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EED-201 (Signals and Systems): ASSIGNMENT 1 Submit on / before Sept. 20, 2020. Solve all the questions.
- A function 𝑔(𝑡) is defined by: 𝑔(𝑡) = {
Plot 3 𝑔(𝑡 + 1 ), ( 1 / 2 )𝑔( 3 𝑡), − 2 𝑔((𝑡 − 1 )/ 2 ).
- Evaluate 𝑥(𝑡) ∗ ℎ(𝑡) for Figures 1 and 2 where 𝑥(𝑡) and ℎ(𝑡) are shown below by analytical and graphical methods: Figure 1 Figure 2
- For each pair of signals 𝑥 1 [𝑛] and 𝑥 2 [𝑛], find the numerical value of 𝑦[𝑛] = 𝑥 1 [𝑛] ⊛ 𝑥 2 [𝑛] at the indicated values of n.
- Find and sketch even and odd parts of the function:
- 𝑔(𝑡) = 𝑡(𝑡^2 + 3 ) 2) 𝑔[𝑛] = 𝑠𝑖𝑛( 2 𝜋𝑛/ 7 )( 1 + 𝑛^2 )
- Consider a signal: ℎ[𝑛] = ( 1 2
𝑛− 1 {𝑢[𝑛 + 3 ] − 𝑢[𝑛 − 10 ]}. Express A and B in terms of n so that the following equation holds: ℎ[𝑛 − 𝑘] = {( 1 2
𝑛−𝑘− 1 , 𝐴 ≤ 𝑘 ≤ 𝐵 0 , elsewhere
- Determine whether the following signal is energy or power signal. Find the corresponding energy or power of the signal. x(t)= {
- The following are the impulse responses of continuous-time LTI systems. Determine whether each system is causal and/or stable:
- ℎ[𝑛] = ( 0. 8 )𝑛𝑢[𝑛 + 2 ]
- ℎ[𝑛] = (− 1 2 ) 𝑛 𝑢[𝑛] + ( 1. 01 )𝑛𝑢[ 1 − 𝑛]
- ℎ(𝑡) = 𝑒^2 𝑡𝑢(− 1 − 𝑡)
- ℎ(𝑡) = ( 2 𝑒−𝑡^ − 𝑒(𝑡−^100 )/^100 )𝑢(𝑡).
- Let ℎ(𝑡) = 𝑒^2 𝑡𝑢(−𝑡 + 4 ) + 𝑒−^2 𝑡𝑢(𝑡 − 5 ). Determine A and B such that: ℎ(𝑡 − 𝜏) = {
𝑒−^2 (𝑡−𝜏), 𝜏 < 𝐴
𝑒^2 (𝑡−𝜏), 𝐵 < 𝜏
- Find the numerical values of: (a) ∑^33 𝑛=− 18 38 𝑛^2 𝛿[𝑛 + 6 ] (b) ∑^7 𝑛=− 4 − 12 ( 0. 4 )𝑛𝑢[𝑛]𝛿 3 [𝑛], where 𝛿𝑁(𝑛) = ∑𝑚 𝑚==∞−∞ 𝛿(𝑛 − 𝑚𝑁).
