Homework for Day 6

Homework for Day 6

Help

Warning: The hard har d deadline has passed. You can attempt it, but you will not get credit for  it. it . You are welcome to try it as a learning exercise.

Every question is rated with its difficulty, that is indicated with the number of stars. : Easy questions, there should be enough to get the 40% of the maxim maximum um grade. : Medium difficulty. : Hard questions

In accordance with the Coursera Honor Code, I (Juan Carlos Vega Oliver) certify that the answers he re are my own work.

Question 1 (Difficulty: (Diffic ulty:

) A ringback tone is the sound you hear in in your landline landline telephone when when the the

remote phone you are ar e trying to call is ringing. In most European European countries, the ringback tone is a single sinusoid turned on and off periodically periodically.. In the USA, the ringbback tone is the sum of 2 sinusoids with relatively close frequencies turned on and off periodically. Here are two samples A and B (.wav audio file) : Sample A Sample B

You should be able a ble to tell which which one is the americ american an tone just by listening listening (you don't need ne ed to know the pitch of the sinusoids nor the on/off timings). Explain which effect  he  helped lped you find the answer answ er (use ( use the wording of o f module 4.7)

No credit, without without a proper p roper ex explanation planation ("I live live there" is not no t a proper pr oper ex e xplanation), and try to use the terminology used in the lecture slides

Question 2 In the setup of the pr evious question. (Difficulty: ) As seen in previous question, the ring-back tones of USA and Europe are respectively two or a single sinusoid multiplied in time by a square-wave taking alternatively the values

and

. This multiplication with a square wave makes the "beep" alternative. Given the

following two DTFT spectrum plots (each plot shows the interval

):

Tick the single correct assertion : (Hints: how many "peaks" does the spectrum of a sinusoid have? What does multiplication by a square wave in the time domain do in the frequency domain?) Spectrum (a) corresponds to the USA ringback tone Spectrum (b) corresponds to the USA ringback tone Spectrum (a) corresponds to the European r ingback tone Spectrum (b) corresponds to the European r ingback tone

Question 3 (Difficulty: )Consider the sequences

Tick all the correct assertions

There exists

for which

has a DFS of size

There exists

for which

has a DFS of size

Question 4 (Difficulty:

) Consider a general signal

For which value(s) of

bandlimited between

, can we demodulate

(Note that the answer should be valid for any signal

and

from

.

? bandlimited to

).

Question 5 (Difficulty: ) We want to compute the DFT of a signal with length 2048. We use the divide-andconquer method until we reach size-2 DFT problems. How many size-2 DFTs do we need to compute?

Question 6 (Difficulty:

) We saw in the lecture that finding the DFT of a finite sequence is equivalent to

multiplying it with the DFT matrix

from left.

.

Suppose the length of the signal is

and we are interested in finding

. Assume

the complexity order when we use simple matrix multiplication as above, and

is is the

complexity order when we use divide and conquer (until we reach DFT-2 size problems).

What is the ratio

?

 Apart from the usual mathematical constants and functions you should only use the (casesensitive) variable names n

(do not forget to validate your syntax by clicking "Preview")

Preview

Help

In accordance with the Coursera Honor Code, I (Juan Carlos Vega Oliver) certify that the answers he re are my own work.

Save Answers You cannot submit your work until you agree to the Honor Code. T hanks!