0.5, ls=:dash, lw=2);

p2 = plot(n,real(product),l=:stem,lw=12,lc=:red,la=0.5,ylim=(-1.1,1.1));
    if Синусоида
        p2 = plot!(n,imag(product),l=:stem,lw=12,lc=:blue,la=0.5);
    end

p2 = hline!([0], lc=:black, la=0.5, ls=:dash, lw=2);
    
w = 0:0.01:1;
fullSummation = zeros(length(w)) + zeros(length(w))*im;
for idx = 1:length(w)
    tempProbe = cos.(w[idx].*n) + sin.(w[idx].*n)*im;
    tempProduct = tempProbe .* timeSignalFreq;
    fullSummation[idx] = sum(tempProduct);
end

p3 = plot(w*2,real(fullSummation), lc=:red, la=0.5, lw=1.5);
if Синусоида  
    p3 = plot!(w*2,imag(fullSummation), lc=:blue, la=0.5, lw=1.5);
end
p3 = scatter!([ОтношениеЧастот], [real(productSum)], ms=5, mc=:red, ma=0.5, lw=2);
if Синусоида
    p3 = scatter!([ОтношениеЧастот], [imag(productSum)], ms=5, mc=:blue, ma=0.5);
end
p3 = hline!([0], lc=:black, la=0.5, ls=:dash, lw=2);

l = @layout [a; b; c]
plot(p1, p2, p3; layout = l, legend = false, size=(800,400))

k = 0 # @param {type:"slider",min:0,max:10,step:1}
Фаза = 0 # @param {type:"slider",min:0,max:360,step:5}
DC = false # @param {type:"boolean"}
Гармоника = false # @param {type:"boolean"}
fs = 11;            # Частота дискретизации
T = 1/fs;             # Период дискретизации
N = 11;
t = (0:N-1).*T;      
phase = Фаза*pi/180;
timeSignal = cos.(2*pi*t .+ phase) .+ DC/3 + (Гармоника/3).*cos.(6*pi*t .+ phase);

# Сигналы для "сравнения"
n = 0:N-1;
ndense = (0:10*N-1)/10;
psdense = exp.(-2*pi*im/N.*ndense*k);
probeSig = exp.(-2*pi*im/N.*n*k);
probeSignalMatrix = exp.(-2*pi*im/N.*n.*transpose(0:10));
productMatrix = timeSignal .* probeSignalMatrix;
productSumVector = vec(sum(productMatrix, dims = 1));

# Верхний график
p1 = scatter(n,timeSignal,mc=:black,ma=0.35,ms=8, xlim = (-1,11), ylim = (-1.5, 1.5));
p1 = plot!(n,timeSignal,lc=:black,la=0.25,lw=3);
p1 = scatter!(n,real(probeSig),mc=:red,ma=0.45,ms=5)
p1 = plot!(ndense,real(psdense),lc=:red,la=0.25,lw=2)
p1 = scatter!(n,imag(probeSig),mc=:blue,ma=0.45,ms=5)
p1 = plot!(ndense,imag(psdense),lc=:blue,la=0.25,lw=2)

# Нижний график
if k > 0
    p2 = plot(0:k,imag.(productSumVector[1:k+1]), l=:stem, lw=6, m=:c, ms = 6, leg=false, xlim=(-1,11),ylim = (-6, 6))
    p2 = plot!(0:k,real.(productSumVector[1:k+1]), l=:stem, lw=6, m=:c, ms = 6, leg=false)
else
    p2 = plot([0],[real.(productSumVector[1])], l=:stem, lc=:red, la=0.5; lw=6, m=:c, ms = 6, mc=:red, ma=0.5, leg=false, xlim=(-1,11),ylim = (-6, 6))
end

l = @layout [a; b]
plot(p1, p2; layout = l, legend = false, size=(800,400))

complexnumber = productSumVector[2]

abs(complexnumber)

180*angle(complexnumber)/pi

plot(0:10,abs.(productSumVector) .* (2/N), l=:stem, lw=6, m=:c, ms = 6, leg=false, xlim=(-1,11))

plot(0:10, (180/pi) .* angle.(productSumVector), l=:stem, lw=6, m=:c, ms = 6, leg=false, xlim=(-1,11), ylim=(-200,200))