Question 3 in the pdf, please!

I‘ve got an answer but it seems to be incorrect.

 

1.For each of following systems,[ ]yndenotes the output and[ ]xnthe input. For eachsystem, determine whether the specified input-output relationship is linear and/orshift-invariant.(a)[ ] [ ]41ynxn=(b)[ ] [ ]2sin58yn xnnππ=+(c)[ ] [ ]( )2ynxn=(d)[ ] [ ]nmnNynxm=−=∑2.Consider the sequence[ ]00n0n<nanxnn≥=(a)Determine the z-transform of[ ]xn.(b)Determine the Fourier transform of[ ]xn. Under what conditions does the Fouriertransform exist?3.Consider the first-order system, causal system,[ ] [ ] [ ]1ynynxnα=−+(a)Find the system function,[ ]Hz, for this system.(b)Find the impulse response of this system.(c)For what values ofαwill the system be stable?(d)Assume that the input is obtained by sampling with periodT. Determine the value ofαsuch that[ ]1hn e−<for4secnTm<i.e., find the value ofαthat gives a time constant of 4msec.4.A speech signal is sampled at a rate of 10000 samples/sec(10 kHz).A segment of length1024 samples is selected and the 1024-point DFT is computed.(a)What is the time duration of segment of speech?(b)What is the frequency resolution (spacing in Hz) between the DFT values?(c)How do your answers to parts (a) and (b) change if we compute the 1024-point DFT of512 samples of the speech signal. (The 512 samples would be augmented with 512 zerosamples before the transform was computed.)

Attachments:

• 1495430163-homework_1.pdf