A more intuitive understanding of music is this:

Figure 1 shows how music looks in time domain, and Figure 2 shows how music looks in frequency domain.

Frequency is, if the horizontal axis is frequency and the vertical axis is amplitude, the frequency domain image is

Sinusoidal function is a single frequency, which is represented by only one vertical line in frequency domain. What we expect is to convert the time domain signal into a single frequency sine function combination, so that it can be represented by vertical lines in the frequency domain to complete the conversion from time domain to frequency domain.

If any waveform can be transformed into a linear combination of a constant and several sine and cosine functions, we can complete the transformation from time domain to frequency domain. Expressed by mathematical formula as follows:

So the question becomes, for any waveform, can we find a set of coefficients to make the above equation hold?

In the paper published in 1807, the French mathematician Fourier put forward a controversial conclusion at that time: any continuous periodic signal can be composed of a set of appropriate sinusoids.

With the increase of frequency, the synthesized waveform is closer to square wave. When n approaches infinity, that is, the spectrum range is infinite, it can approach a square wave infinitely.

From the perspective of frequency domain

For those who do image processing, each digital image is a set of signals, which means that image processing is equivalent to signal processing. Because the signal has frequency domain characteristics and time domain characteristics, the channel connecting time domain and frequency domain is Fourier transform.

Analysis of image frequency characteristics

Each pixel on the spectrum represents a frequency value, and the amplitude is obtained by encoding the brightness of the pixel. For images, the frequency characteristics of image signals are as follows:

Note: Low-pass filtering here refers to leaving low-frequency waves and filtering out high-frequency waves. The schematic diagram is a centered spectrum, that is, from the center of the spectrum to the surrounding frequencies from low to high. The schematic diagram shows that the middle and low frequencies and high frequencies around the center of the filter point are left behind. We know that the low frequency corresponds to the part of the image that does not change obviously, so the image becomes very blurred. This is also called smoothing filtering in image processing.

Compared with smoothing, the effect of sharpening the image is obviously to enhance the edge of the image.