We will study three sine waves and a signal which is composed of all of them: z(

Question

We will study three sine waves and a signal which is composed of all of them: z(t) where A, is the amplitude, f is the sampling frequency and oi is the phase for component i 1, 2, 3. Here, we are only concerned with the frequencies of the sine waves so we let the amplitudes be Ai 1 and phases be oi 30. The signal z(t) is continuous and we sample it using fs 1/T. sampling frequency, so that we have, for each component: zi(t) sin(2T Let the sampling frequency be f, 38000 Hz and let fi 3300 Hz, f2 730 Hz og f3 1500 Hz. Examine the signals for n e 400) 1. Draw ziln], 22 n og zalal using stem. Use subplot and compare the components. Does the frequency increase? 2. Listen to the sine wave by using soundsc. Does the tone become higher? 3. Draw rin on a separate plot and listen to it. Can you distinguish the frequencies? 4. Repeat 1-3 using fi 2500 Hz, fe 3500 Hz and fo 5500 Hz. Does the frequency increase? Does the tone become higher? 5. What is the Nyquist frequency if the sampling frequency is 8000 Hz

Explanation / Answer

The Nyquist freqis the highest frequency that can be coded at a given sampling rate in order to be able to fully reconstruct the signal, i.e.,
Fnyst = 1/2 x V = 0.5 x 8000 = 4000 Hz nyquist frequency .....

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