这个作业是实现离散时间的傅里叶变换

EE5410 Signal Processing

Assignment 2

1. Consider a linear time-invariant (LTI) system with impulse response . The

discrete-time Fourier transform (DTFT) of is:

(a) Determine the transfer function and its region of convergence (ROC).

(b) Find .

2. Find the frequency response of a discrete-time stable system whose input

and output satisfy the following difference equation:

Then determine the system impulse response .

3. Figure 1 shows the block diagram representation of a causal LTI discrete-time

system with input and output .

Figure 1

(a) Determine the system transfer function where and

are the transforms of the input and output , respectively.

(b) Draw the block diagram representation of the system using canonic form.

(c) Is the system stable? Explain your answer.

4. Consider a causal LTI system whose system function is

Draw one signal flow graph for the system in each of the following forms:

(a) Direct form

(b) Cascade form using canonic form sections

(c) Parallel form using canonic form sections

5. Consider an ideal bandpass filter whose frequency response in is:

where and .

(a) Use the window method with rectangular window to design a causal and linearphase finite impulse response (FIR) filter of length 7 that approximates

Write down the filter transfer function with numerical values.

(b) When implementing the FIR filter with transfer function , determine the

minimum numbers of multiplications and additions for computing each output

sample.

6. Consider a causal and linear-phase FIR filter of length 3 such that

and . It is known that the magnitude of the filter frequency response

is at , while at . Determine the

values of and .

**程序辅导定制C/C++/JAVA/安卓/PYTHON/留学生/PHP/APP开发/MATLAB**

本网站支持 Alipay WeChatPay PayPal等支付方式

**E-mail:** vipdue@outlook.com **微信号:**vipnxx

如果您使用手机请先保存二维码，微信识别。如果用电脑，直接掏出手机果断扫描。