Convolution Presentation PDF

LIONVOTOC UN  CONVOLUT ION PRESENTATION BY MC DHEMZEL  CONVOLUTION It is one of the most important concepts in engineering, can be used to determine the output a system produces for a given input signal. It can be shown that a linear time invariant sys...

LIONVOTOC UN  CONVOLUT ION PRESENTATION BY MC DHEMZEL  CONVOLUTION It is one of the most important concepts in engineering, can be used to determine the output a system produces for a given input signal. It can be shown that a linear time invariant system is completely characterized by its impulse response. It is a fundamental operation in signal processing that combines two signals to produce a third signal.  CONVOLUTION vs CORRELATIOMN Convolution is the relationship between a system’s input signal, output signal, and impulse response. Correlation is a way to detect a known waveform in a nosy background.  TYPES CONTINUO DISCRE US TE It uses integration to sum It uses summation to combine contributions of the overlapping values of sequences at specific areas of two continuous functions indices WHERE: x(t) or x[n] is the input signal h(t) or h[n] is the impulse response of a system. y(t) or y[n] is the output signal CONTINUOUS TIME CONVOLUTION  CONTINUOUS TIME CONVOLUTION The shifting property of the continuous time impulse function tells us that the input signal to a system can be represented as an integral of scaled and shifted impulses and, therefore, as the limit of a sum of scaled and shifted approximate unit impulses. Thus, by linearity, it would seem reasonable to compute of the output signal as the limit of a sum of scaled and shifted unit impulse responses and, therefore, as the integral of a scaled and shifted impulse response. That is exactly what the operation of convolution accomplishes. Hence, convolution can be used to determine a linear time invariant system's output from knowledge of the input and the impulse response. CONTINUOUS TIME CONVOLUTION EXAMPLE DISCRETE-TIME CONVOLUTION EXAMPLE EXAMPLE Question: The input and impulse response of DT LTI system are given as: x(n) = {1,1,0.5,0.5} and h(n) = {1,0.5,0.25}. Find the system output y(n). ASA ANG SOLUSYON? I-SOLVE REPORTER! Illustrate daun EXAMPLE Convolute two sequences x[n] = {1,2,3} & h[n] = {-1,2,2} SOLUTION Convoluted output y[n] = [ -1, - 2+2, -3+4+2, 6+4, 6] = [-1, 0, 3, 10, 6] Here x[n] contains 3 samples and h[n] is also having 3 samples so the resulting sequence having 3+3-1 = 5 samples.  APPLICATIONS 1. Filtering Purpose: To modify or enhance specific features of a signal. 2. Signal Smoothing and Denoising Purpose: To reduce noise and smooth out rapid fluctuations in data. 3. Image Processing Purpose: To enhance, filter, or manipulate images 03 References https://eng.libretexts.org/Bookshelves/Electrical_Engineering/ Signal_Processing_and_Modeling/ Signals_and_Systems_(Baraniuk_et_al.)/ 03%3A_Time_Domain_Analysis_of_Continuous_Time_Systems/ 3.03%3A_Continuous_Time_Convolution https://engineerstutor.com/2018/11/04/convolution-of-signals-solved- problems/ https://math.libretexts.org/Bookshelves/Differential_Equations/ Introduction_to_Partial_Differential_Equations_(Herman)/ 09%3A_Transform_Techniques_in_Physics/ 9.06%3A_The_Convolution_Operation https://youtu.be/2kTA6HReMc4?si=ZFLKx6P8l_3eA6I4 https://youtu.be/hl2T2adZWFI?si=Vzg8NSsSYgD_QU9P https://youtu.be/Xw4YvLGdQlQ?si=40F4Os4Yk67IvRJ1 https://youtu.be/X8k16jP3H0E?si=AyJDR_l0B5N_oRW1 sauTHA’NK YOU 08 THANK YOU Always Pray and Never Give Up 08 Luke 18:1