The impulse response of LTI System h(n) = ቀଵቁ⋅ 𝑢(𝑛)Find the response of the system when inputx(n) = (𝑎) ⋅ 𝑢(𝑛)by Fold, Shift, Multiply and sum concept.Verify your results using Tabular Method
Question
The impulse response of LTI System h(n) = ቀଵቁ⋅ 𝑢(𝑛)Find the response of the system when inputx(n) = (𝑎) ⋅ 𝑢(𝑛)by Fold, Shift, Multiply and sum concept.Verify your results using Tabular Method
Solution
To find the response of the system, we will follow the steps of Fold, Shift, Multiply, and Sum concept.
Step 1: Fold the impulse response h(n) The given impulse response h(n) = ቀଵቁ⋅ 𝑢(𝑛) is already in folded form.
Step 2: Shift the folded impulse response Since the input signal x(n) = (𝑎) ⋅ 𝑢(𝑛), we need to shift the folded impulse response h(n) by n units to the right.
Step 3: Multiply the shifted impulse response with the input signal Multiply the shifted impulse response with the input signal (𝑎) ⋅ 𝑢(𝑛) element-wise.
Step 4: Sum the multiplied values Sum all the multiplied values to obtain the response of the system.
To verify the results using the Tabular Method, we can create a table with columns for n, x(n), h(n), and the product of x(n) and h(n). Then, we can sum the products to obtain the response of the system.
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