Before understanding how digital data is encoded over a radio spectrum in the form of frames and sub-frames, the fundamentals about how to convey the digital data over an analog waveform needs to be understood.

In this series of digital communication fundamentals - I will resort to prose explanation of the concepts and provide links to detailed explanations already available at various sources in the internet.

A radio wave that is transmitted has the following characteristics

1. It has a wavelength, denoted by lambda (and hence a frequency where f = 1/lambda).

2. It has an amplitude.

3. It has a phase.

Digital information can be carried over the radio waves by altering one or more of the above properties of the carrier wave. Such altering of properties is called modulation.

The fundamental modulations are alterations of one of each of the properties listed above.

1. Frequency Modulation

2. Amplitude Modulation

3. Phase Modulation

In later posts lets look into variations of each of the above modulations like Quadrature Amplitude Modulations (QAM), Phase Shift Keying (PSK which in turn has Binary PSK and Quadrature PSK).

When talking about modulating digital data over a sinusoidal wave we talk about frequency domain and time domain. Frequency domain is the representation of the digital data over a set of carrier frequencies and time domain representation is how the signal (sinusoidal wave) is spread over time.

The representation of digital data as discrete co-efficients in frequency domain can be converted to discrete representations of points in a sine wave over time domain by taking Inverse Discrete Fourier Transform (IDFT). Inverse Fast Fourier Transform (IFFT) is an efficient algorithm for generating the same.

When playing around with a carrier wave to encode the digital data, it is easier to consider the representation of the digital data as a point in a 2 dimensional plane. The amplitude and phase can be represented as polar co-ordinates in this plane with the distance of a point in the plane from the origin representing the amplitude and the angle it makes with the X axis as the phase.

The plane is represented as a complex number with the horizontal axis representing the real axis (represented by I)

Such mapping of digital data to amplitude and phase representation is considered for a particular carrier frequency (i.e in the frequency domain).

Once it is mapped, the modulated signal has to generated as a wave form which is nothing but a variation of the amplitude and phase of the wave with respect to time. So when transmitting the signal, its time domain representation has to be arrived at.

To convert a signal from its frequency domain representation to time domain representation, Inverse Fast Fourier Transform (IFFT) is used.

This article from National Instruments has a clear explanation of how digital data is mapped to I/Q axes and how the frequency domain and time domain representation of the signal look like

When representing digital data as points in a 2D plane as polar co-ordinates, these points can be considered as a modulation state. These points / state of modulation are called symbols.

Some detailed explanations are available in the following articles:

1. https://www.electronicdesign.com/communications/modulation-symbols-and-bits-building-your-wireless-vocabulary

2. http://ecee.colorado.edu/~liue/teaching/comm_standards/UMB/modulate.htm

In this series of digital communication fundamentals - I will resort to prose explanation of the concepts and provide links to detailed explanations already available at various sources in the internet.

**Modulation**A radio wave that is transmitted has the following characteristics

1. It has a wavelength, denoted by lambda (and hence a frequency where f = 1/lambda).

2. It has an amplitude.

3. It has a phase.

Digital information can be carried over the radio waves by altering one or more of the above properties of the carrier wave. Such altering of properties is called modulation.

**Types of Modulation**The fundamental modulations are alterations of one of each of the properties listed above.

1. Frequency Modulation

2. Amplitude Modulation

3. Phase Modulation

In later posts lets look into variations of each of the above modulations like Quadrature Amplitude Modulations (QAM), Phase Shift Keying (PSK which in turn has Binary PSK and Quadrature PSK).

**Frequency Domain and Time Domain**When talking about modulating digital data over a sinusoidal wave we talk about frequency domain and time domain. Frequency domain is the representation of the digital data over a set of carrier frequencies and time domain representation is how the signal (sinusoidal wave) is spread over time.

The representation of digital data as discrete co-efficients in frequency domain can be converted to discrete representations of points in a sine wave over time domain by taking Inverse Discrete Fourier Transform (IDFT). Inverse Fast Fourier Transform (IFFT) is an efficient algorithm for generating the same.

When playing around with a carrier wave to encode the digital data, it is easier to consider the representation of the digital data as a point in a 2 dimensional plane. The amplitude and phase can be represented as polar co-ordinates in this plane with the distance of a point in the plane from the origin representing the amplitude and the angle it makes with the X axis as the phase.

The plane is represented as a complex number with the horizontal axis representing the real axis (represented by I)

**and vertical axis representing the imaginary axis (represented by Q).**Such mapping of digital data to amplitude and phase representation is considered for a particular carrier frequency (i.e in the frequency domain).

Once it is mapped, the modulated signal has to generated as a wave form which is nothing but a variation of the amplitude and phase of the wave with respect to time. So when transmitting the signal, its time domain representation has to be arrived at.

To convert a signal from its frequency domain representation to time domain representation, Inverse Fast Fourier Transform (IFFT) is used.

This article from National Instruments has a clear explanation of how digital data is mapped to I/Q axes and how the frequency domain and time domain representation of the signal look like

**.**

**State of a Carrier - Symbol**When representing digital data as points in a 2D plane as polar co-ordinates, these points can be considered as a modulation state. These points / state of modulation are called symbols.

Some detailed explanations are available in the following articles:

1. https://www.electronicdesign.com/communications/modulation-symbols-and-bits-building-your-wireless-vocabulary

2. http://ecee.colorado.edu/~liue/teaching/comm_standards/UMB/modulate.htm

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