[...]... Signal samples x (t ) Analog signal/continuous-time signal Sampling interval T 5 0 −5 nT 0 FIGURE 2.2 2T 4T 6T 8T 10T 12T Display of the analog (continuous) signal and display of digital samples versus the sampling time instants Tan: Digital Signaling Processing 0123740908_chap02 Final Proof page 15 21.6.2007 10:57pm Compositor Name: MRaja 2.1 Sampling of Continuous Signal x (t ) 15 Voltage for ADC... obtained by sampling the continuous signal x(t) at a sampling rate of fs samples per second Mathematically, this process can be written as the product of the continuous signal and the sampling pulses (pulse train): xs (t) ¼ x(t)p(t), (2:1) Tan: Digital Signaling Processing 0123740908_chap02 Final Proof page 17 21.6.2007 10:57pm Compositor Name: MRaja 2.1 Sampling of Continuous Signal 17 p(t ) 1 t T... members at Elsevier Science publishing for their encouragement and guidance in developing the complete manuscript I also wish to thank Jamey Stegmaier (publishing project manager) at SPi for coordinating the copyediting of the manuscript Thanks to all the faculty and staff at DeVry University, Decatur, for their encouragement and support The book has benefited from many constructive comments and suggestions... decreasing and their performance increasing, DSP will continue to affect engineering design in our modern daily life Some application examples using DSP are listed in Table 1.1 However, the list in the table by no means covers all DSP applications Many more areas are increasingly being explored by engineers and scientists Applications of DSP techniques will continue to have profound impacts and improve our lives... biomedical signal enhancement, dual-tone multifrequency (DTMF) tone generation and detection with the Goertzel algorithm & Chapter 9 introduces DSP architectures, software and hardware, and fixed-point and floating-point implementations of digital filters & Chapter 10 covers adaptive filters with applications such as noise cancellation, system modeling, line enhancement, cancellation of periodic interferences,... guidance, and sharing of their insight into DSP over the years A special thanks goes to Dr Jean Jiang (professor at DeVry University in Decatur) for her encouragement, support, insightful suggestions, and testing of the manuscript in her DSP course Special thanks go to Tim Pitts (senior commissioning editor), Rick Adams (senior acquistions editor), and Rachel Roumeliotis (acquisitions editor) and to the team... 24-Bit Color Image Equalization 13.2.3 8-Bit Indexed Color Image Equalization 13.2.4 MATLAB Functions for Equalization 13.3 Image Level Adjustment and Contrast 13.3.1 Linear Level Adjustment 13.3.2 Adjusting the Level for Display 525 530 533 534 550 557 557 558 564 570 575 578 583 589 590 593 599 601 609 610 617 617 618 619 620 621 622 624 625 625 632 633 636 637 638 641 Tan: Digital Signaling Processing... University, Kansas City, MO Professor Ling Hou, St Cloud State University, St Cloud, MN Professor Robert C (Rob) Maher, Montana State University, Bozeman, MT Professor Abdulmagid Omar, DeVry University, Tinley Park, IL Professor Ravi P Ramachandran, Rowan University, Glassboro, NJ Professor William (Bill) Routt, Wake Technical Community College, Raleigh, NC Professor Samuel D Stearns, University of New... digital x-rays and medical image systems We would also live in many less efficient ways, since we would not be equipped with voice recognition systems, speech synthesis systems, and image and video editing systems Without DSP, scientists, engineers, and technologists would have no powerful tools to analyze and visualize data and perform their design, and so on Tan: Digital Signaling Processing 0123740908_chap01... conversion (ADC) unit, a digital signal (DS) processor, a digital-to-analog conversion (DAC) unit, and a reconstruction (anti-image) filter As shown in the diagram, the analog input signal, which is continuous in time and amplitude, is generally encountered in our real life Examples of such analog signals include current, voltage, temperature, pressure, and light intensity Usually a transducer (sensor) . 12 2 Signal Sampling and Quantization 13 2. 1 Sampling of Continuous Signal 13 2. 2 Signal Reconstruction 20 2. 2.1 Practical Considerations for Signal Sampling: Anti-Aliasing Filtering 25 2. 2 .2. 624 13 .2 Image Histogram and Equalization 625 13 .2. 1 Grayscale Histogram and Equalization 625 13 .2. 2 24 -Bit Color Image Equalization 6 32 13 .2. 3 8-Bit Indexed Color Image Equalization 633 13 .2. 4. Format 21 5 7 .2 Fourier Transform Design 21 7 7.3 Window Method 22 9 7.4 Applications: Noise Reduction and Two-Band Digital Crossover 25 3 7.4.1 Noise Reduction 25 3 7.4 .2 Speech Noise Reduction 25 5 7.4.3