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Questions and Answers
What is a signal and what information does it convey?
A signal is a function that conveys information about a phenomenon. It represents physical quantities that vary with time, space, or any other independent variable.
Label the following signals as causal, non-causal, or anti-causal sequences.
What is a continuous signal? Describe its characteristics.
A continuous signal is a signal that is defined for every value of time. Its characteristics include having an infinite number of possible values at each point in time and being represented by a continuous function.
List examples of continuous-time (CT) signals found in nature.
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Differentiate discrete-time (DT) signals and digital signals.
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What is the unit impulse function?
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The unit impulse sequence has an amplitude of _______ at all samples except at _______.
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If $x[n] = 4δ[n]$, what does this represent?
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What is the formula for determining the values of the unit impulse function?
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Study Notes
Digital Functions
- The unit impulse function or unit sample sequence is defined as the sequence with values 𝜹 𝒏.
- 𝜹 𝒏 = 𝟏 for 𝒏 = 𝟎
- 𝜹 𝒏 = 𝟎 for 𝒏 ≠ 𝟎
- 𝜹 𝒏 = 𝟏 for 𝒏 = 𝟎
- Every digital signal can be expressed as a summation of several impulse functions, using the amplitude at each sample.
- Any impulse signal can be a scaled or time variant (shifted ver.) of the unit impulse (δ) function.
- For example: 𝑥[𝑛] = 4𝛿[𝑛]
- A digital signal 𝑥 is given the notation 𝒙[𝒏] to indicate that it has values only where the samples are taken at a finite interval.
- 𝒏 - sample’s index, taken at time 𝑡 = 𝑛𝑇𝑆, where 𝑇𝑆 is the sampling period.
Unit-Impulse Function
- Every digital signal can be written as a sum of several impulse functions, using the amplitude at each sample.
- Determine the values of the following:
- 𝛿[𝟎] = 𝟏
- 𝛿[𝟏] = 𝟎
- 𝛿[−2] = 𝟎
- Determine the values of the following:
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Description
This quiz explores digital functions, particularly the unit impulse function and its representations in digital signals. You'll learn how every digital signal can be expressed as a summation of impulse functions and understand the notation used for discrete signals. Test your knowledge on the values of the unit impulse function for different indices.
