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Why the amplitude of the final pulses are different from the input pulse?

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SUBHO MITRA
SUBHO MITRA 2021년 1월 4일
댓글: SUBHO MITRA 2022년 11월 3일
I have a gaussian pulse in time. I want to shift it in time. So I am putting the linear spectral phase modulation to it. But the amplitude is different from the input pulse while I take the input as Cos(wt) and Exp(iwt). please give some suggestions.
Codes are following:
t=-50:0.0001:50;
f=0.375; %centre frequency
w0=2*pi*f; %centre frequency in rad/s
t0=0;
alpha=17
T=5;
F=(-500000:500000)/((1000001)*0.0001); %frequency scale
w=2*pi*F;
m=length(w);
d=mean(diff(w));
Fs=(w(2)-w(1))*m/(2*pi);
Ts=1/Fs;
t1=Ts*(-(m)/2:(m-1)/2); %time scale after IFFT
w_ref=2*pi*0.375;
y=exp(-((t-t0)/T).^2).*cos(1*w0*(t)); %Input pulse (It is giving smaller amplitude)
% OR
%y=exp(-((t-t0)/T).^2).*exp(i*w0*(t));
y0=0.1*cos(w0*t);
Y=(fft((y)));
Y1=fftshift(Y);
M_w=exp(1i*(alpha*(w-w_ref))); %linear mask
Ew=Y.*M_w; %Modulated spectrum
Ew1=Y1.*M_w;
Et=ifft(ifftshift(Ew1)); %Shaped pulse
I=(Et).^2;
P=angle(Ew1);
P=unwrap(P); %Phase
subplot(2,2,1)
plot(t,(y))
%xlim([-0.5 4])
title('Input Pulse')
xlabel('Time')
ylabel('Intensity')
axis square
grid on
subplot(2,2,2)
yyaxis left
plot(F,abs(Ew1))
yyaxis right
plot(F,P)
xlim([0.35 0.45])
title('Modulated Spectrum')
xlabel('Frequency')
ylabel('Intensity')
axis square
grid on
subplot(2,2,3)
plot(t1,(real(Et)))
ylim([-1.1 1.1])
hold all
plot(t1,y0)
title('Temporal profile of the Shaped Pulse')
xlabel('Time')
ylabel('Intensity')
axis square
grid on
subplot(2,2,4)
plot(F,(P))
%xlim([0 50])
title('Spectral Phase of the shaped pulse')
xlabel('Freq')
ylabel('Phase')
axis square
grid on
Here you can see that the Input y as Cosine function gives smaller amplitude after appling the mask function M_w than the input y as Exp function. I want to know is it like that? pls help!

답변 (1개)

Gokul Nath S J
Gokul Nath S J 2022년 10월 17일
Dear Subho,
The amplitudes of the function won’t be same. This can be verified mathematically by expanding cosine in terms of its complex exponential. This will give you a factor of 2 in the denominator.
Moreover, as mentioned in question multiplying with a complex exponential will shift the signal. However, the amplitude scaling occurs if multiplied with a cosine or sine.

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