Question

Sample F(t)= sin(at)+sin(bt) at different sampling rate, perform FFT on the sampled data, and determine the frequency of F(t).

Answer 1

To determine the frequency of F(t) = sin(at) + sin(bt) at different sampling rates, perform FFT on the sampled data and identify the frequency component in the resulting spectrum.

Step-by-step explanation:

The beat frequency can be determined by adding two waves mathematically. In this case, we have two sine waves, F(t) = sin(at) + sin(bt). By sampling the data at different rates and performing the Fast Fourier Transform (FFT), we can determine the frequency of F(t).

Here are the steps to determine the frequency:

1. Choose appropriate values for a and b, which represent the frequencies of the sinusoidal waves.
2. Sample the data at different rates, ensuring the sampling rate is greater than twice the highest frequency present in F(t) as per the Nyquist-Shannon sampling theorem.
3. Perform the FFT on the sampled data to obtain the frequency spectrum.
4. Identify the frequency component in the spectrum that corresponds to the frequency of F(t).