A Fascinating Case of Signal Sampling: Calculating Sample Numbers 703 to 709

Understanding Sampling Rate:

Sampling rate is the number of samples obtained in one second. In this case, the sampling rate is 1.3 times the Nyquist rate, where the Nyquist rate is double the highest frequency present in the signal. By sampling at a rate higher than the Nyquist rate, we ensure accurate representation of the signal.

Calculating Time Period of Signal:

Time period of a signal can be determined using the formula 2π/f, where f represents the frequency of the signal. For the given signal, the frequencies are 10,000 Hz and 15,000 Hz. Thus, the time periods are calculated as 2π/10,000 seconds and 2π/15,000 seconds respectively.

Determining Sampling Interval:

The sampling interval is 1/1.3 times the time period of the signal in this scenario. Once the sampling interval is obtained, we can proceed to calculate the values of the signal at sample numbers 703 to 709 using the cosine and sine functions.

Applying Cosine and Sine Functions:

With the sampling interval and signal frequencies known, we can confirm the values of the sample numbers by plugging the values into the equations for cosine and sine functions. These mathematical functions help us determine the precise values of the signal at various sample points.

By understanding the sampling process and applying the appropriate mathematical calculations, we can accurately calculate the values of sample numbers 703 to 709 for the given signal sampling scenario. This detailed analysis ensures a thorough understanding of signal sampling procedures.

For further insights into the concepts of Sampling of signals, you can refer to additional resources and explanations available online.