To understand the most basic things of complex functions, such as some basic operations of complex numbers, you should grasp an idea of signal system: in order to get a response when a signal passes through a linear time-invariant system, firstly, the input signal is expressed as a linear combination of basic signals according to its linear properties and time invariance. If you know the response of the basic signal, then the response of the system is a linear combination of the basic signal responses.

In essence, convolution represents a signal as a weighted sum (integral) of shift pulses, and its basic signal is a unit pulse.

Fourier transform represents the signal as a linear combination of a set of complex exponents, and its basic signal is the complex exponential signal e^jwt.

In fact, convolution did not lay a foundation for the subsequent study of Fourier transform. Their essence is the same, and they are all ideas of signal decomposition. What you need to understand deeply here are two formulas of Fourier transform and convolution formula. You should always think about the dynamic process of convolution in your mind, which means the physical meaning, not the three-step convolution algorithm.

In fact, whether this course is good or not depends on whether you really know convolution. If you don't understand, then you only know how to calculate Fourier transform, but you can't understand its essence. So spend more time on convolution, don't immerse yourself in mathematical deduction, and think about intuitive physical meaning. Although the theory is not rigorous, it is still very useful for deep understanding.