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Signal Processing Homework Solutions | Convolution Problems and Fourier Transform

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Explore solutions for signal processing problems including convolution and Fourier transform calculations for various sequences. Learn to determine output signals based on given input sequences.

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Signal Processing Homework Solutions | Convolution Problems and Fourier Transform

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  1. Homework Solutions #2

  2. Problem 2.11 • Given: • Determine y[n] if • Solution: • Find transform of x[n] • Compute • Compute y[n] =

  3. Problem 2.11 • Compute

  4. Problem 2.11

  5. Problem 2.11

  6. Problem 2.29 • Given an LTI system: • h[n]= • Plot y[n], when: • x[n]=u[n], x[n]=u[n-4], x[n]=u[n]-u[n-4]

  7. Problem 2.29 • Using Convolution: • (a) • (b) Use shift property on (a) y[n]=

  8. Problem 2.29 • (c) Subtract (b) from (a) • y[n]={1,2,3,4,1,-2,-3,-4,-2,0,0….}u[n]

  9. Problem 2.42 • Given • Find • Is it causal?

  10. Problem 2.42 causal

  11. Problem 2.55 • Given • +1+2+2++2 • +1+2+2++2 = 8 • +1+2+2++2 = -4

  12. Problem 2.55 • Evaluate • Inverse Fourier transform:

  13. Problem 2.55 • Evaluate • +1+2+2++2

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