Slide - Aula 1 Introdução - 2024-1

ELF51 - EL66D - PDS Prof. Daniel R. Pipa Introduc¸˜ao Dom´ınio de tempo cont´ınuo e discreto Aplicac¸˜oes de PDS Processamento Digital de Sinais ELF51 - EL66D - Engenharia Eletrˆonica Introduc¸˜ao Prof. Daniel R. Pipa danielpipa@utfpr.edu.br ELF51 - EL66D - PDS Prof. Daniel R. Pipa Introduc¸˜ao Dom´ınio de tempo cont´ınuo e discreto Aplicac¸˜oes de PDS Sinais no tempo cont´ınuo O que ´e um sinal? Grandeza f´ısica que varia em func¸˜ao do tempo, espac¸o ou qualquer outra vari´avel ou vari´aveis. Sinais contˆem informac¸˜ao sobre sobre uma quantidade de interesse. Forma de onda representando a variac¸˜ao de press˜ao ac´ustica quando a palavra signal ´e dita. 2 Introduction 1.1 Signals • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • For our purposes a signal is defined as any physical quantity that varies as a function of time, space, or any other variable or variables. Signals convey information in their pat- terns of variation. The manipulation of this information involves the acquisition, storage, transmission, and transformation of signals. There are many signals that could be used as examples in this section. However, we shall restrict our attention to a few signals that can be used to illustrate several important concepts and they will be useful in later chapters. The speech signal, shown as a time waveform in Figure 1.1, represents the variations of acoustic pressure converted into an electric signal by a microphone. We note that different sounds correspond to different patterns of temporal pressure variation. To better understand the nature of and differences between analog and digital signal pro- cessing, we shall use an analog system which is near extinction and probably unknown to many readers. This is the magnetic tape system, used for recording and playback of sounds such as speech or music, shown in Figure 1.2(a). The recording process and playback process, which is the inverse of the recording process, involve the following steps: • Sound waves are picked up by a microphone and converted to a small analog voltage called the audio signal. • The audio signal, which varies continuously to “mimic” the volume and frequency of the sound waves, is amplified and then converted to a magnetic field by the recording head. • As the magnetic tape moves under the head, the intensity of the magnetic field is recorded (“stored”) on the tape. • As the magnetic tape moves under the read head, the magnetic field on the tape is converted to an electrical signal, which is applied to a linear amplifier. • The output of the amplifier goes to the speaker, which changes the amplified audio signal back to sound waves. The volume of the reproduced sound waves is controlled by the amplifier. Time (t) Acoustic Pressure s(t) “Signal” Figure 1.1 Example of a recording of speech. The time waveform shows the variation of acoustic pressure as a function s(t) of time for the word “signal.” ELF51 - EL66D - PDS Prof. Daniel R. Pipa Introduc¸˜ao Dom´ınio de tempo cont´ınuo e discreto Aplicac¸˜oes de PDS Tipos de sinais ▶ Monocanal: “informac¸˜ao” escalar, func¸˜ao f : · → R ▶ Multicanal: “informac¸˜ao” vetorial, func¸˜ao f : · → Rm ▶ Unidimensional: “vari´avel” escalar, func¸˜ao f : R → · ▶ Multidimensional: “vari´avel” vetorial, func¸˜ao f : Rn → · Exemplos ▶ ´Audio mono: monocanal, unidimensional ▶ ´Audio est´ereo: multicanal, unidimensional ▶ Imagem em escala de cinza: monocanal, multidimensional ▶ Imagem colorida: multicanal, multidimensional Tipos de sinais cont. ELFS1 - EL66D - PDS Sinal no tempo continuo Sinal no tempo discreto 1 1 ‘\ s(t) = e~* cos (378) u(t) os s[n] = e~°?" cos (0.37) u[n] 0.5}! . ONO RRC Rae) = 0 : = 0 -0.5 0.5 0 0.5 1 1.5 2 0 10 20 30 40 t (sec) Sample index (n) Quantizado em amplitude > Sinal no tempo continuo I b] 08 te R,s(the R = 03 > Sinal no tempo discreto, * 03 n€ Z,s|jnj}e R -0.4 : oo 06 > Sinal digital,n € Z,sg[n] € ~~ 0 10 =©20 = 30.—Ss« 40 {.