How to Sketch the Spectrum of a PAM Signal with a Cosine Input?

[zak8000]

sketch the spectrum of the PAM signal S(f) if the input is m(t)=cos(2*pi*fm*t) where fm=3000 at a sampling rate of 10000 using rectangular pulses of duration 0.04ms. in the range +-15Khz

S(f)=H(f)*M'(f)

taking the Fourier transform of the rectangular pulse we obtain: H(f)=Tsinc(Tf) where T=0.04ms

and M'(f)= ∫(m(t)*p(t))exp(-i2∏ft)

but p(t) is periodic and so we can use Fourier transform to obtain: fsƩexp(i2∏fskt)

fourier transform of M(f) from m(t) is: M(f)=∫(m(t))exp(-i2∏ft)=0.5[δ(f-fm)+δ(f+fm)]

so all together S(f)=M'(f)H(f)=fsT0.5sinc(fT)Ʃ[δ(f-fm-kfs)+δ(f+fm-kfs)]

subbing values into get: 0.2sinc(0.04e-3f)Ʃ[δ(f-3000-10000k)+δ(f+3000-10000k)]

but how do i plot the frequency spectrum i know that delta functions have infinite amplitude and i am not sure how show the magnitude and frequency components between +-15Khz any help please?

 

[Valkarie]

This is a good question. The answer depends on what type of plot you would like to make. If you are looking to make a frequency spectrum plot, then you can use the Fourier transform of the signal to determine the magnitude and phase at each frequency. You can then use this information to create a graph that shows the magnitude and phase of the signal at each frequency. Additionally, you can use tools such as MATLAB or Python to generate a more detailed plot.