Sketch the spectrum of the DSB-SC signal

[Fatima Hasan]

Homework Statement

Attached below.

Relevant Equations

cos(t) <--> 1/2 [δ (f-fc) + δ(f+fc) ]

Here's my work:

Could someone please confirm my answer?

 

[Master1022]

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.

View attachment 279784

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.

 

[rude man]

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 $\omega_c - \omega_s$.

 

[Master1022]

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)...