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

In summary: Overall, the spectrum of the PAM signal S(f) would consist of a series of peaks at frequencies of +/- 3000 Hz, with a sinc-shaped envelope that decays as the frequency increases. In summary, the spectrum of the PAM signal S(f) with an input of 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 would consist of a series of peaks at frequencies of +/- 3000 Hz with a sinc-shaped envelope. The magnitude and phase at each frequency can be determined through the Fourier transform of the signal and can be plotted using various tools such as MATLAB or Python.
  • #1
zak8000
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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?
 
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  • #2
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.
 

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

1. What is a PAM signal with a cosine input?

A PAM (Pulse Amplitude Modulation) signal with a cosine input is a type of digital modulation technique that uses a pulse waveform with varying amplitude to transmit information. The input signal is a cosine function, which is used to modulate the amplitude of the pulse signal.

2. How does a PAM signal with a cosine input work?

In a PAM signal with a cosine input, the cosine function is used to modulate the amplitude of the pulse signal. This means that the amplitude of the pulse signal varies according to the values of the cosine function. This modulation allows for the transmission of digital data through the pulse signal.

3. What are the advantages of using a PAM signal with a cosine input?

One advantage of using a PAM signal with a cosine input is that it is less susceptible to noise and interference compared to other modulation techniques. The use of a cosine function also allows for efficient use of bandwidth, making it suitable for digital data transmission.

4. What are the applications of PAM signal with a cosine input?

PAM signals with a cosine input are commonly used in telecommunications, particularly in digital communication systems. They are also used in data communication, such as in Ethernet networks, and in various digital audio and video systems.

5. How is a PAM signal with a cosine input different from other PAM signals?

A PAM signal with a cosine input differs from other PAM signals in terms of the input signal used for modulation. While other PAM signals may use a square or triangular input, a PAM signal with a cosine input uses a cosine function. This can result in different performance characteristics and applications for each type of PAM signal.

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