Engineering Sketch the spectrum of the DSB-SC signal

AI Thread Summary
The discussion centers on the frequency spectrum of a DSB-SC signal, with participants confirming and correcting calculations. A potential typo was identified, suggesting that the frequency should be 5000 instead of 500 in the equation for S(f). Clarifications were made regarding the absence of carrier power in the DSB-SC spectrum, emphasizing that only sidebands exist at frequencies above and below the carrier. The mathematical relationship between the modulated signal and its spectrum was highlighted, reinforcing the understanding of DSB-SC characteristics. Overall, the conversation focuses on ensuring accuracy in the frequency representation of the DSB-SC signal.
Fatima Hasan
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Homework Statement
Attached below.
Relevant Equations
cos(t) <--> 1/2 [δ (f-fc) + δ(f+fc) ]
Here's my work:

5k%29%20+%5Cdelta%20%28f-5.5k%29+%20%5Cdelta%28f+5.gif


1615761629365.png


Could someone please confirm my answer?
 

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Fatima Hasan said:
Could someone please confirm my answer?

I think the frequency spectrum is correct. However, I think there is perhaps a little typo in the working - it doesn't change the final answer though.

Fatima Hasan said:

I think the line ## S(f) = \frac{1}{2} ( M(f - 500) + M(f + 500) ) ## should instead have ## 5000 ## in the brackets rather than 500 right? We are convolving ## M(f) ## with ## \frac{1}{2}(\delta(f - 5000) + \delta(f + 5000)) ## which would lead to:

S(f) = \frac{1}{2} ( M(f - 5000) + M(f + 5000) )
Then we substitute ## M(f) = \frac{1}{2}(\delta(f - 500) + \delta(f + 500)) ## for the first part which should lead to the same final expression that you have.
 
Fatima Hasan said:
Homework Statement:: Attached below.
Relevant Equations:: cos(t) <--> 1/2 [δ (f-fc) + δ(f+fc) ]

Here's my work:

View attachment 279784

View attachment 279782

Could someone please confirm my answer?
Can't read your notes but it looks like your S(f) is the carrier in the frequency spectrum.

"DSB-SC" has no carrier power in the spectrum.
The sidebands are above and below the carrier frequency.
If you multiply a signal ## sin(\omega_st ## by the carrier ## sin(\omega_ct ## you get DSB-SC spectrum as high school trig will reveal. Sidebands at ## (\omega_c + \omega_s) ## and ##\omega_c - \omega_s ##.
 
rude man said:
Can't read your notes but it looks like your S(f) is the carrier in the frequency spectrum.

"DSB-SC" has no carrier power in the spectrum.
The sidebands are above and below the carrier frequency.
If you multiply a signal ## sin(\omega_st ## by the carrier ## sin(\omega_ct ## you get DSB-SC spectrum as high school trig will reveal. Sidebands at ## (\omega_c + \omega_s) ## and ##\omega_c - \omega_s ##.
Sorry, I don't quite understand. From the image in the picture, it looks as if there are only the two side bands present (and the -ve frequency versions as well)...
 

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