# 代做unity | ee代写 | 电路代写 – ELEC2100 HW3

### ELEC2100 HW3 ELEC2100 HW3

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##### Q.1 (16)

The block diagram of C/D and D/C system is shown below.

A CT signal

`````` has bilateral bandwidth of 10 kHz and its frequency spectrum is shown below.
``````

a) (2) What is the value of

`````` (in rad/s) ?
``````

If

`````` is sampled using
``````
``````
``````
``````
``````
`````` where 50 .
``````

b) (2) If the time duration of

`````` is one second, specify the total number of sample points contained in
``````
``````
``````
##### .

c) (2) Sketch the frequency spectrum of

``````
``````
``````. Show important values.
``````

d) (2) Sketch the frequency spectrum of

`````` for
``````
##### |
``````3. Show important values.
``````

The DT LTI system

``````
``````
`````` is an ideal  unity gain highpass filter with cutoff frequency of 0.2.
``````

e) (2) Sketch the frequency spectrum of

``````  for |  |3. Show important values.
``````

f) (2) Sketch the frequency spectrum of

``````. Show important values.
``````

If the CT signal

`````` is applied to the following system,
``````

g) (2) Find FS coefficients of for 1,0,1.

h) (2) Sketch the frequency spectrum of

``````. Show important values.
``````
``````DT LTI System
``````
``````
``````
``````
``````
``````CT lowpass Filter
``````
##### 1
``````   25s
``````
##### …
``````t
``````
`````` 50             0              50           100       (s)
``````

``````
``````
##### 0
``````
``````
``````
``````
``````
``````
##### Q.2 (24)

The system function of a causal LTI system is given as

``````
``````
``````
``````
``````
``````
``````
``````
##### .

a) (2) Write down the differential equation relating the input

`````` and the output
``````
##### .

b) (2) Determine the output when the input is

``````
``````
`````` is applied to
``````
``````
``````
##### .

Another causal LTI system has the system function

``````
``````
``````
``````
``````
``````
``````
``````
##### .

c) (2) Sketch the polezero plot.

f) (2) What is the value of the natural frequency of this system? What is the value of its zeta parameter ?

h) (2) Is the system overdamped, underdamped or critically damped ? Explain your answer.

i) (2) Specify the maximum gain, the halfpower gain and the halfpower frequency / frequencies.

j) (2) Roughly sketch the magnitude response. Show important values.

If an input

``````14sin
``````
##### 52
``````2sin
``````
##### 1000
`````` is applied to this stable LTI system,
``````

k) (2) Estimate the frequency response (in exponential form) at 0, 52 rad/s and 1000 rad/s.

l) (2) Represent the output

`````` as the sum of real sine signals.
``````