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For the following code:fs=12.88e3;Ts=1/fs;tlen=7.6;t=0:Ts:tlen − Ts;fmin=0.25e3;fmax=2.6e3;fstep=(fmax − fmin)/length(t);f=fmin:fstep:fmax − fstep;x=sin(2*pi*f.*t);sound(x,fs)plot(t,x)xlabel('time, s')ylabel('amplitude, arbitary units')axis([0 1/fmin*5 − 1 1])What are the minimum number of samples that can be found in any complete cycle of the signal?

Question

For the following code:fs=12.88e3;Ts=1/fs;tlen=7.6;t=0:Ts:tlen − Ts;fmin=0.25e3;fmax=2.6e3;fstep=(fmax − fmin)/length(t);f=fmin:fstep:fmax − fstep;x=sin(2pif.t);sound(x,fs)plot(t,x)xlabel('time, s')ylabel('amplitude, arbitary units')axis([0 1/fmin5 − 1 1])What are the minimum number of samples that can be found in any complete cycle of the signal?

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Solution 1

The code provided is written in MATLAB, a high-level language and interactive environment used by millions of engineers and scientists worldwide. It is used for matrix manipulation, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.

The code generates a sinusoidal signal with a frequency that varies linearly with time, from fmin to fmax. The signal is then played as a sound and plotted.

The minimum number of samples in any complete cycle of the signal can be found by considering the highest frequency of the signal, fmax. According to the Nyquist-Shannon sampling theorem, the sampling frequency must be at least twice the highest frequency of the signal to avoid aliasing. Therefore, the minimum number of samples in any complete cycle at the highest frequency is 2.

However, this is the theoretical minimum. In practice, to accurately represent the signal, you would typically use a much higher sampling rate, resulting in more samples per cycle.

This problem has been solved

Solution 2

The code provided is written in MATLAB, a high-level language and interactive environment used by millions of engineers and scientists worldwide. It is used for matrix manipulation, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.

The code generates a sinusoidal signal with a frequency that varies linearly with time, from fmin to fmax. The signal is then played as a sound and plotted.

The minimum number of samples in any complete cycle of the signal can be found by considering the highest frequency of the signal, fmax. According to the Nyquist-Shannon sampling theorem, the sampling frequency must be at least twice the highest frequency of the signal to avoid aliasing. Therefore, the minimum number of samples in any complete cycle at the highest frequency is 2.

However, this is the theoretical minimum. In practice, to accurately represent the signal, you would typically use a much higher sampling rate, resulting in more samples per cycle.

This problem has been solved

Similar Questions

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