Summary

The sampling theorem has several important implications, including aliasing and spectrum replication. These, along with other key aspects of sampling, will be explored in greater detail in later chapters.

At this stage, I want to keep things simple and focus on understanding the Fourier Transform. For now, we will assume that we are dealing with periodic frequencies where the period is an exact multiple of the sampling interval.

Additionally, we will assume that the actual frequency is the lowest possible frequency that matches the observations (\(f_0\)). In later chapters, we will explore two methods for treating aliasing.