-- ,—0.2, —0.1,0,0.1,0.2,--+} Sample index (n) Tipos de sistemas an > No tempo continuo: Um sinal continuo x(t) é transformado em outro sinal Prof. Daniel R. Pipa continuo y(t). Penna somentinnor ay x(t) Continuous-Time yt) System H x(t) y(t) ou y(t) = H {x()} > No tempo discreto: Um sinal discreto x[n] é transformado em outro sinal discreto y[n]. xn] Discrete-Time yin] System H x|n] = yl] ou yln] = H {aln]} Processamento Digital de Sinais (PDS) ELFS1 - EL66D - PDS Prof. Daniel R. Pipa ie) vue Sy Oe Processamento de sinais é a area que estuda a aquisi¢ao, representacao, nr manipulacdo e transformacao de sinais. Seus resultados tem uso numa vasta gama de aplicagoes praticas. O Processamento Digital de Sinais realiza tais estudos no dominio do tempo discreto. Vantagens em relacao ao analégico cosh [In (|x(t)|) + 23(t) + cos? (Ve!) | t) = —,A—, _ yo 5x5(t) +e) + tan (x(t) > Flexibilidade: equagao acima dificil de implementar em hardware, porém facil num computador / processador. ELF51 - EL66D - PDS Prof. Daniel R. Pipa Introduc¸˜ao Dom´ınio de tempo cont´ınuo e discreto Aplicac¸˜oes de PDS Outras vantagens ▶ Func¸˜oes sofisticadas podem ser implementadas em dispositivos digitais de baixo custo. ▶ Sistemas digitais s˜ao inerentemente mais confi´aveis, compactos e menos sens´ıveis a condic¸˜oes ambientais e variac¸˜ao de parˆametros de componentes devido `a fabricac¸˜ao e envelhecimento, como nos sistemas anal´ogicos. ▶ A abordagem digital permite o compartilhamento de tempo em processadores, possibilitando realizar v´arias operac¸˜oes numa ´unica unidade de processamento. ELF51 - EL66D - PDS Prof. Daniel R. Pipa Introduc¸˜ao Dom´ınio de tempo cont´ınuo e discreto Aplicac¸˜oes de PDS Desvantagens Desvantagens em relac¸˜ao ao processamento anal´ogico ▶ Convers˜oes A/D e D/A (quase) sempre necess´arias ▶ Ru´ıdo de quantizac¸˜ao ▶ Para sinais de banda extremamente larga ou sistemas em tempo real, soluc¸˜oes por PDS podem ser imposs´ıveis ou muito caras. ELF51 - EL66D - PDS Prof. Daniel R. Pipa Introduc¸˜ao Dom´ınio de tempo cont´ınuo e discreto Aplicac¸˜oes de PDS Etapas para PDS Para processar digitalmente um sinal 15 1.3 Analog, digital, and mixed signal processing T T (a) T T DSP ADC DAC Sensor (b) Analog post-filter Analog output Digital output to DAC Digital input from ADC Analog pre-filter Analog input Ideal ADC Discrete-Time System Ideal DAC Figure 1.13 Simplified block diagram of idealized system for (a) continuous-time processing of discrete-time signals, and (b) its practical counterpart for digital processing of analog signals. 2. An analog filter (known as pre-filter or antialiasing filter) used to “smooth” the input signal before sampling to avoid a serious sampling artifact known as aliasing distortion (see Chapter 6). 3. An A/D converter that converts the analog signal to a digital signal. After the samples of a discrete-time signal have been stored in memory, time-scale information is lost. The sampling rate and the number of bits used by the ADC determine the accuracy of the system. 4. A digital signal processor (DSP) that executes the signal processing algorithms. The DSP is a computer chip that is similar in many ways to the microprocessor used in personal computers. A DSP is, however, designed to perform certain numerical com- putations extremely fast. Discrete-time systems can be implemented in real-time or off-line, but ADC and DAC always operate in real-time. Real-time means completing the processing within the allowable or available time between samples. 5. A D/A converter that converts the digital signal to an analog signal. The DAC, which reintroduces the lost time-scale information, is usually followed by a sample-and-hold circuit. Usually, the A/D and D/A converters operate at the same sampling rate. 6. An analog filter (known as reconstruction or anti-imaging filter) used to smooth the staircase output of the DAC to provide a more faithful analog reproduction of the digital signal (see Chapter 6). We note that the DAC is required only if the DSP output must be converted back into an analog signal. There are many applications, like speech recognition, where the results of processing remain in digital form. Alternatively, there are applications, such as CD players, which do not require an ADC. The fundamental distinction between digital signal processing and discrete-time sig- nal processing, is that the samples of digital signals are described and manipulated with finite numerical accuracy. Because the discrete nature of signal amplitudes complicates the analysis, the usual practice is to deal with discrete-time signals and then to consider the 1. Sensor 2. Pr´e-filtragem anal´ogica 3. Convers˜ao anal´ogica / digital 4. Processamento Digital 5. Convers˜ao digital / anal´ogica 6. P´os-filtragem anal´ogica = 22 090 Conversao analdgico / digital ELFS1 - EL66D - PDS Prof. Daniel R. Pipa x) | x[n] =x(nT) ; xalr] .-O1OIOLL... Sampler Quantzer Q Coder Pore RCT RC Rene nec) nn Kaz (a) Digital Signal xg[n] Discrete-Time Signal rot \ oe aie TUT) pg ATT Continuous-Time Signal AT | oy A oe oe Noe HLA t nT (b) ELF51 - EL66D - PDS Prof. Daniel R. Pipa Introduc¸˜ao Dom´ınio de tempo cont´ınuo e discreto Aplicac¸˜oes de PDS Telefone celular digital 18 Introduction Amplifier Speaker Microphone Codec Filter Filter ADC Keypad Display Control RF section (modulation, demodulation, frequency conversion. rf amplifier) Antenna DSP DAC Amplifier Figure 1.14 Simplified block diagram of a digital cellular phone. 