3 Time vs. FrequencyDomain
Electrical signals  periodic or nonperiodic  can be measured in the time domain (e.g. with an oscilloscope) or in the frequency domain (e.g. with a spectrum analyzer). This means that an electrical signal can be described either in the timedomain or in the frequencydomain. The timedomain representation helps you to determine the signal integrity (ringing, reflections), whereas the frequency domain representation helps you to determine at which frequencies a signal may lead to radiated emissions.
Fourier Analysis.
Fourier analysis is an integral transform and refers to the mathematical principle that every signal can be represented by the sum of simple trigonometric functions (sine, cosine, etc.). The Fourier analysis enables a transformation of a signal in the time domain x(t) to a signal in the frequency domain X(ω), where ω=2𝝅f (notation: x(t)○─●X(ω)). In other words, a Fourier analysis is a mathematical operation for calculating the frequencydomain representation (frequency spectrum) of a signal in the timedomain.
The picture below shows a representation of a square wave signal (1V amplitude) with the sum of only 4 harmonic sine waves and a direct current (DC) component of 0.5V. For the representation of an ideal square wave, an indefinite number of sine waves would be necessary (because the rise and falltime of an ideal square wave is 0sec).
The different variants of integral transforms are presented in the list below. All variants have in common that they present the necessary math for converting a signal from the time to the frequencydomain and vice versa: X(ω)●─○x(t). Every integral transform variant has its own field of application.

Fourier series. Time signal = continuous, periodic. Frequency spectrum = discrete. Formulas for the calculation of the complex Fourier coefficients cn of a signal x(t) are presented below [3.1]:
T is the period length of the signal x(t) in [sec], f0 is the first harmonic of the signal x(t) in [Hz], ω0 is the first harmonic of the signal x(t) in [rad], j=√(1) is the complex number and n stands for the nth harmonic frequency [0, 1, 2, ...].

Fourier transform. Time signal = continuous, nonperiodic. Frequency spectrum = continuous. Formulas of the Fourier transform of a signal x(t) (left) and the inverseFourier transform (right) are given below [3.2]:
X(ω) is the Fourier transform (spectrum) of x(t), ω is the frequency in [rad], j=√(1) is the complex number and t the time in [sec].

Discrete Fourier transform (DFT). Time signal = discrete, periodic. Frequency spectrum = discrete. The DFT is also applied to nonperiodic signals in the time domain by periodically continuing the nonperiodic signals in order to make them computable with the DFT. The DFT is by far the most common method of modern Fourier analysis. The Fast Fourier Transformation (FFT) is a fast algorithm for calculating the DFT (in case the bock length N is a power of two) [3.3].
X is the spectrum of x and X[k] is the kth sample of the spectrum at ωk. x[n] is the nth sample of the discrete time signal, which is sampled with the sampling time Ts [sec] and the sampling frequency fs [Hz].

Discretetime Fourier transform (DTFT). Time signal = discrete, nonperiodic. Frequency spectrum = continuous. The DTFT can be viewed as the form of the DFT when its length N approaches infinity [3.4].
X is the spectrum of x. x[n] is the nth sample of the discrete time signal, which is sampled with the sampling time Ts [sec] and the sampling frequency fs [Hz]. ῶ denotes the continuous normalized radian frequency variable [π...+π]. ῶ is the product of the radian frequency ω [rad] and the sampling time Ts.

Laplace transform. The Laplace transformation belongs  like the Fourier analyses  to the group of integral transformations. It is mentioned here for the sake of completeness. The Laplace transform is used for system analysis (e.g. control systems, filters), whereas the Fourier transform is used for signal analysis [3.5].
X is the Laplace transform of x. s=σ+jω is a complex variable with a real part σ and a imaginary part with the radian frequency ω [rad]. In case of σ=0, the Laplace transform reduces to the Fourier transform.

