Introduction to Digital Signal and System Analysis - Tutorsindia

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Introduction to Digital Signal and System Analysis Basic Types of Digital Signals 2 Basic Types of Digital Signals 2.1 Three basic signals Unit impulse ⎧1 n = 0 d[ n] = ⎨ (2.1) ⎩0 n ≠ 0 i.e. the unit impulse has only one non-zero value 1 at n=0, and all other samples are 0. It is the simplest signal but will be seen later very important. Unit step ⎧1 u[ n] = ⎨ ⎩0 n ≥ 0 n < 0 (2.2) where the sample value rises at n=0 from 0 to 1 and keeps it to n → ∞ . Ramp Please click the advert In Paris or Online International programs taught by professors and professionals from all over the world BBA in Global Business MBA in International Management / International Marketing DBA in International Business / International Management MA in International Education MA in Cross-Cultural Communication MA in Foreign Languages Innovative – Practical – Flexible – Affordable Visit: www.HorizonsUniversity.org Write: Admissions@horizonsuniversity.org Call: 01.42.77.20.66 www.HorizonsUniversity.org Download free ebooks at bookboon.com 16
Introduction to Digital Signal and System Analysis Basic Types of Digital Signals ⎧n r[ n] = ⎨ ⎩0 n ≥ 0 n < 0 (2.3) Figure 2.1 illustrates the unit impulse, unit step and ramp signals. Alternatively, the three basic signals can be expressed by a tabular form as below: n … -3 -2 -1 0 1 2 3 … d[n] … 0 0 0 1 0 0 0 . . . u[n] … 0 0 0 1 1 1 1 … r[n] … 0 0 0 0 1 2 3 … The unit impulse, unit step and ramp signals are simple and basic signals. Unit impulse is the basic of basic signals. The unit step can be regarded as a sum of unit impulse on the positive side of n-axis. The ramp signal can be a set of unit impulses shifted to the right axis and scaled by sample number n. Or it can be regarded as the unit step scaled by the corresponding sample number n. Actually, later, we will know all signals can be regarded as a sum of shifted and scaled unit impulses. 17 Download free ebooks at bookboon.com
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