1.5 Book organization • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Chapter 1 Introduction Chapter 1 (this chapter) provides an introduction to the concepts of signals, systems, and signal processing in both the continuous-time and discrete-time domains. The topics of analog and digital signals, analog and digital systems, and analog- digital interface systems are also discussed. Chapter 2 Discrete-time signals and systems The subject of Chapter 2 is the math- ematical properties and analysis of linear time-invariant systems with emphasis on the convolution representation. A detailed discussion of the software implementation of convolution and difference equations is also provided. Chapter 3 The z-transform Chapter 3 introduces the z-transform of a sequence and shows how the properties of the sequence are related to the properties of its z-transform. The z-transform facilitates the representation and analysis of LTI systems using the powerful concepts of system function, poles, and zeros. Chapter 4 Fourier representation of signals All signals of practical interest can be expressed as a superposition of sinusoidal components (Fourier representation). Chapter 4 introduces the mathematical tools, Fourier series and Fourier transforms, for the representation of continuous-time and discrete-time signals. Chapter 5 Transform analysis of LTI systems Chapter 5 introduces the concept of fre- quency response function and shows a close coupling of its shape to the poles and zeros of the system function. This leads to a set of tools which are then utilized for the analysis and design of LTI systems. A section reviewing similar techniques for continuous-time systems is included at the end of the chapter. ELF51 - EL66D - PDS Prof. Daniel R. Pipa Introduc¸˜ao Dom´ınio de tempo cont´ınuo e discreto Aplicac¸˜oes de PDS Telefone celular digital 18 Introduction Amplifier Speaker Microphone Codec Filter Filter ADC Keypad Display Control RF section (modulation, demodulation, frequency conversion. rf amplifier) Antenna DSP DAC Amplifier Figure 1.14 Simplified block diagram of a digital cellular phone. 1.5 Book organization • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Chapter 1 Introduction Chapter 1 (this chapter) provides an introduction to the concepts of signals, systems, and signal processing in both the continuous-time and discrete-time domains. The topics of analog and digital signals, analog and digital systems, and analog- digital interface systems are also discussed. Chapter 2 Discrete-time signals and systems The subject of Chapter 2 is the math- ematical properties and analysis of linear time-invariant systems with emphasis on the convolution representation. A detailed discussion of the software implementation of convolution and difference equations is also provided. Chapter 3 The z-transform Chapter 3 introduces the z-transform of a sequence and shows how the properties of the sequence are related to the properties of its z-transform. The z-transform facilitates the representation and analysis of LTI systems using the powerful concepts of system function, poles, and zeros. Chapter 4 Fourier representation of signals All signals of practical interest can be expressed as a superposition of sinusoidal components (Fourier representation). Chapter 4 introduces the mathematical tools, Fourier series and Fourier transforms, for the representation of continuous-time and discrete-time signals. Chapter 5 Transform analysis of LTI systems Chapter 5 introduces the concept of fre- quency response function and shows a close coupling of its shape to the poles and zeros of the system function. This leads to a set of tools which are then utilized for the analysis and design of LTI systems. A section reviewing similar techniques for continuous-time systems is included at the end of the chapter. Processador Digital de Sinais Operac¸˜oes realizadas no DSP: ▶ Compress˜ao de voz, correc¸˜ao de erro, criptografia, equalizac¸˜ao de canal, modulac¸˜ao e demodulac¸˜ao, cancelamento de interferˆencia entre canais e outros. ELF51 - EL66D - PDS Prof. Daniel R. Pipa Introduc¸˜ao Dom´ınio de tempo cont´ınuo e discreto Aplicac¸˜oes de PDS Outras aplicac¸˜oes S˜ao exemplos de “processar” um sinal: ▶ Filtrar de ru´ıdos e interferˆencia ▶ Reconhecer voz, letras, s´ılabas, etc. ▶ Comprimir ´audio, imagem, texto. ▶ Modular sinal para telecom. ▶ Reconstruir imagens (ultrassom, tomografia, ressonˆancia, etc).