UPD EEE 113 Communications Online Quiz on Channel-Sharing (2025-2026 First Semester)

This worksheet is an unlimited-attempt review material that features channel effects. Below, there is a combination of multiple-choice, true-or-false, and cloze items. This page is interactive, and no data will be uploaded when answering this page.

Questions

1. Consider a linear time invariant channel with amplitude response $S(f)=\frac{0.2}{\sqrt{1.64-<!----->1.6cos(2\mathrm{\pi <!--\pi -->}f)}}$. Suppose that the channel input has the form $x(n)=3.7cos(2\mathrm{\pi <!--\pi -->}0.02n)$ for all $n$ from −∞ to +∞. The channel output can be written as $y(n)=Acos(2\mathrm{\pi <!--\pi -->}0.04n+\mathrm{\varphi <!--\varphi -->})$ where $-\mathrm{\pi <!--\pi -->}\le \varphi \le \mathrm{\pi <!--\pi -->}$. What is the numerical value of A? Please provide your answer in at least 3 significant figures.
2. Which of the following statements is/are true:
• Lossy compression reduces the effects of bit errors.
• Channel coding reduces the number of bits required to transmit a signal.
• The proper choice of a source coding algorithm depends upon the properties of what is to be encoded.
• Source coding is also known as compression.
3. Consider the following discrete time signal with 100 samples.

   

   Which of the plots below shows the corresponding Fourier series amplitude spectrum? Hint: Count the number of cycles over samples (e.g. count how many big oscillations you see, corresponding to a low frequency component).

   

4. 

   Recall that for a discrete-time sinusoid, the normalized frequency, f, is the ratio of the number of cycles over the number of samples. In the plot above, what is the normalized frequency expressed in decimal?
5. Suppose a 105 Hz cosine wave modulates a 0.8 kHz cosinusoidal carrier signal. The resulting signal consists of two cosines with frequencies ____ Hz and ____ Hz.
   • 695, 1010
   • 0.70, 0.91
   • 695, 905
   • 0.59, 1.01
   • 590, 905
   • 590, 1010
6. Suppose that a signal $cos(2\mathrm{\pi <!--\pi -->}17t)$ modulates a cosinusoidal carrier $cos(2\mathrm{\pi <!--\pi -->}236t)$, and then mixed with another cosine at the same carrier frequency, i.e. $y(t)=cos(2\mathrm{\pi <!--\pi -->}17t)\cdot cos(2\mathrm{\pi <!--\pi -->}236t)\cdot cos(2\mathrm{\pi <!--\pi -->}236t)$ . Which of the following is an equivalent expression for y(t)?
   • 0.25cos⁡(2π489t) + 0.25cos⁡(2π455t) + 0.5cos⁡(2π219t) + 0.5cos⁡(2π253t)
   • 0.25cos⁡(2π253t) + 0.25cos⁡(2π219t)
   • 0.25cos⁡(2π489t) + 0.25cos⁡(2π455t) + 0.5cos⁡(2π17t)
   • 0.25cos⁡(2π253t) + 0.25cos⁡(2π219t) + 0.5cos⁡(2π236t)
   • 0.25cos⁡(2π489t) + 0.25cos⁡(2π455t)
7. Suppose that a modulated signal x(t) is created by taking a baseband signal and mixing it with a 250 Hz cosine signal, resulting in the passband spectrum X(f) shown below. Suppose that the modulated signal x(t) is mixed with a 200 Hz cosine signal c(t). The spectrum of the 200 Hz cosine is shown below as C(f).

   

   Which of the spectra below is the spectrum of the after mixing x(t) and c(t)?

   

8. Consider a received signal containing two baseband signals modulating two different carriers so that they occupy non-overlapping regions of the spectrum. One of the baseband signals has a rectangular spectrum, and the other has a triangular spectrum. The spectrum of the received signal, Y(f), is shown below. The desired signal is demodulated by first mixing the received signal with a cosine with frequency 110kHz. Which of the following is the bandwidth of an ideal low pass filter that will isolate the desired baseband signal only?
1. 85 kHz
2. 25 kHz
3. 15 kHz
4. 55 kHz
9. Consider the two signals whose Fourier Series Spectrum as shown below. Assume that the units of frequency are kiloHertz (kHz).

   

   What is the Fourier Series Spectrum of the product of these two signals?

   

10. Suppose a 120Hz cosine wave modulates a 1kHz co-sinusoidal carrier signal. The resulting signal consists of two cosines with frequencies 880 Hz and Hz.

Markscheme

1. 0.797
2. “Source coding is also known as compression” and “The proper choice of a source coding algorithm depends upon the properties of what is to be encoded”
4. 0.1
5. 695, 905
6. 0.25cos⁡(2π489t) + 0.25cos⁡(2π455t) + 0.5cos⁡(2π17t)
7. B
8. B
9. D
10. 1120