HOOGHLY ENGINEERING AND TECHNOLOGY COLLEGE.pptx

time shifting

1. HOOGHLY ENGINEERING AND TECHNOLOGY COLLEGE NAME : AKANKSHA SINGH UNIVERSITY ROLL NO. : 17600321016 DEPARTMENT : ECE YEAR : 2 ND SEMESTER : 5 TH SUBJECT : DIGITAL SYSTEM AND PROCESSING TOPIC : TIME SHIFTING

2. INTRODUCTION Welcome to the Time Shifting presentation! In the realm of signal processing, time shifting plays a crucial role in optimizing the efficiency and performance of various applications. It involves manipulating the timing or phase of signals to achieve specific objectives, such as synchronization, filtering, or alignment. In this presentation, we will delve into the concept of time shifting, exploring its significance and practical applications. We'll discuss how time shifting is utilized in different signal processing scenarios and the benefits it brings to signal analysis and communication systems. Let's embark on this journey to better understand the world of time shifting in signal systems and its impact on modern technologies.

3. Suppose that we have a signal  x ( t ) and we define a new signal by adding/subtracting a finite time value to/from it. We now have a new signal,  y ( t ). The mathematical expression for this would be  x ( t  ±  t ). Graphically, this kind of signal operation results in a positive or negative “shift” of the signal along its time axis. However, note that while doing so, none of its characteristics are altered. This means that the time-shifting operation results in the change of just the positioning of the signal without affecting its amplitude or span. Let's consider the examples of the signals in the following figures in order to gain better insight into the above information. Here the original signal,  x [ n ], spans from  n  = -3 to  n  = 3 and has the values -2, 0, 1, -3, 2, -1, and 3, as shown in Figure.

4. Time shifting in signal systems involves altering the temporal characteristics of signals while preserving their essential properties. Key aspects to understand include: Time Domain vs. Frequency Domain: Time shifting predominantly occurs in the time domain, affecting the time-scale of signals. This process often leads to corresponding changes in the frequency domain due to the Fourier Transform relationship. Phase Shift and Delay: Time shifting can be achieved through phase shifting or introducing delays to the signal. Phase shifting adjusts the phase angle of sinusoidal components, while delays displace the signal along the time axis. Applications: Time shifting finds applications in various signal processing tasks, such as synchronization of data streams, signal alignment for analysis, and designing efficient communication systems.

5. Time-Delayed Signals Suppose that we want to move this signal right by three units (i.e., we want a new signal whose amplitudes are the same but are shifted right three times). This means that we desire our output signal  y [ n ] to span from  n  = 0to  n  = 6. Such a signal is shown as Figure 1(b) and can be mathematically written as  y [ n ] =  x [ n -3]. This kind of signal is referred to as time-delayed because we have made the signal arrive three units late. Time-Advanced Signals On the other hand, let's say that we want the same signal to arrive early. Consider a case where we want our output signal to be advanced by, say, two units. This objective can be accomplished by shifting the signal to the left by two time units, i.e.,  y [ n ] =  x [ n +2]. The corresponding input and output signals are shown in Figure 2(a) and 2(b), respectively. Our output signal has the same values as the original signal but spans from  n  = -5 to  n  = 1 instead of  n  = -3 to  n  = 3. The signal shown in Figure 2(b) is aptly referred to as a time-advanced signal.

6. BENEFITS OF TIME SHIFTING Signal Synchronization Efficient Signal Processing Compensation for Signal Delays Improved Signal Reception Signal Alignment

7. APPLICATION OF TIME SHIFTING Wireless Communication Radar and Sonar Systems Signal Analysis and Processing Multimedia Synchronization Control Systems Medical Imaging

8. CONCLUSION Time shifting in signal systems is a fundamental concept with widespread implications in modern technologies. By understanding and applying time shifting techniques effectively, we can enhance signal processing efficiency, improve communication systems, and achieve more accurate analyses of signals. As technology continues to advance, mastering time shifting in signal systems becomes increasingly vital in harnessing the full potential of signal processing applications. We hope this presentation has provided you with valuable insights into the world of time shifting in signal systems.

9. THANK YOU