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Problem 3. (inverse DTFT) Find the iDTFT of the following signals: a. X (cfw) > انا > = { 0; los , OSWI< $ ,
b. X (ejw) = cos? (W) + sin? (3) hint: using double angle formulas and Euler's equation to express the DTFT as complex exponentials may make this easier. C. المطار -1 X (eu) = 1 - e-jw - e2jw Hint: Can you re-write the DTFT expression as a combination of fractions with forms like common DTFTs in table 5.2? Problem 4. (Frequency Response of an LTI System via DTFT) Consider the DT causal LTI system defined by 6y[n] – 5y[n – 1] + y[n – 2] = 6x[r] a. Find the frequency response H (jw). b. Find the impulse response h[n]. c. Use part a to calculate the response of the system y[n] to the input: 1 [n] = 8[n] – 38[n – 1] d. Use part a the response of the system y[n] to the input 12[n] = ejen