Example 2.4: Your Guide to Discrete Time Convolution Techniques || Signals and systems by oppenheim

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S&S 2.1.2(2)(English) (Oppenheim) || Example 2.4.
A particularly convenient way of displaying this calculation graphically begins with the two
signals x[k] and h[n - k] viewed as functions of k. Multiplying these two functions, we
obtain a sequence g[k] = x[k]h[n - k], which, at each time k, is seen to represent the
contribution of x[ k] to the output at time n. We conclude that summing all the samples
in the sequence of g[k] yields the output value at the selected time n. Thus, to calculate
y[n] for all values of n requires repeating this procedure for each value of n.
In this video we discuss techniques for solving discrete time convolution problem with the help of example 2.4
In this video, we delve into Discrete Time Convolution, focusing specifically on Example 2.4. Understanding discrete time convolution is crucial for analyzing signals in digital signal processing. We will break down the steps involved in performing convolution, using Example 2.4 to illustrate the process clearly. This tutorial is designed for students and professionals alike, providing a comprehensive guide to mastering this essential concept. Whether you're new to the topic or looking to reinforce your knowledge, this video will enhance your understanding of discrete time systems. Don't forget to like, subscribe, and hit the notification bell for more insightful content!
Example 2.4: As a further example, consider the two sequences
[ ] { 1, 0 :::; n :::; 4 x n = 0, otherwise
and
h[n] = { a 11, 0 :::; n .:::; 6.
0, otherwise
These signals are depicted in Figure 2.8 for a positive value of a greater than 1. In order to calculate the convolution of the two signals, it is convenient to consider five separate intervals for n. This is illustrated in Figure 2.9.
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