Why the amplitude of the final pulses are different from the input pulse?
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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:
f=0.375; %centre frequency
w0=2*pi*f; %centre frequency in rad/s
F=(-500000:500000)/((1000001)*0.0001); %frequency scale
t1=Ts*(-(m)/2:(m-1)/2); %time scale after IFFT
y=exp(-((t-t0)/T).^2).*cos(1*w0*(t)); %Input pulse (It is giving smaller amplitude)
M_w=exp(1i*(alpha*(w-w_ref))); %linear mask
Ew=Y.*M_w; %Modulated spectrum
Et=ifft(ifftshift(Ew1)); %Shaped pulse
title('Temporal profile of the Shaped Pulse')
title('Spectral Phase of the shaped pulse')
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!
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Gokul Nath S J 2022년 10월 17일
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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