This cource unit provides a general introduction to digitization and digital processing of signals in the context of telecommunications. The basic issues of the transition from the continuous field to the discrete one through sampling are highlighted, such as the generation of spectral images and the problem of aliasing. The Discrete Fourier Transform, as the spectral representation of discrete time signals in the discrete frequency domain, is introduced and the reader is introduced to the design and implementation of digital filters. Examples and laboratory exercises in digital spectral analysis and digital filters are provided. In appendices, basic theorems and properties of continuous and discrete-time Fourier transforms are given in tabular form.

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.Introduction, Simple AM-DSB modulation, Sampling grid: Brief theory, Example: AM-DSB modulation of a signal. SSB simulation: Brief theory, Example - SSB modulation of a discrete tone signal. VSB simulation: Example - VSB Filter, VSB Modulation, Example - SSB-VSB Comparison in Modulation with Continuous Spectrum Signal. Digital Implementation of FM system: Brief Theory of Exponential Modulations (PM, FM), PM and FM Modulation with Discrete Tone Signal, Example - FM Modulation with a discrete-tone signal, Example: FM modulation with a continuous-spectrum signal. Lab exercises to be implemented.

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This course unit is devoted to the method of optimal identification of pulses, which carry digital data and have been corrupted during transmission with additive, white noise. The method is implemented with the so-called matched filter, which is basically a signal correlator. At the receiver, a bank of matched filters (corresponding to the different, linearly independent pulses of the agreed transmission repertoire – referred to as signal constellation) calculate the correlation of their pulse with each incoming pulse (multiplication and integration over the fundamental period, T). The filter with the largest output value indicates the pulse with the highest likelihood (ie, the highest probability of having been emitted, under the condition of the signal received).After presenting the basic features of matched filters, a generalization to N-dimensional linear signal spaces is made. Error analysis is briefly discussed and worked examples of sinusoidal pulse (FSK) and pulse amplitude modulated (PAM or ASK) recognition are given.

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The spectral characteristics of pulse trains (digital waveforms) are studied. For static amplitude-modulated pulse sequences, the power spectral density depends on: (a) the Fourier transform of the (deterministic) pulses and (b) the autocorrelation of the discrete sequence of amplitudes. Digital amplitude modulation (Amplitude Shift Keying - ASK), also called Pulse Amplitude Modulation (PAM), Phase modulation (Phase Shift Keying - PSK) and Quadrature Amplitude Modulation (QAM) fall directly into this category. For the last two the amplitude sequences are, obviously, complex numbers. For white (completely random) amplitude sequences, the spectral characteristics of the pulse trains are determined solely by the shape and duration of the pulses used. Also presented and analyzed in this unit are pulse shaping filters that minimize the required bandwidth while ensuring zero interference between pulses in the sequence (Nyquist signaling). A similar class of filters allows controlled interference, which can be removed at the receiver (partial response signaling).

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The (a) Quadrature Amplitude Modulation (QAM) and (b) Phase Shift Keying (PSK) digital modulations are presented. For each of them are given: (i) the signal constellation, (ii) the transmitter and receiver structure, (iii) the error analysis in a white additive noise environment and (iv) the spectral characteristics. Worked simulation examples are also given.

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Digital frequency modulations (also called Frequency Shift Keying – FSK) is presented, with reference, as in the previous chapter, to the four main topics: the signal constellation, the transmitter and receiver structure, the noise behavior (with a measure of the bit error probability) and the spectral characteristics. A special section is devoted to the coherent binary version of FSK with minimum bandwidth, that of Minimum Shift Keying – MSK. Worked simulation examples are given.

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The results of the previous units are combined, in order to design and compare practical digital modulation systems, with specific bandwidth and (maximum) error rate (Bit Error Rate - BER) requirements. After the Shannon-Hartley theorem for channel capacity is formulated, the relationships that link the main design parameters are summarized, such as: the transmission bit rate, R, the transmission symbol rate– or baud rate, 1/T – the bandwidth, W, the signal-to-noise ratio, S/N or (in normalized form) Eb/No. Here is a series of worked examples with comparative results for the various configuration systems.

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The challenges of broadband transmission are presented and the Orthogonal Frequency Division Multiplexing (OFDM) technique is introduced. In principle, the environment and the benefits of applying this specific modulation method, its mathematical formulation, as well as the structure of the transmitter and the receiver are given. At the end, a complete implementation/simulation example is presented, while the main (currently) standards that include this modulation method are listed in the Appendix

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This Unit is dedicated to channel coding, i.e. those techniques that, by adding structured bits to the transmitted message sequences, enable the receiver to detect and correct errors that may have occurred during transmission through unreliable (e.g. noisy) communication channels. The study is limited to the block coding category, posttponing to a future edition of the book the corresponding study of convolutional coding. Emphasis is placed on cyclic block Codes and especially on the widely used Reed-Solomon codes. A brief theory on Finite Fields (or Galois Fields), as the basis of some cyclic codes, is given in an Appendix.

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