Given the signal [x(n)=sin left(frac{omega_{mathrm{s}}}{10} n ight)+sin left[left(frac{omega_{mathrm{s}}}{10}+frac{omega_{mathrm{s}}}{l} ight) n ight]] then: (a) For (l=100), compute the

Given the signal

\[x(n)=\sin \left(\frac{\omega_{\mathrm{s}}}{10} n\right)+\sin \left[\left(\frac{\omega_{\mathrm{s}}}{10}+\frac{\omega_{\mathrm{s}}}{l}\right) n\right]\]

then:

(a) For \(l=100\), compute the DFT of \(x(n)\) using 64 samples. Can you observe the presence of both sinusoids?

(b) Increase the length of the DFT to 128 samples by padding 64 zeros to the original samples of \(x(n)\). Comment on the results.

(c) Compute the DFT of \(x(n)\) using 128 samples. Can you now observe the presence of both sinusoids?

(d) Increase the length of the DFT of \(x(n)\) by 128 samples by padding 128 zeros to the samples of \(x(n)\). Repeat for a padding of 384 zeros. Comment on the results.