Hi Anuja,
I understand that you are asking for the bandwidth of a signal with a message frequency of 3 kHz, given a sampling frequency of 20 kHz.
I assume you are referring to the bandwidth of a simple sinusoidal message signal and not considering additional modulation or filtering effects.
In order to determine the bandwidth of the signal, you can follow the below steps:
Identify the Message Frequency:
The message frequency is given as 3 kHz. For a sinusoidal signal, the bandwidth is typically twice the message frequency.
Calculate the Bandwidth:
Since a sinusoidal signal has energy at only one frequency, its bandwidth is effectively zero. However, if we consider a more practical signal with harmonics, the bandwidth would be considered around the fundamental frequency.
For a basic sinusoidal message signal, the bandwidth is 0 Hz, but if harmonics are considered, it would be approximately 6 kHz (twice the fundamental frequency).
Consider the Sampling Frequency:
The sampling frequency of 20 kHz is relevant for ensuring that the signal is sampled adequately according to the Nyquist theorem, which requires the sampling frequency to be at least twice the highest frequency component of the signal.
Example:
If you were to generate a sampled version of this signal in MATLAB, ensure your sampling frequency is adequate to capture the signal without aliasing.
fs = 20000; % Sampling frequency in Hz
fm = 3000; % Message frequency in Hz
t = 0:1/fs:1; % Time vector
messageSignal = cos(2*pi*fm*t); % Sinusoidal message signal
Conclusion:
For a pure sinusoidal signal, the effective bandwidth is zero. However, if harmonics or sidebands are considered, the bandwidth would be approximately 6 kHz.
Refer to the documentation of "cos" function for more information: https://www.mathworks.com/help/matlab/ref/cos.html
Hope this helps!