Ztransform. The Ztransform is the timediscrete counterpart to the Laplace transform with z = e^(sTsampling) = e^((σ+jω)Tsampling) [3.6].
X is the Ztransform of x. z is a complex variable. x[n] is the nth sample of the discrete time signal, which is sampled with the sampling time Ts [sec] and the sampling frequency fs [Hz].
Spectra of digital waveforms.
Waveforms of primary importance in electronic circuits are clock and data signals. Digital signals in the time domain can be represented by trapezoidshaped pulses with a period time T [sec], a pulse width tpw [sec], a risetime tr [sec] and a falltime tf [sec]. The two pictures below show an extract of a digital waveform in the timedomain and an amplitude frequency spectrum of a digital signal with its envelope curve [3.7].
The frequency spectrum envelope of a trapezoidwaveform signal compared to an ideal square wave signal is shown below. It can be seen, that there is no 40dB dropoff for the ideal square wave. Instead, the frequency spectrum envelope of an ideal square wave drops constantly with 20dB/decade.
The picture below compares the frequency spectrum of two trapezoid waveforms with different pulsewidth tpw [sec], but with identical periodicity T [sec], rise and falltime tr [sec] and tf [sec] and amplitude A [V]. It can be seen how the dutycycle D=tpw/T [%] of a digital signal influences the frequency spectrum. However, it is remarkable that a clock signal with a 90% dutycycle has a lower amplitude of the first harmonic than a clock signal with a 50% dutycycle (of the same frequency [Hz] and with the same rise/falltime [sec]). The clock signal with a 90% dutycycle has more power, but this power adds to the DC component (0 Hz).
The picture below compares the frequency spectrum of two trapezoid waveforms with different rise and falltime tr [sec] and tf [sec], but with identical periodicity T [sec], pulsewidth tpw [sec] and amplitude A [V]. It can be seen that a reduction of the rise and falltime leads to lower amplitudes at the higher frequencies in the spectrum (and therefore to potentially lower radiated emissions). In this example, an increase of the rise and falltime [sec] by factor 10, reduces the amplitude of the highfrequency harmonics ( f > 32MHz) also by factor 10 (20 dB).
Bandwidth of digital signals.
Bandwidth [Hz] of a digital signal means: What is the highest significant sinewave frequency component in the digital signal? Significant in this case means that the power [W] in the frequency component is bigger than 50% of the power in an ideal square wave's signal with the same amplitude A [V] and dutycycle D=tpw/T [%]. A drop in 50% of the power [W] is the same as a drop of 70% in amplitude [V] or a drop of 3dB.
The rule of thumb for calculating the bandwidth [Hz]  or the highest significant sine wave frequency  of a trapezoid digital signal is [3.8]:
Where t10%90% is the rising or falltime (whichever is smaller) from 10% to 90% of the slope of a digital signal in [sec].
The picture below shows the frequency spectrum envelop curves of an ideal square wave (t10%90%=0) and a real waveform (trapezoid with t10%90%≠0). The bandwidth of the real waveform can be found at f=0.35/t10%90%. Note: It is assumed that there is no ringing in the real waveform. In case of ringing, the frequency spectrum envelope for f>1/(πt10%90%) would not drop off with 40dB/decade.
References:
[3.2] Clayton R. Paul. Introduction to electromagnetic compatibility. John Wiley & Sons Inc., 2nd Edition, 2008, pp. 148149
[3.4] Stanford University, Center for Computer Research in Music and Acoustics (CCRMA), Julius O. Smith III. Discrete Time Fourier Transform (DTFT). [23.Dec.2020]
[3.6] Stanford University, Center for Computer Research in Music and Acoustics (CCRMA), Julius O. Smith III. Z Transform. [23.Dec.2020]
[3.7] Clayton R. Paul. Introduction to electromagnetic compatibility. John Wiley & Sons Inc., 2nd Edition, 2008, pp. 122132
[3.8] Eric Bogatin. Signal and Power Integrity  Simplified. Prentice Hall Signal Integrity Library, 3rd Edition, 2018, p.7277