what is arbitrary signal

arbitrary waveform generator vs signal generator and siglent arbitrary signal generator
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Prof.EvanBaros,United Kingdom,Teacher
Published Date:26-07-2017
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Multiple Representations of CT and DT Systems Verbal descriptions: preserve the rationale. Difference/differential equations: mathematically compact. yn = xn + z yn − 1 y ˙(t) = x(t) + s y(t) 0 0 Block diagrams: illustrate signal flow paths. + + X Y X A Y z s 0 0 R Operator representations: analyze systems as polynomials. Y 1 Y A = = X 1 − z R X 1 − s A 0 0 Transforms: representing diff. equations with algebraic equations. z 1 H(z) = H(s) = z − z s − s 0 0 3Convolution Representing a system by a single signal. 4Responses to arbitrary signals Although we have focused on responses to simple signals (δn,δ(t)) we are generally interested in responses to more complicated signals. How do we compute responses to a more complicated input signals? No problem for difference equations / block diagrams. → use step-by-step analysis. 5Check Yourself Example: Find y3 + + X Y R R when the input is xn 1 n 1. 1 2. 2 3. 3 4. 4 5. 5 0. none of the above 6Responses to arbitrary signals Example. + + 0 0 R R 0 0 xn yn n n 7Responses to arbitrary signals Example. + + 1 1 R R 0 0 xn yn n n 8Responses to arbitrary signals Example. + + 1 2 R R 1 0 xn yn n n 9Responses to arbitrary signals Example. + + 1 3 R R 1 1 xn yn n n 10Responses to arbitrary signals Example. + + 0 2 R R 1 1 xn yn n n 11Responses to arbitrary signals Example. + + 0 1 R R 0 1 xn yn n n 12Responses to arbitrary signals Example. + + 0 0 R R 0 0 xn yn n n 13Check Yourself What is y3? 2 0 + + 0 R R 0 0 xn yn 1 n n 1. 1 2. 2 3. 3 4. 4 5. 5 0. none of the above 14Superposition Break input into additive parts and sum the responses to the parts. xn n yn = n n + + n n + + n n −1 0 1 2 3 4 5 = n −1 0 1 2 3 4 5 15Linearity A system is linear if its response to a weighted sum of inputs is equal to the weighted sum of its responses to each of the inputs. Given x n system y n 1 1 and x n system y n 2 2 the system is linear if αx n +βx n αy n +βy n system 1 2 1 2 is true for all α and β. 16Superposition Break input into additive parts and sum the responses to the parts. xn n yn = n n + + n n + + n n −1 0 1 2 3 4 5 = n −1 0 1 2 3 4 5 Superposition works if the system is linear. 17Superposition Break input into additive parts and sum the responses to the parts. xn n yn = n n + + n n + + n n −1 0 1 2 3 4 5 = n −1 0 1 2 3 4 5 Reponses to parts are easy to compute if system is time-invariant. 18Time-Invariance A system is time-invariant if delaying the input to the system simply delays the output by the same amount of time. Given xn system yn the system is time invariant if xn−n system yn−n 0 0 is true for all n . 0 19Superposition Break input into additive parts and sum the responses to the parts. xn n yn = n n + + n n + + n n −1 0 1 2 3 4 5 = n −1 0 1 2 3 4 5 Superposition is easy if the system is linear and time-invariant. 20Structure of Superposition If a system is linear and time-invariant (LTI) then its output is the sum of weighted and shifted unit-sample responses. δn hn system δn−k hn−k system xkδn−k xkhn−k system ∞ ∞ X X xn = xkδn−k yn = xkhn−k system k=−∞ k=−∞ 21Convolution Response of an LTI system to an arbitrary input. xn yn LTI ∞ X yn = xkhn−k≡ (x∗h)n k=−∞ This operation is called convolution. 22

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