Group 2: Discrete-Time System Analysis PDF

GROUP 2 KING STEPHEN CUANO ARIEL GUMAPAC CLARISSE ANARETA CHRISTIAN ARSENUE IVAN JEREMY  CONTENTS 01 02 03 04 DISCRETE-TIME FREQUENCY CONVOLUTION CORRELATION SYSTEM RESPONSE OF DISCRETE-TIME ...

GROUP 2 KING STEPHEN CUANO ARIEL GUMAPAC CLARISSE ANARETA CHRISTIAN ARSENUE IVAN JEREMY  CONTENTS 01 02 03 04 DISCRETE-TIME FREQUENCY CONVOLUTION CORRELATION SYSTEM RESPONSE OF DISCRETE-TIME  01 DISCRETE-TIME SYSTEM DISCRETE-TIME SYSTEM A discrete-time system is defined mathematically as a transformation or operator that maps an input sequence with values x[n] into an output sequence with values y[n].  02 FREQUENCY RESPONSE OF DISCRETE-TIME The frequency response of a discrete-time system describes how the system processes input signals of different frequencies. The transfer function is derived from the system's impulse response and characterizes the system's frequency behavior. FORMULA : , Where H is the frequency response.  03 CONVOLUTION  y (t) = x (t) * h x (t) = input of LTI h (t) = impulse response of LTI (t) Convolution is a mathematical operation used Where y (t) = output of LTI to express the relation between input and output of an LTI system.  04 CORRELATION  FORMULA OF CORRELATION What is CORRELATION? Correlation is a measure of similarity between two signals.  Comparison of CONVOLUTION and CORRELATION Similarities Difference Application - Both convolution and correlation - Convolution is a directional operation, - Convolution is commonly used in involve the element-wise multiplication where the order of the signals matters. applications such as image filtering, and summation of two signals. The convolution of signal A with signal B signal smoothing, and the - They can be used to measure the is not the same as the convolution of implementation of linear time-invariant similarity or "overlap" between two signal B with signal A. systems. signals as a function of the relative shift - Correlation is a symmetric operation, - Correlation is commonly used in or displacement between them. where the order of the signals does not applications such as signal detection, matter. The correlation of signal A with pattern matching, and the estimation of signal B is the same as the correlation of time delays between two signals. signal B with signal A. THANK YOU FOR YOUR ATTENTION