# PAM signal with a cosine input

1. May 10, 2012

### 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 in to 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?

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